ABSTRACT
Title of Document: A PHYSICAL CHEMIST'S GUIDE TO 
APPLIED COMPUTATIONAL CHEMISTRY:
PRACTICAL CALCULATION OF 
POLYPROTIC ACID PKA VALUES, 
MERCURY HALIDES, THIOLS, AND 
METHYLMERCURY ANALOGUES' 
STABILITIES AND STRUCTURES, AND 
RAMAN SPECTRA OF MYO-INOSITOL 
HEXAKIS PHOSPHATE.
Merle McKinley Dickerson Zimmermann, Ph. 
D., 2011
Directed By: Dr. John Tossell, Chemistry Department
In this thesis, we present both ab-initio investigation of the series of compounds 
HgClxy and the charges of each system running x=(0,1,2,3,4) and y=(+2,+1,0,-1,-2).
We investigate the energies of formation using Gaussian 03 (G03), a quantum 
chemistry package.  In our calculations, HgCl3-1 was most stable in the gas phase, and 
HgCl20 the most stable in the polarizable continuum model water-solvated phase.  The 
addition of a solvent layer of H2O molecules did not significantly affect the results.
DFT calculations on the series running between HgCl+, through HgCl20, and HgCl3-1 
compounds done with the Amsterdam Density Functional (ADF) program from 
Scientific Computing and Modeling (SCM) yielded absolute Hg NMR shieldings 
with a ? of approximately -1000 ppm for each additional atom of Chlorine bonding to 
the Mercury for the first two additions.
We also investigate H3PO4, H3AsO4, and the HClOx acid series with x=(1,2,3,4). We 
have succeeded in determining pKas with theoretical quality results within 2 kcal/mol 
of experimental measurement for the majority of the systems examined by use of a 
discovered linear correlation between experimental and calculated pKa values.
Finally, we present our contribution to a joint project involving myo-inositol hexakis 
phosphate with an experimental group, confirming the observed experimental trends 
seen in the Raman spectra.
A PHYSICAL CHEMIST'S GUIDE TO APPLIED COMPUTATIONAL 
CHEMISTRY: PRACTICAL CALCULATION OF POLYPROTIC ACID PKA 
VALUES, MERCURY HALIDES, THIOLS, AND METHYLMERCURY 
ANALOGUES' STABILITIES AND STRUCTURES, AND RAMAN SPECTRA OF 
MYO-INOSITOL HEXAKIS PHOSPHATE.   
By
Merle McKinley Dickerson Zimmermann.
Dissertation submitted to the Faculty of the Graduate School of the 
University of Maryland, College Park, in partial fulfillment
of the requirements for the degree of
Ph. D.
2011
Advisory Committee:
Professor John Tossell, Chair
Janice Reutt-Robey
Millard Alexander
Wendell T. Hill, III
Yu Huang Wang
? Copyright by
Merle McKinley Dickerson Zimmermann
2011
Preface
The following work is presented in the hope that it may inspire further cooperation 
and collaboration between physical chemistry experimentalists and applied 
computational theory, and hope that the included successes and suggestions are useful 
both to new applied computational chemists getting started and physical chemists 
interested in applying computational chemistry techniques to shed more light on 
experimental problems.
ii
Dedication
We would like to dedicate this work to Dr. Tossell, who showed near infinite amounts 
care and patience as this work was slowly completed under his supervision, and his 
laboratory, whose focus on applying computational chemistry to environmental and 
geochemical mysteries shed much useful light and inspiration across the dark world 
of the unknown. We also would like to acknowledge the invaluable support provided 
by friends and family, especially S. Vinnikova, whose help with proofreading was 
indispensable.  Thank all of you very much.  This would not have been possible 
without you.
iii
Acknowledgements
This thesis is the result of support from many different people and groups, to all of 
whom we would like to extend our highest gratitude.
To begin, we would like to thank our sources of funding and financial support, 
including NSF Grant EAR0539109, DOE Grant DE-FG02-94ER14467,  the NSF-
MRSEC at the University of Maryland, College Park DMR#0520471, and an ARCS 
Foundation's Achievement Awards for College Scientists Fellowship received in 
2008 by the author.
We would also like to acknowledge G. R. Helz for suggesting the arsenic system for 
study, D.A. Dixon and M. H. Alexander for suggesting excellent references, fellow 
graduate students E. Khaskin, and Liang T. for suggestions and .  We would also like 
to thank L. Heighton for collaborating on the myo-inositol phosphate theoretical 
study with experimental results.  We would also like to acknowledge the invaluable 
assistance of Parallel Quantum Solutions for both kindly and excellent after-market 
technical support of their QuantumCubeTM chemistry cluster used to calculate the 
NMR data presented in Chapter 4.
Finally, we also acknowledge S. Vinnikova for her great assistance in proofreading, 
countless helpful suggestions and moral support during the writing of this thesis.
iv
Table of Contents
Preface                                                                                                                              ...........................................................................................................................ii  
Dedication                                                                                                                        .....................................................................................................................iii  
Acknowledgements                                                                                                          .......................................................................................................iv  
Table of Contents                                                                                                              ...........................................................................................................v  
List of Tables                                                                                                                 ..............................................................................................................viii  
List of Figures                                                                                                                 ..............................................................................................................xii  
List of Equations                                                                                                            .........................................................................................................xvi  
Chapter 1: General Overview                                                                                           ........................................................................................1  
1.1 Background                                                                                                             ..........................................................................................................1  
1.2 Overview                                                                                                                 ..............................................................................................................4  
1.2.1 ? Mercury-Chloride Compounds in Solution                                                  ...............................................5  
1.2.2 ? Mercury-Thiol Complexes                                                                           ........................................................................8  
1.2.3 ? Methylmercury compounds                                                                         ......................................................................8  
1.2.4 ? Polyprotic Acid pKa Calculations: phosphoric, arsenic, and others             ..........9  
1.2.5 ? Raman Spectra of Myo-Inositol Phosphates                                               ............................................14  
1.3 Initial Results and Discussion                                                                               ............................................................................15  
1.4 Conclusions                                                                                                           ........................................................................................................21  
1.5 References                                                                                                             ..........................................................................................................22  
Chapter 2: Mercury Compounds in the Environment: An Overview of their Human 
Impact                                                                                                                             ..........................................................................................................................28  
2.1 Background                                                                                                           ........................................................................................................28  
2.2 Previous Work                                                                                                      ...................................................................................................37  
2.3 References                                                                                                             ..........................................................................................................39  
Chapter 3: An Overview of Computational Chemistry Techniques                               ............................48  
3.1 Introduction                                                                                                           ........................................................................................................48  
3.2 ? Key Basics                                                                                                         ......................................................................................................49  
3.2.1 ? An overview of the Hartree-Fock self-consistent field method                  ...............49  
3.2.2 ? The Hartree Fock Method (explained in detail)                                          .......................................51  
3.2.3 ? Background on Basis Set Selection                                                            .........................................................62  
3.3 ? An Overview of Computational Chemistry Methods                                        .....................................64  
3.4 ? An Overview of Basis Sets                                                                                .............................................................................71  
3.5 ? The Importance of Quality                                                                                 ..............................................................................77  
3.6 ? Approaches to Verifying Quality                                                                       ....................................................................79  
3.7 References                                                                                                             ..........................................................................................................82  
Chapter 4: Mercury Chloride Free energies in solution: equilibrium constants from 
theoretical calculations at the CCSD(T) level and above                                               ............................................91  
4.1 Introduction                                                                                                           ........................................................................................................91  
4.2 Methods                                                                                                                  ..............................................................................................................92  
4.2.1 Basis Set Selection                                                                                         ......................................................................................94  
4.2.2 Complete Basis Set Extrapolation                                                                 ..............................................................95  
v
4.3 Results and Discussion                                                                                         ......................................................................................96  
4.4 Conclusions                                                                                                         ......................................................................................................117  
4.5 Acknowledgements                                                                                             ..........................................................................................117  
4.6 References                                                                                                           ........................................................................................................118  
Chapter 5:  Ab Initio Phosphoric acid pKa calculations using CBS-QB3 and MP2 
methods                                                                                                                         ......................................................................................................................121  
5.1 Introduction                                                                                                         ......................................................................................................121  
5.2 Methods                                                                                                                ............................................................................................................126  
5.3 Results                                                                                                                 ..............................................................................................................127  
5.4 Discussion and Conclusions                                                                               ............................................................................130  
5.5 Acknowledgements                                                                                             ..........................................................................................132  
5.6 References                                                                                                           ........................................................................................................133  
Chapter 6:  Arsenic and Phosphoric Acid pKa calculations using the CBS-QB3 model 
chemistry and the CPCM SCRF solvation method                                                        ....................................................136  
6.1 Introduction                                                                                                         ......................................................................................................136  
6.2 Methods                                                                                                                ............................................................................................................138  
6.3 Results and Discussion                                                                                       ....................................................................................145  
6.4 Conclusions                                                                                                         ......................................................................................................161  
6.5 Acknowledgements                                                                                             ..........................................................................................162  
6.6 References                                                                                                           ........................................................................................................163  
Chapter 7:  HClOx ab initio calculations in the CPCM with previously explored 
fitting and counterions                                                                                                  ...............................................................................................166  
7.1 Introduction                                                                                                         ......................................................................................................166  
7.2 Methods                                                                                                                ............................................................................................................167  
7.3 Results and Discussion                                                                                       ...................................................................................167  
7.4 Conclusions                                                                                                         ......................................................................................................176  
7.5 References                                                                                                           ...................................................................................................177  
Chapter 8:  Hg(SH)2 gas phase formation reactions.                                                   ................................................181  
8.1 Introduction                                                                                                         ......................................................................................................181  
8.2 Methods                                                                                                                ............................................................................................................181  
8.3 Results and Discussion                                                                                       ....................................................................................182  
8.4 Conclusions                                                                                                         ......................................................................................................188  
8.5 References                                                                                                           ........................................................................................................188  
Chapter 9:  Methylmercury compound chemistry in Aqueous Solution                     ...................191  
9.1 Introduction                                                                                                         ......................................................................................................191  
9.2 Methods                                                                                                                ............................................................................................................193  
9.3 Results and Discussion                                                                                       ....................................................................................195  
9.4 Conclusions                                                                                                         ......................................................................................................218  
9.5 References                                                                                                           ........................................................................................................219  
Chapter 10:  Ab-Initio modeling of pH dependant Raman Spectra of Myo-Inositol 
Hexakis Phosphate                                                                                                        .....................................................................................................222  
10.1 Introduction                                                                                                       ....................................................................................................222  
10.2 Methods                                                                                                              ..........................................................................................................224  
10.3 Results and Discussion                                                                                     ..................................................................................225  
vi
10.4 Conclusions                                                                                                       ....................................................................................................236  
10.5 Acknowledgements                                                                                           ........................................................................................238  
10.6 References                                                                                                         ......................................................................................................238  
Chapter 11:  Conclusions and Future Work                                                                  ...............................................................241  
11.1 Introduction                                                                                                       ....................................................................................................241  
11.2 Results and Discussion                                                                                     ..................................................................................242  
11.3 Acknowledgements                                                                                           ........................................................................................246  
11.4 References                                                                                                         ......................................................................................................246  
Glossary                                                                                                                        .....................................................................................................................250  
Bibliography                                                                                                                 ..............................................................................................................252  
vii
List of Tables
Table 1.1: HgClx compound energies of reaction in the gas phase and with CPCM 
hydration.
Table 1.2: ADF NMR calculation results for compounds in HgClx series.
Table 1.3: Ghost atom calculations for Counterpoise Correction in HgCl2 system.
Table 4.1: Extra diffuse functions used in the calculations conducted in this chapter.
Table 4.2: Stabilization Energies for Successive Cl- addition to Hg2+
Table 4.3: CCSD CEP-31G Energy Calculations for Successive Cl- addition
Table 4.4: CCSD CEP-121G+ Calculations for Successive Cl- addition
Table 4.5: B3LYP CEP-121G+ Energy Calculations of Successive Cl- addition to 
Hg2+
Table 4.6:  Comparison of methods in calculating the ?Grxn free energy of reaction for 
the explicitly Solvated System:  Hg2+ . 6H2O + Cl- ?  HgCl+ . 5H2O + H2O 
Table 4.7: Complete Basis Set CCSD(T) CBS model results for successive Cl- 
additions to Hg2+. 
Table 4.8: HgCl Compound energies of formation
Table 4.9: Solvated Cluster Calculation energies of formation for HgCl system
Table 4.10(a): HgCl series cc-pV*Z basis calculated energies
Table 4.10(b): HgCl series aug-cc-pV*Z basis calculated energies
Table 4.10(c): HgBr series cc-pV*Z basis calculated energies
Table 4.10(d): HgI series calculated energies with cc-pV*Z-PP basis
viii
Table 4.10(e): Reaction Energetics with extrapolated CBS from the above mercury 
halogen compounds HgClx, HgBrx, and HgIx.
Table 4.11:  ADF NMR calculation results for compounds in HgClx series calculated 
with excitations.
Table 4.12: ADF NMR calculation results for compounds in HgClx series calculated 
without excitations.
Table 5.1: Experimentally measured pKa values (from William L. Jolly, Modern 
Inorganic Chemistry, 2nd edition).
Table 5.2: CBS-QB3 Gas Phase Free Energies + CPCM Stabilization (with various 
basis sets) on phosphoric acid.
Table 5.3: CBS-QB3 and MP2 Calculations on Phosphoric Acid solvated with 
CPCM.
Table 5.4: Phosphoric Acid CBS-QB3 calculations with counterion.
Table 6.1: Calculated deprotonation energetics for acid deprotonation reactions.
Table 6.2: pKa values for H3AsO4 and H3PO4 multiple deprotonations with each CBS-
QB3 based method.
Table 6.3: pKa values for H3AsO4 and H3PO4 multiple deprotonations with  the 
CCSD(T) method under 6-311G(2d,p), aug-cc-pVDZ, and CEP-121G basis sets.
Table 6.4: Linear Extrapolations for phosphoric and arsenic acids calculated from 
previous pKa tables.
Table 6.5: Fitted pKas for each polyprotic acid species using the linear extrapolation.
ix
Table 7.1: Calculated Gas-phase solvation energies and Free Energies for (H/Na)ClOx 
(x=1 to 4).
Table 7.2: Deprotonation reaction energies in kcal/mol for solvated system calculated 
both at SCRF and gas phase geometry with solvation energy added in.
Table 7.3: Calculated pKas for each HClOx acid.
Table 7.4: HClOx pKas as fitted by adjustment method.
Table 7.5: Percent error in unfitted HClOx pKas
Table 7.6: Percent error in fitted pKa values
Table 7.7: ?Grxn Reaction energies (kcal/mol) for counterion-assisted calculations.
Table 7.8: Calculated and experimental pKa values for each counterion-assisted 
HClOx calculation.
Table 7.9: HClOx pKa values fitted by the previously developed linear extrapolation.
Table 7.10: % error in directly calculated HClOx pKa values versus experimental 
measurements.
Table 7.11: % error in fitted pKa values compared to experimental measurements.
Table 8.1: Extra diffuse functions used in the calculations in this chapter.
Table 8.2(a): HgSH compound free energies of formation.
Table 8.2(b): HgSH compound gas phase reaction energies with different basis sets.
Table 8.2(c): Additional energy calculated released with additional diffuse basis 
function present.
Table 9.1: Extra diffuse functions used in the calculations in this chapter.
x
Table 9.2: Sum of Electronic and Thermal Free Energies at 298K  (in Hartrees) 
calculated for each methylmercury species with HF, MP2, B3LYP, and CCSD, 
calculated with the CEP-121G basis set augmented with our additional functions.
Table 9.3: Energy differences (Hatrees) in adding additional S atoms to the MeHgSxH 
chain.
Table 9.4: CPCM Solvated HF and B3LYP energies for MeHgX and MeHgSxH 
(X=F, Cl, Br, I,), (x=1...4).
xi
List of Figures
Figure 4.1: HgClx series Hg calculated ADF NMR shielding (ppm) (with excitations)
Figure 4.2: HgClx series Cl calculated ADF NMR shielding (ppm) (with excitations)
Figure 4.3: HgClx series Hg calculated ADF NMR shielding (ppm) (no excitations)
Figure 4.4: HgClx series Cl calculated ADF NMR shielding (ppm) (no excitations)
Figure 6.1: H3AsO4 Hydrogen-bonding from explicit water molecule to the 
compound.
Figure 6.2: H3AsO3 hydrogen-bonding from acidic hydrogen on arsenic complex to 
the explicit water molecule.
Figure 6.3: H3AsO4 . H2O complex optimized CBS-QB3 geometry showing typical 
cyclic hydrogen-bonding structure seen in singly solvated systems.
Figure 6.4: Hydrated HAsO4-2 . H2O complex CBS-QB3 optimized geometry as 
calculated in the polarizable continuum.
Figure 6.5: Illustration of the most hydrogen-bonding pattern seen in the hydrated 
H3AsS3 . H2O complex found from CBS-QB3 geometry optimization in the 
polarizable continuum.
Figure 6.6: Similar multiple hydrogen-bonding interaction seen in H3AsO3 . H2O 
complex calculated under CBS-QB3 method with the CPCM present.
Figure 6.7: Long hydrogen-bonding interaction seen in the CBS-QB3 calculation with 
the polarizable continuum when optimizing the H3AsS4 . H2O explicitly hydrated 
system.
xii
Figure 6.8: Graphs of experimental versus theoretical pKas for As(V) and P(V) 
systems.
Figure 6.9: Linearity in results calculated with CCSD(T) methods compared to the 
results from systems calculated via CBS-QB3 in the CPCM.
Figure 7.1: pKas for each method (including both direct and counterion assisted 
calculation results).
Figure 8.1: Calculated energetics for each reaction using different methods.
Figure 8.2: Calculated energies of reaction with diffuse basis functions added to the 
CEP-121G basis used in the previous figure.
Figure 9.1: Energies calculated from Table 9.2.
Figure 9.2: B3LYP/CEP-121G CPCM IR Spectrum for MeHgF
Figure 9.3: B3LYP/CEP-121G CPCM IR Spectrum for MeHgCl
Figure 9.4: B3LYP/CEP-121G CPCM IR Spectrum for MeHgBr
Figure 9.5: B3LYP/CEP-121G CPCM IR Spectrum for MeHgI
Figure 9.6: B3LYP/CEP-121G CPCM Imaginary Mode for MeHgI.
Figure 9.7: Typical imaginary mode for eclipsed conformation of MeHgSxH as seen 
in MeHgSH (B3LYP/CEP-121G CPCM)
Figure 9.8: Typical imaginary mode for MeHgS2H
Figure 9.9: MeHgSH IR Spectra (B3LYP/CEP-121G CPCM)
Figure 9.10: MeHgS2H IR Spectra (B3LYP/CEP-121G CPCM)
Figure 9.11: MeHgS3H IR Spectra (B3LYP/CEP-121G CPCM)
Figure 9.12: MeHgF IR Spectra (B3LYP/CEP-121G)
xiii
Figure 9.13: MeHgCl IR Spectra (B3LYP/CEP-121G)
Figure 9.14: MeHgBr IR Spectra (B3LYP/CEP-121G)
Figure 9.15: MeHgI IR Spectra (B3LYP/CEP-121G)
Figure 9.16: MeHgSH Spectra (B3LYP/CEP-121G)
Figure 9.17: MeHgS2H Spectra (B3LYP/CEP-121G)
Figure 9.18: MeHgS3H Spectra (B3LYP/CEP-121G)
Figure 9.19: MeHgS4H Spectra (B3LYP/CEP-121G)
Figure 9.20: MeHgF Symmetric Stretching Mode displacement vectors from 
B3LYP/CEP-121G CPCM calculation
Figure 9.21: MeHgS3H asymmetric stretching mode calculated in the gas phase under 
B3LYP/CEP-121G.
Figure 9.22: MeHgS3H symmetric stretching mode calculated in the gas phase under 
B3LYP/CEP-121G.
Figure 10.1: IHP structure without stereochemistry.  Around a single bonded C6H6 
ring are six H2PO3 groups.
Figure 10.2: H12IHP HF optimized structure (3d, crosseyed stereogram)
Figure 10.3: H12IHP B3LYP re-optimized structure (3d, crosseyed stereogram)
Figure 10.4: H6IHP6- HF structure (3d, crosseyed stereogram)
Figure 10.5: H6IHP6- B3LYP structure (3d, crosseyed stereogram)
Figure 10.6: H6IHP6- HF structure, explicitly solvated explicitly by 6 H2O molecules 
(3d, crosseyed stereogram)
xiv
Figure 10.7: HF synthetic IR and Raman spectra for H12IHP calculated with the 6-
31G basis set..
Figure 10.8: B3LYP synthetic IR spectrum for H12IHP calculated with the 6-31G 
basis set.
Figure 10.9: B3LYP vibrational mode at at 2644 cm-1.
Figure 10.10: HF synthetic IR and Raman spectra for gas phase H6IHP-6 calculated 
with the 6-31G basis set.
Figure 10.11: B3LYP synthetic IR spectrum for gas phase H6IHP-6 calculated with the 
6-31G basis set.
Figure 10.12: HF synthetic IR and Raman spectra for H6IHP6- . 6H2O calculated with 
the 6-31G basis set.
Figure 10.13: Phosphate group symmetric stretch observed in HF/6-31G calculated 
Raman spectrum for H6IHP6- . 6 H2O at 967 cm-1.
Figure 10.14: Experimentally Measured Raman Spectra under various pH conditions 
as measured by L. Heighton.
xv
List of Equations
(3.1) ?H=? ?
2
2m?i=1
n
?i2??
i=1
n Ze'2
ri ??i=1
n ?
j?i
e'2
rij
(3.2) ?H?=E?
(3.3) ?=?i si?ri,?i,?i?
(3.3a) si=?k cikbk?ri,?i,?i?
(3.4) Vij=e' 2??sj?
2
rij dvj
(3.5) Vi?ri,?i,?i?=?
j?i
e'2??sj?
2
rij dvj?
Ze'2
ri
(3.6) V?ri?=
?
0
2?
?
0
?
V?ri,?,??sin?d?d?
?
0
2?
?
0
?
sin?d?d?
(3.7) [? ?
2
2m ?i?V?ri?]ti?1?=?iti?1?
(3.8) [? ?
2
2m ?i?V?ri?]ti?1???iti?1?=0
xvi
(3.9) Eatomic=?
i=1
n
?i??
i
?
j?i
??e'2?si?i??2?sj? j??2r
ij
dvidvj
(3.10) ?H=? ?
2
2m?i ?i
2??
?
?
i=1
n Z
?e
'2
ri ??i=1
n ?
j?i
e'2
rij ?
?2
2m??? ??
2??
?
?
???
Z?Z?
r??
(3.11) VNN=?
?
?
???
Z?Z?
r??
(3.12) ?Hel=? ?
2
2m?i ?i
2??
?
?
i=1
n Z
?e
'2
ri ??i=1
n ?
j?i
e'2
rij
(3.13) ?F= ?Hel?VNN=? ?
2
2m?i ?i
2??
?
?
i=1
n Z
?e
' 2
ri ??i=1
n ?
j?i
e'2
rij ??? ????
Z?Z?
r??
(3.14) EHF=?D??F?D?=?D? ?Hel?VNN?D?=2?
i=1
n/2
hi??
i=1
n/2 ?
j=1
n/2
?2Jij?Kij??VNN
(3.15) hi=??i?1???12?i2??
?
Z?
r1???i?1??
(3.16) Jij=??i?1??j?2?? 1r
12
??i?1??j?2??
(3.17) Kij=??i?1??j?2?? 1r
12
??j?1??k?2??
(3.18) ?F?1??i?1?=?i?1??i?1?
xvii
(3.19) ?i=?k cki?k
(3.20) ?F?i= ?F?k cki?k=?k cki ?F?k=?i?k cki?k
(3.21) ?k cki?F jk??iS jk?=0
(3.22) F jk=??j??F??k?
(3.23) Sjk=??j??k?
(3.24) det?F jk??iS jk?=?
F11??iS11 F21??iS21 ?
F12??iS12 F22??iS22 ?
? ? ??
=0
(3.25)  R(r) = rn-1 e-? r (r = radial distance to the nucleus)
(3.26) En = ECBS + An-3
(4.1) En = ECBS + An-3
(4.2) ECBS = En ? An-3
(4.3) ECBS = (27/19)E3 ? (8/19)E2
(5.1) Ka=[H+][A-][HA]
(5.2) pKa=?logKa=?log?[H+][A-][HA] ?
(5.3) pH=?log[H+]
(6.1) ?Grxn = ?G(A-gas) ? ?G(AHgas) + ?Gs(AH) ? ?Gs(AH) ? 269.0 kcal/mol
(6.2) pKaexpt = 0.429 pKaCBS-QB3 CPCM w/H2O ? 0.233
xviii
(7.1) pKafitted = 0.429 pKaCBS-QB3 ? 0.233
(11.1) pKaexpt = 0.429 pKaCBS-QB3 CPCM w/H2O ? 0.233
xix
Chapter 1: General Overview
1.1 Background
Theoretical chemistry as a science has continued to develop as the years have passed 
and computational technology has advanced.  At the current time, it is possible to 
apply computational chemistry to analyze many physical chemistry situations which 
were not within reach in the past.  While a dedicated theoretician is essential for 
detailed study, it is also possible for a general physical chemistry laboratory to do 
calculations on their on or in conjunction with a theoretical group.
We hope in this thesis to promote further collaboration between experimental and 
theoretical groups, and to encourage experimental groups without access to a 
dedicated theorist to consider the possibilities of adding such calculations to their 
repertoire of scientific tools.
We therefore present the following, where we show an example of theoretical 
chemistry as applied to computational analysis of molecules including mercury (with 
Gaussian 03[1], for example), and present it as a safe way to explore these hazardous 
compounds [2] and supplement experimental results with less risk to the scientific 
group.
Our selection of mercury as our focus of study was twofold.
1
Mercury pollution from human sources is ongoing, and an improved understanding of 
the chemistry of the chemical will provide opportunities for us to deal with the 
consequences of an industrialized society in a logical and well-informed manner.  We 
discuss some of the anthropological consequences of mercury chemistry in Chapter 2.
And in a pure scientific point of view, there are several notable things about mercury 
chemistry which are unique to this particular element:
? Mercury depletion during spring in the Arctic[3-8] is a notable phenomenon 
which has several successful computational contributions[3, 4], but with 
additional knowledge of mercury's stability and behavior could be further 
explained.
? Methylmercury compounds1, especially as environmental pollutants, are one 
of the most recognized dangerous forms of mercury available in the 
environment[2, 9-21].
? Biological consequences of mercury pollution are well understood from a 
symptomatic side[2, 18, 19, 21, 22].  However, deeper understanding of the 
reasons why particular body systems are targeted by the compound would be 
useful in developing possible treatments.
? Solvation effects on relevant Mercury compounds.  As we will show later, the 
1  Sadly, medical journals are quite vague about the particular formulae of the methylmercury 
compounds they mention.  Presumably dimethylmercury, and CH3Hg+Cl-  compounds are to blame.
2
change in chemical environment for a particular set of HgCl compounds going 
between the gas phase and the aqueous solution is enough to change which 
species is the most thermodynamically stable.
Modeling and understanding how mercury compounds behave in solution in addition 
to the gas phase is doubly important because most biological systems involve 
solvated phases (both aqueous and organic).  We would suggest a future study 
examining how  mercury compounds behave in a variety of common organic solvents 
aside from water, such as octanol, methanol, ethanol, THF, or ether2.
We have modeled a variety of likely mercury compounds for a selection of the above 
listed situations via software: GAUSSIAN 03[1] and ADF[34-36] in particular were 
in use for these explorations.
In order to further understand the quality and reliability of the results of the mercury 
calculations which did not have experimental results readily available for comparison, 
we conducted a series of computations on the acidities of a variety of triply and 
doubly protonated polyprotic acid systems as well. Our goal in this case was to 
predict the deprotonation behavior of unknown polyprotic acids.
These systems were chosen with both light phosphorus central atoms and moderately 
2 We acknowledge Eugene Khaskan from Dr. Vedernikov's laboratory for suggesting most of these 
solvents from his work with catalysts in a discussion in early 2006.
3
heavy arsenic central atoms, to introduce d-shell electrons to the calculation and to 
show the behavior of our solvation methods on elements moving towards the part of 
the periodic table where mercury appears at atomic number 80.
Finally, the calculations on the phosphoric acid systems were extended by a 
collaboration with an experimental lab in calculating a set of spectra on Myo-Inositol 
hexakis phosphates to provide further insight into their identification and behavior 
and further demonstrate the contributions that applied theory can bring to an 
experimental problem.
1.2 Overview
For a guide to computational chemistry terms used in the discussion below, please 
see Chapter 3, An Overview of Computational Chemistry Techniques, where they 
are defined in sections 3.2 to 3.4 and discussed at further length.
There were five main things which we explored in the production of this thesis.
Our primary goal was a study of mercury-halogen compounds in solvated systems. 
These calculations were most successful on the chloride compounds, which became 
our focus, and appear in Chapter 4.
We also discuss a series of Mercury thiol compounds for their application to undersea 
4
sulfuous vents where mercury and sulfur would both be present naturally, and a 
number of methylated mercury compounds (methylmercury having been shown to be 
one of the most hazardous forms of the heavy metal).  Our results in these areas 
appear in Chapter 8 and 9, after our discussion of the polyprotic acids, which were 
used as a measuring-stick to estimate the accuracy of the results in this type of 
theoretical calculation and appear in the thesis in Chapters 5 through 7.
Finally, we discuss the ab inito calculations on the pH dependence of Myo-Inositol 
Hexakis Phosphate's Raman Spectra, which appear in Chapter 10.
In each case, we present the set-up for our selected problem and discuss possible 
future calculations which would expand upon what we presented here.
Finally, we discuss a few of the initial results which we produced for the mercury 
chloride systems discussed at length in Chapter 4.
1.2.1 ? Mercury-Chloride Compounds in Solution
The main species of interest in this series were as follows:
Hg+2, HgCl+, HgCl2, HgCl3-, HgCl4-2, and Cl-.
5
We planned to use CCSD[24] with a CEP-121G basis[25, 26] to run the calculations. 
The CCSD method is advantageous to us because we expect that mercury will show 
significant electron correlation effects because of the large number of near-valence 
electrons.  Our preferred choice of basis set is CEP-121G, since mercury exhibits 
relativistic effects and the core effective potential basis allows us to take some of 
these into account implicitly.  We also intended to conduct a selection of these 
calculations using MP2 and B3LYP as well.
 
B3LYP[27] is a hybrid method that allows for higher quality results than Hartree-
Fock, but at a more modest computational cost than corresponding higher-level 
methods (such as Gaussian-1[28]).  This method has been shown [29] to provide 
reasonable results in comparison to CCSD(T) calculations for some Hg complexes 
already.
Second, after running each calculation in the gas phase, we will calculate the 
stabilization energy of hydration using a polarizable continuum model, CPCM with a 
reduced basis set.  This type of model accounts for solvation energies by placing the 
calculated electron density in a cavity of an infinite dielectric modeled to match the 
characteristics of the solvent. The solvation energy depends on electron density, and 
we assume here, based upon unpublished internal lab experience, that it converges 
spatially to a scale where those numbers are stable at a level of theory.  In many 
cases, we also modeled the CCSD or B3LYP calculations in the polarizable 
6
continuum model.  Explicit water molecules were also used for solvation in some 
cases.
Third, we use ADF[34-36] to calculate NMR shieldings[37-39] on the HgCl 
compounds after the Gaussian calculations are done.  In ADF, we will use the Zeroth 
Order Relativistic Approximation[30] to take into account the effects of relativity on 
the inner shell electrons of Mercury in our all-electron calculations of the compounds.
Finally, we run portions of the above series of calculations with F-, Br-, and I- 
substituted for Cl-.  This extension provides us with a better understanding of the 
differences in halogen chemistry exhibited by mercury.  We also did a variety of 
Complete Basis Set extrapolations for the four systems.
In some cases calculations with the solvating water molecules were not conducted 
due to limited time.  The completed calculations are described in the appropriate 
chapters.  The remainder of the systems mentioned above, but not explored, would be 
an ideal project for further explorations.
A future effort would definitely include additional solvation calculations with 
polarizable continuums tuned to the properties of the other solvent compounds.  This 
would allow us to compare the effects of different solvents on the equilibria of the 
compounds above, and if time allowed, we would also substitute the alcohols and 
7
other solvating agents mentioned in the introduction for water in some of the smaller 
complexes (the larger ones, we calculate with B3LYP instead of CCSD).
Explicit solvation could also be further explored via use of a molecular dynamics 
study.  In the future, calculations with the CPMD [23] molecular dynamics package, 
for example, could be used to conduct further calculations.  Its direct support of 
periodic boundary conditions would allow sampling of many different explicit 
bonding situations and the collection of statistical mechanics information about the 
behavior of the complexes.  A possible plus is that the high computational cost of this 
kind of calculation will be less of an expense in the future, as this kind of model 
scales well with the number of CPUs working on the problem and it appears that 
increasing parallelization is the direction that computer system development is 
currently taking.
1.2.2 ? Mercury-Thiol Complexes 
Another project was to examine Hg(SH)2 complex formation, geometries, and the 
resulting energetics of each different type of complex using B3LYP, MP2, CCSD, 
MP3, and MP4 with the CEP-121G basis set and the differences between these 
approaches compared to each other.
1.2.3 ? Methylmercury compounds 
One of the main goals of this segment of research was to do a variety of calculations 
upon methylmercury compounds, which have a (well-deserved) reputation for being 
dangerous to experimenters handling them.  In a recent occurrence written up in 
8
1998, a researcher at Dartmouth was conducting NMR research on mercury 
compounds and was exposed to a dimethylmercury standard through her latex gloves, 
which did not provide protection against the compound [33].  The slight exposure 
lead to a condition of mental degeneration which rapidly progressed over the course 
of a year, resulting in the researcher's death.  Chelation therapy treatments were 
unfortunately not effective enough to prevent the scholar's fate.
We conducted a number of stability and structure calculations on methylmercury 
halides, described in Chapter 4, with the goal of demonstrating it is currently possible 
to safely investigate the behavior of these hazardous compounds via theoretical 
chemistry.
However, the calculations on the mercury compounds are of charged ion species, 
which stresses the theory applied to produce their results.  We therefore started a side 
project to further confirm the quality of those other results by proceeding with 
calculations on a few systems which have been exhaustively explored in experiments. 
In this way, the quality of the results in the mercury calculations can be measured 
practically by comparing the quality of the similar systems against experimental 
results.
1.2.4 ? Polyprotic Acid pKa Calculations: phosphoric, arsenic, and others
We selected a variety of polyprotic acids to investigate to address this concern.  These 
9
would give us a system which both matched the mercury ones in having moderately 
sized ionic species of different total charges such as the phosphoric acids, as well as 
having moderately heavier central atoms in the case of the As-based systems.
As arsenic appears in the middle of the periodic table with 33 electrons, the accuracy 
of the results calculated on it will give a better feel for the 80-electron mercury atom 
calculations than results on lighter atoms.
To begin, we did a number of calculations on H3PO4 in detail to reproduce 
experimental pKa values for the multiply deprotonated ion.  pKa values depend 
strongly on the free energy of the ion, to the order of 1 kcal/mol, which is 
approximately 0.0015 Hartrees.  Therefore, a study of pKa values and their relation to 
the experimental measurements of the same would be a good ?acid? test of the 
accuracy of our chosen models.
We therefore calculated optimized geometries and single point energies for H3PO4, 
H2PO4-, HPO42-, and PO43- using the CBS-QB3 model chemistry, MP2 with the 
CBSB7 basis set, and CPCM polarizable continuum calculations done both separately 
(on the gas phase geometries of the species) and in conjunction (during the CBS-QB3 
and MP2 calculations) with the two computational methods.  We also did solvation 
calculations with an explicit Na+ counterion which was used to reduce dependence on 
the CPCM model for finding the stabilized energy.
10
The CPCM single point stabilization energies were calculated in the gas phase 
conditions with self-consistent electron cloud geometries found from HF calculations 
at the gas phase geometries with three different basis sets, 6-31G, 6-31G**, and G-
31+G**.
Overall, the energies found from the solvation calculations with explicit Na+ 
counterions were closest to experimental measurement, although there were issues 
with converging the geometries in some cases.
Possible future calculations might include molecular dynamics (MD) calculations 
with each species and Na+ counterions to sample their statistical behavior. 
Anticipated difficulties would of course include the usual concern with MD, where 
the size of the periodic boundary conditions causes an effective concentration of the 
analyte that is not realistic, but future advances in computer speeds as well as the 
inherent parallelizability of MD methods should allow for easy calculations in 
sufficiently large reaction volumes that the concentration of the acid would be quite 
reasonable in the near future.
Another possible avenue of exploration would be to do more modeling using  the 
CBS-QB3 model chemistry with additional explicit solvent molecules.  This would 
provide more opportunities for directly calculated solute-solvent interactions rather 
11
than the simpler and less computationally expensive solvation models such as the 
polarizable continuum (used extensively in our work here), which have some 
shortcomings such as not allowing for hydrogen bonding.
We continued demonstration of the quality of the calculations by doing some more in 
a similar direction on a variety of arsenic compounds.
Arsenic compounds were chosen for several reasons.  First, they are important both 
environmentally, due to their easy availability in the geosphere, and the ease by 
which arsenic compounds can affect the human condition.  A semi-metal of atomic 
number 33, arsenic is a good way down the periodic table towards mercury (atomic 
number 80).  Arsenic has a full 3d orbital while mercury compounds usually has three 
filled d shells.  Arsenic was therefore a middle step in going from the light P atoms to 
the heavy Hg atoms in similar chemical conditions.
Therefore, we followed up our calculations on phosphoric acid with similar ones on 
some common arsenic and arsenous acids.  The species of interest were H3AsS3, 
H3AsS4, H3AsO3, H3AsO4, H3PO4, H3SO4.  Later we also did calculations on the 
deprotonations of H3SO3 species.
Methods used were CBS-QB3, CCSD, and CCSD(T).  The CBS-QB3 model 
chemistry included geometry optimization and vibrational frequency calculations, and 
12
the CCSD and CCSD(T) calculations were done with these as well.
Hydration was modeled in several ways.  Arguably the most successful in this case 
was conducted with a single explicit water molecule and the CPCM solvation model 
applied to the system at the same time as the geometry optimizations.   Solvation 
calculations were done with and without the explicit water molecule's presence and 
either with the geometry optimization done with the solvation model present or the 
solvation energy estimated at the gas phase geometry of the system.
Optimization with the CPCM therefore produced B3LYP/CBSB7 CPCM optimized 
geometries in the case of the CBS-QB3, as the geometry optimization step in that 
method uses the B3LYP hybrid density-functional model.
The final results for the H3PO4 and H3AsO4 and H3AsO3 were then compared to 
available experimental data, and we noticed a distinct correlation between the 
theoretical calculations and the measurements.  This led us to construct a linear fit 
between the two sets of data which was then checked against H3SO3 theoretical 
calculations and experimental measurements conducted later.  The results for H3SO3 
were not used to construct the fit.
Finally, a series of the same sort of calculations were conducted on HClO, HClO2, 
HClO3, and HClO4 with counterions. 
13
The quality of the data before and after the fit can be used to evaluate some of the 
assumptions made for the mercury calculations.  We can see that although before 
fitting our calculated trends were OK for the highly charged anions, the higher the 
charge the lower the quality of the results, very much so when compared to the ones 
with neutral or singly-charged species.
1.2.5 ? Raman Spectra of Myo-Inositol Phosphates
The final project was to calculate theoretical Raman (and IR) spectra of different 
forms of Myo-Inositol hexakis phosphate (IHP)  to compare and shed light on an 
experimental study of the compound[40] conducted across a variety of pH conditions 
from strongly acidic to neutral to strongly basic.  In this case we decided to begin 
with Hartree-Fock (HF) calculations done with a minimal 6-31G basis due to the size 
of IHP, followed by higher level methods.  Raman and IR spectra from the HF 
calculations as well as some B3LYP IR spectra were ready as of the time of this 
writing, and they are presented here.  The results were favorable, reproducing the 
experimental trends presented at ACS[40], and further calculations currently in 
progress as well as those described here will be the subject of a future joint paper.
14
1.3 Initial Results and Discussion
As was presented at the NOBCChE Conference in 2006, many of our first 
calculations on the HgClx series of species were completed using GAUSSIAN 03 
(G03) and ADF.  Interpretations of the raw results (which are summarized in Tables 
1.1 and 1.2) are in the following Conclusions section.
GAUSSIAN 03 (G03) calculations were set up with starting geometries slightly 
differing from the highest symmetry, to allow for possible asymmetric bond distances 
to develop or be extinguished as the geometry optimizations saw fit.  This avoided 
some cases which appeared when symmetric starting geometries were chosen 
accidentally on saddle points, such as appeared in some of the 
Table 1.1 summarizes the G03 calculations, and appears below.  They were run using 
CCSD with the CEP-31G and CEP-121G basis sets.  The CEP-121G calculations 
showed less of an apparent basis set overlap error than the CEP-31G calculations; the 
energies of the smaller complexes were closer to that of the larger ones.
Hydration energy calculations are done with HF and the CEP-31G basis at the single 
point of the final geometry.  We used the Conducting Polarizable Continuum Method, 
CPCM, to run the self-consistent reaction field (SCRF) calculation.
15
Table 1.1: HgClx compound energies of reaction in the gas phase and with CPCM 
hydration.
Calculations were first run with the specified basis sets and the OPT FREQ keywords. 
On the occasions where the first run was unsuccessful in attaining the final geometry 
(due to our starting geometries being too distant from equilibria to converge in the 
default short run length), the geometries were then copied out in Cartesian 
coordinates, and the software used its standard symmetry detection methods to 
16
HgClx CCSD Energy 1 Hartree = 627.5 kcal/mol Delta G
CEP-31G CEP-121G basis Hydration E
Hartrees kcal/mol Hartrees kcal/mol kcal/mol
Cl- (singlet) -14.873432 -9333.0786 -14.902545 -9351.34699 -76.55
Cl0 (doublet) -14.775784 -9271.80446
Cl2 (singlet) -29.613822 -18582.6733 1.43
Cl+ (singlet) -14.252053 -8943.16326 -68.79
Hg+2 -152.141721 -95468.93 -152.159227 -95479.9149 -407.17
Hg0 -153.181514 -96121.4 -0.46
HgCl+ -167.646138 -105197.95 -167.68025 -105219.357 -139.85
HgCl2 0 -182.87579 -114754.558 -182.922266 -114783.722 -20.68
HgCl3 - -197.824502 -124134.875 -197.890057 -124176.011 -47.26
HgCl4 -2 -212.636335 -133429.3 -212.717105 -133479.983 -160.89
Delta E
CEP-31G Hg+2 + Cl- -> HgCl+ Sum(Prod.)-Sum(React.)
CCSD E -95468.93 -9333.0786 -105197.95 -395.943088 Total Delta E
Hydration E -407.17 -76.55 -139.85 343.87 -52.07
CEP-121G E= -44.22
CEP-31G HgCl+ + Cl- -> HgCl2 0
CCSD E -105197.952 -9333.07858 -114754.558 -223.52805
Hydration E -139.85 -76.55 -20.68 195.72 -27.81
CEP-121G E= -17.30
CEP-31G HgCl2 0 +Cl- -> HgCl3 -
CCSD E -114754.558 -9333.07858 -124134.875 -47.2382
Hydration E -20.68 -76.55 -47.26 49.97 2.73
CEP-121G E= 9.03
CEP-31G HgCl3 - +Cl- -> HgCl4 2-
CCSD E -124134.875 -9333.07858 -133429.3 38.6533725
Hydration E -47.26 -76.55 -160.89 -37.08 1.57
CEP-121G E= 10.29
accelerate computation.
After the geometry was converged, second calculations with HF 6-31G and 
SCF=CPCM were executed at the final geometries of the calculation.  This schema, 
recommended by Dr. Tossell from experience and so the results would be compatible 
with other ones within the Tossell Group, is used to estimate the solvation energy of 
each complex.
As is outlined in Table 1.1 (where following the bold numbers to illustrates how each 
figure is calculated), we determine the change in free energy of reaction from our 
intermediate calculations.  The ?G values are reported in each of the GAUSSIAN 
results for vibrational spectra calculations as the ?Gformation of each species.
We would like to suggest that the new GAUSSIAN user read the excellent text 
Exploring Chemistry with Electronic Structure Methods, which we would like to 
acknowledge for its usefulness in getting familiar with the GAUSSIAN system and its 
implementation of theoretical chemistry methods.
ADF (Amsterdam Density Functional)[34-36], a program from SCM (Scientific 
Computing and Modeling), was used to do DFT[31] calculations with a TZ2P basis 
set without frozen core electrons.  The XC was GGA Becke Perdew[32].  The 
ZORA[30] was used to model relativistic effects on the Hg electrons, and the 
17
calculations were run with and without excitations allowed, and NMR shieldings 
were calculated[37-39].
Table 1.2, below, summarizes the ADF calculation results.
Table 1.2:  ADF NMR calculation results for compounds in HgClx series.
18
ADF Calculations on HgClx series
HgClx with Excitations
Bond Energy NMR Shielding
LDA+GGA-XC (ppm)
(atomic units) Hg Cl
Hg atom (solvated) 0.52212496 9909.5
HgCl 0.29870258 10077.44 -867.59
HgCl (solvated) 0.14661713 9109.17 618.35
HgCl2 -0.18954049 7306.67 807.37
HgCl2 (solvated) -0.20115095 7444.05 894.14
HgCl3 -0.39838704 6538.59 892.1
HgCl3 (solvated) -0.47154059 6639.91 924.4
HgCl4 -0.47052597 6764.95 929
HgCl4 (solvated) -0.73686043 6483.6 967
HgClx with No Excitations
Cl atom 0.07361672
Hg atom 1.09951364 9909.71
HgCl 0.29870215 10077.22 -867.23
HgCl (solvated) 0.14661688 9109.25 618.29
HgCl - H2O -0.293957 8198.2 580.16
HgCl - H2O (solvated) -0.39646566 8055.78 792.71
HgCl2 -0.18954118 7306.71 807.33
HgCl2 (solvated) -0.20115224 7443.37 894.22
HgCl2 - 2H2O -1.23904561 7259.04 841
HgCl2 - 2H2O (solvated) -1.25297228 7335.65 865
HgCl3 -0.39838715 6538.56 892.1
HgCl3 (solvated) -0.4715399 6639.9 924.4
HgCl3 - H2O -0.93251747 6571.58 2x869, 1x895
HgCl3 - H2O (solv) -0.99475377 6715.55 937
HgCl3 - 2H2O (solv) -1.52886988 6651.42 910
HgCl4 -0.47052725 6764.95 929
HgCl4 (solvated) -0.7368604 6483.76 967
HgCl4 - 2H2O -1.56246352 6702.4 914
HgCl4 - 2H2O (solvated) -1.80401526 6510.32 935
HgCl4 (flat) 0.47050426 6778.92 927
HgCl5 (Geometry did not converge)
HgCl5 (solvated) -0.95764149 6971.03 3x960, 2x810
HgCl6 (Geometry did not converge)
HgCl6 (solvated) -1.17432797 7137.75 890, 905, and 969
   
The ADF data include both gas phase and PCM stabilized calculations (with and 
without explicit water molecules in the case of the calculations without excitations). 
The results with excitations were similar enough to the corresponding ones without 
that the author feels he has a reasonable case for confidence in the conclusions of the 
simpler computation3.  These results are considered in detail at the end of Chapter 1.
We would like to thank the SCM team for their rather essential ADF-GUI, which was 
indispensible in setting up all of the jobs used to calculate NMRs.
Table 1.3, below, summarizes the counterpoise correction calculations we conducted 
at the beginning of the project.  In the past, to correct for using smaller basis sets than 
were optimal, the counterpoise correction was developed to address the problem of 
the presence of nearby atoms increasing the quality of the basis sets near them.  We 
attempted a number of calculations in GAUSSIAN 03 with ghost atoms in an effort to 
see the effects on the energy of stabilization by the basis size.
The author wishes to withhold judgment on these counterpoise results, however, 
since a related experiment which he observed yielded electron distributions well 
beyond the border of absurdity, having layouts where, for example, ligands' electrons 
ended up in (otherwise occupied) orbitals of the ghost heavy atom, and the electron 
clouds for these calculations were not shown to be reasonable.
3  The simpler also being much easier for the author to converge, as it turned out.
19
Table 1.3: Ghost atom calculations for Counterpoise Correction in HgCl2 system.
The results of the calculation indicated a correction between HgCl+ and HgCl20 on the 
order of 200 kcal/mol (Conversion used: 1 Hartree = 627.5 kcal/mol) worth of 
apparent false stabilization.  Comfortingly, the difference for the two species most 
interesting to us, HgCl20 and HgCl3-1 is much less, being nearly a tenth that number. 
However, this figure is still quite significant, considering that 20kcal/mol is certainly 
on the scale of the differences in energy we calculated for the species.
To address any concerns about basis set size which may have appeared to be the case 
in the counterpoise calculation, we increased the basis set size by adding additional 
diffuse functions to all of the heavy atoms and focusing on the CEP-121G basis 
20
Cl- in Hartrees
HgCl+ CEP121G -14.926598 1 -14.926598
HgCl+ CEP31G -14.91592 1 -14.91592
HgCl2 0 CEP121G -14.934319 2 -29.868638
HgCl2 0 CEP31G -14.924157 2 -29.848314
HgCl3- CEP121G -14.943416 3 -44.830248
HgCl3- CEP31G -14.92414 3 -44.77242
HgCl4-- CEP121G -14.938398 4 -59.753592
HgCl4-- CEP31G -14.939102 4 -59.756408
Hg2+ Hartrees Actual Calc. Delta
Sum Hartrees Hartrees
HgCl+ CEP121G -152.167682 -167.09428 -167.68025 -0.58597
HgCl+ CEP31G -152.167631 -167.083551 -167.646138 -0.562587
HgCl2 0 CEP121G -152.173626 -182.042264 -182.922266 -0.880002
HgCl2 0 CEP31G -152.173557 -182.021871 -182.87579 -0.853919
HgCl3- CEP121G -152.182321 -197.012569 -197.890057 -0.877488
HgCl3- CEP31G -152.182305 -196.954725 -197.824502 -0.869777
HgCl4-- CEP121G -152.190814 -211.944406 -212.717105 -0.772699
HgCl4-- CEP31G -152.190793 -211.947201 -212.636335 -0.689134
Hg+2 Cl-
Lone Atom -152.159227 -14.902545
Energy -152.141721 -14.873432
Ghost Atom Calculations
Sum of electronic and thermal free energies
*N Cl atoms
instead of using the smaller CEP-31G.
The results were also assisted by including counterions in some cases, which reduced 
the total charges of the systems studied, and by showing that similar calculations done 
on As compounds with similar sizes of basis sets provided reasonable results without 
use of counterpoise corrections.
1.4 Conclusions
To summarize the conclusions of the calculations covered here, for the G03 
calculations the most stable complex in solution was calculated to be HgCl20.  HgCl3- 
was the most stable in the gas phase.  This is presumably due to the lost hydration 
energy of the Cl- ion, which is less easy to hydrate when combined with HgCl2 than 
alone.
In the ADF calculations, shieldings for Hg decrease by approximately 1000 ppm per 
Cl- added up to HgCl3-.  HgCl4-2 does not continue the trend, however.  Solvation by 
both the conducting polarizable continuum model (CPCM) alone and a CPCM system 
assisted by explicit H2O molecules yielded the same results as the gas phase ones.
21
1.5 References
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22
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18. Morel, F.M.M., A.M.L. Kraepiel, and M. Amyot, The chemical cycle and 
bioaccumulation of mercury. Annual Review of Ecology and Systematics, 
1998. 29: p. 543-566.
19. Harada, M., Minamata Disease - Methylmercury Poisoning in Japan Caused 
by Environmental-Pollution. Critical Reviews in Toxicology, 1995. 25(1): p. 
1-24.
20. Boffetta, P., E. Merler, and H. Vainio,  Carcinogenicity of Mercury and 
Mercury-Compounds. Scandinavian Journal of Work Environment & Health, 
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21. Bakir, F., et al., Methylmercury Poisoning in Iraq - Interuniversity Report. 
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22. Lohman, K., et al., Sensitivity analysis of mercury human exposure. Science 
of the Total Environment, 2000. 259(1-3): p. 3-11.
23. CPMD,  Copyright  IBM  Corp  1990-2006,  Copyright  MPI  f?r 
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correlation problem. Int. J. Quant. Chem., 1978. 14(5): p. 561-581.
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shared-exponent basis sets for the third-, fourth-, and fifth-row atoms. Can. J. 
Chem./Rev. can. chim., 1992. 70(2): p. 612-630.
27. Becke, A.D.,  Density-functional thermochemistry. III. The role of exact 
exchange. J. Chem. Phys., 1993. 98(7): p. 5648-5652.
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p. 5622-5629.
29. Riedel, S., M. Straka, and M. Kaupp, Validation of density functional methods 
for computing structures and energies of mercury(IV) complexes. Physical 
Chemistry Chemical Physics, 2004. 6(6): p. 1122-1127.
30. van Lenthe, E., E.J. Baerends, and J.G. Snijders, Relativistic regular two-
component Hamiltonians. J. Chem. Phys., 1993. 99(6): p. 4597-4610.
31. Perdew, J.P., et al.,  Prescription for the design and selection of density 
functional approximations: More constraint satisfaction with fewer fits. The 
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32. Perdew, J.P., et al., Atoms, molecules, solids, and surfaces: Applications of 
the generalized gradient approximation for exchange and correlation. Phys. 
Rev. B, 1992. 46(11): p. 6671-6687.
33. Nierenberg, D.W., et al.,  Delayed cerebellar disease and death after 
accidental exposure to dimethylmercury. New England Journal of Medicine, 
1998. 338(23): p. 1672-1676.
34. Guerra, C.F., et al., Towards an order-N DFT method. Theoretical Chemistry 
Accounts, 1998. 99.
35. Velde, G.t., et al.,  Chemistry with  ADF. Journal of Compututational 
Chemistry, 2001. 22: p. 931.
36. Baerends, E.J., et al., ADF2004.01, SCM, Theoretical Chemistry, Vrije 
Universiteit, Amsterdam, The Netherlands,  http://www.scm.com. 2004.
37. Wolff, S.K., et al.,  Density functional calculations of  nuclear magnetic 
shieldings using the  zeroth-order regular approximation (ZORA) for 
relativistic effects: ZORA nuclear magnetic  resonance. Journal of Chemical 
Physics, 1999. 110: p. 7689 
38. Schreckenbach, G. and T. Ziegler, The calculation  of NMR shielding tensors 
based on density  functional theory and the frozen-core  approximation. 
International Journal of Quantum  Chemistry, 1996. 60.
39. Schreckenbach, G. and T. Ziegler, The calculation  of NMR shielding tensors 
using GIAO's and modern  density functional theory. Journal of Physical 
Chemistry, 1995. 99.
26
40. Heighton, L.P. and W.F. Schmidt. Raman spectra of organic (myo-inositol 
hexakis phosphate) and inorganic P spectra show pH dependence. in 
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Washington, D.C.
27
Chapter 2: Mercury Compounds in the Environment: An 
Overview of their Human Impact
2.1 Background
The study of mercury is one fraught with hazard and danger.  Since mercury is 
extremely hazardous in some forms, research has been understandably difficult to 
conduct with safety.  The organic forms of mercury, especially methylmercury, are 
intensely poisonous. Since the death of a researcher at Dartmouth College caused by 
acute methylmercury poisoning [1], there is even more caution exercised when 
dealing with this hazardous compound.  But although there is less experimentation 
with organic mercury complexes, it is important to understand them thoroughly, 
because they are one of the main ways that people are exposed to this toxic metal [2]. 
Mercury chemistry is also important for other reasons; its behavior in some situations 
is determined by relativistic quantum effects, such as its liquidity at room 
temperatures.
There are several current problems which merit more understanding, but which are 
difficult to approach.  Every year, upon polar sunrise, the concentrations of mercury 
in the atmosphere are observed to drop precipitously in both the arctic [3] / [4] and 
Antarctic poles [5].  At the same time, a drop in concentration of ozone, another 
28
important environmental chemical, is also observed [6].  The behavior of arctic 
formaldehyde during this same critical time window is also irregular [7].
These depletion observations are a phenomenon that is not yet fully understood. 
There are strong suspicions that a reaction with a halide species [8] in a process 
similar to that known in ozone depletion [9], [10] is involved in the mercury 
depletions.  Computer simulation studies have produced results that confirm an 
inverse correlation between the concentrations of mercury as well as ozone against 
several halide species [11]. There have been studies that suggested HgO was formed 
as a product [5], but this result is disputed by models that indicate that the formation 
of HgO from BrO and Hg-0 isn?t energetically favorable [12], [13].  A later paper 
suggests that perhaps the species of interest is HgBr2, not HgO [14], and that this 
species might be the result of reactions with atomic bromine in the atmosphere [15]. 
Further compounding matters, an earlier study showed that measuring concentrations 
of HgCl2 using different methods did not produce the same resultant data [16].
Whatever the process, the mercury displaced from the atmosphere ends up primarily 
in the snowpack on the arctic surface.  Modeling indicates that slightly more than 200 
tons of mercury could be deposited in the arctic every year [17], which is triple what 
it was several centuries ago [18].  One laboratory has already developed an 
instrument for measuring mercury compound concentrations at different depths in the 
snow [19].  Using this instrument, they determined that the amount of elemental 
29
mercury in the air embedded in the snow increases by approximately a factor of two 
during the daylight hours, and falls during the nighttime [20].  The same group has 
also come to the conclusion that the majority of the mercury in the snowpack ends up 
dissolved in the water when it melts [21], as nearly all (99%) of it is associated with 
the ice crystals rather than in gaseous form [22].
This observation brings us to our next topic, the prevalence and chemistry of mercury 
in waterways and lakes.  Although the concentrations of mercury in arctic waters 
weren?t observed to be especially higher when compared to concentrations in other 
nonpopulated areas (one study measured [23] less than half a nanogram of mercury 
per liter of water), concentrations in excess of 0.5 micrograms per gram of animal 
muscle tissue were observed in animals living in the arctic in the early 1990s [24]. 
This factor of a thousand difference in the two concentrations is an example of how 
biomagnification can increase the concentrations of pollutants where it counts.
It has been observed that the release of mercury from the surfaces of lakes in a study 
in Sweden occurs at a higher rate during the day than at night, and mercury emission 
wasn?t observed at all when the water was close to 0 degrees Centigrade [25].  This 
correlates well with the observations in the arctic, where little mercury was observed 
between the ice crystals in the snowpack [22].
30
There are three main categories which mercury contamination in waterways falls into: 
elemental mercury, methylmercury, and ionic compounds with mercury 2+ [26]. 
Elemental mercury isn?t very soluble in water and generally either migrates to the 
riverbeds, where it ends up converted to HgS(s) and precipitated into the silt, or is 
released intact into the air above. Mercury 2+ was shown to be present mostly in 
complexed form in urban wastewater [27], and one eighth to one half of the ions were 
held extremely tightly, with dissociation constants on the order of 10-3.  Of the three 
species, methylmercury is probably the most dangerous, since it is readily absorbed 
and concentrated by fish and other water creatures, and can cross cell walls 
straightforwardly using existing channels [28]. The same anaerobic bacteria that 
reduce sulfates can also convert mercury to methylmercury [29], which compounds 
the problem.  Interestingly enough, in conditions where iron would be reduced there 
is less methylation observed [30]. 
Luckily, photochemical decomposition of methylmercury, both observed [26] and 
successfully modeled in simulations [31], helps this situation somewhat, converting it 
back into elemental mercury, which is less harmful to us.
We can?t ignore mercury depositing into the ocean either.  Several studies have 
started to study the dynamics of mercury redistribution in the ocean [32]. 
Examination of concentrations compared to time show that photochemical oxidation 
of mercury is important in the dissolution of elemental mercury in the seawater [33]. 
31
Studies in the St. Lawrence estuary determined that there, the rate of photo-oxidation 
increased by a factor of seven when the light used contained UV-A radiation [34]. 
Concentrations of bromine are also involved in the emission and absorption of 
mercury over the ocean.
One study of Tuna had some better news, however.  The modeling method which 
they were using indicated that they should have observed an increase in the 
concentrations of methylmercury in the fish, but this was not seen [35].  This initially 
surprising result would make some sense upon further review, since the anoxic 
bacteria which are generally responsible for converting elemental mercury fallout into 
methylmercury would not be found in the same water that tuna inhabit.
Mercury poisoning can occur to both animals and humans. A very recent study of 
mercury exposure in zebrafish [36] observed the activations of several genes in fish 
fed between 0.08 and 13.5 micrograms of methylmercury per gram of food and 
found, surprisingly, that the brains of the fish did not show greater gene expression in 
any of the ones they monitored even though they accumulated more than 60 
micrograms of mercury per gram of dried fish tissue at the end of their 63 day 
experiment.  This lack of an extraction method might shed some light on the poor 
clinical performance of human victims of mercury poisoning, who often end up sick 
for several months after exposure before beginning to improve [2].  Symptoms of 
Mercury poisoning include progressive deteriorations of the senses, especially visual, 
32
loss of motor control, and death from central nervous system failure [37].   Even with 
chelation  therapy to  help  the  body eliminate  mercury,  the  rate  at  which 
methylmercury damages the nervous system can be fast enough that intense treatment 
after the asymptomatic period (which can last from one half to two months [38]) is 
over is not enough to effectively save lives [1].
Although the elemental form of mercury isn?t as hazardous to people as organic 
complexes (especially methylmercury), it is still dangerous, as its vapor can enter the 
body through the lungs, and it can also be converted to methylmercury by the action 
of anaerobic bacteria.  The vapor inhalation of elemental mercury is probably the 
cause of the mad hatter?s ailment, as they used mercury to cure the felt used to make 
hats in the latter half of the nineteenth century and as such were chronically exposed 
to mercury vapors.
The chemical industry in Japan caused one of the largest episodes of acute mercury 
poisoning in the recent past [39].  Nippon Nitrogen Fertilizer Company (now known 
as Chisso Corporation) released methyl mercury into the waterways near Minamata 
Bay, and many people there ended up sick or dead?nearly three thousand in total 
[40].  The first indication that there was something wrong was when cats began acting 
strange and throwing themselves into the water and drowning, but the people there 
weren?t able to determine the cause of the scourge until much later, although a 
scientist in the Chisso Company determined what was going on and was silenced by 
33
the corporation until much later.  Now, over three thousand people or their families 
have qualified for reimbursement due to the disaster. Computer modeling [41] has 
been used to project future conditions of Minamata bay and its environs as well as the 
Gulf of Trieste.  Minamata bay is expected to do no further damage to the 
environment.
There was a larger disaster in Iraq in the early 1970s, where farmers accustomed to 
consuming bread made from the grain they were planting caused more than six 
thousand people to become sick from methylmercury poisoning when the grain they 
were provided with from the government had been treated with a different variety of 
fungicide than usual [38].  From the epidemiological data, they determined that 
deaths only began occurring in earnest once victims ingested more than 200mg of 
methylmercury, upon which the death rate quickly rose to above 20% at 250mg. 
Tingling in extremities was observed above 25mg of exposure, and blindness above 
approximately 100mg.  The problem was compounded by the fact that symptoms 
took a long time to develop, so people who tested the food to see if it was poisonous 
on animals didn?t observe any ill effects until well after they had already exposed 
themselves and their families to large amounts of the chemical.
Industrial negligence is not the only cause of mercury pollution, however.  Coal 
powered plants and factories are moving significant amounts of the element into the 
atmosphere as they burn fuel that contains traces of the element [42]. There are 
34
processes being used to remove mercury from the gas emitted by these plants which 
are successful in removing over half of the chemical [43], and new methods are in 
development [44], but there is a great challenge presented in removing the relatively 
non-reactive Hg-0 elemental mercury from the emissions, especially when the 
temperatures involved are so high (typical coal flue gasses are between 50 and 400 
degrees centigrade, although they can be cooled as they are emitted), because 
mercury has a very high vapor pressure compared to other metals.  It is easier to 
remove other mercury compounds, like HgCl2 [45], although in the quest for more 
effective solutions there is constant development on new methods and materials [46]. 
The chemistry of mercury in the unusual environment of combustion products is also 
novel, and there are multiple studies investigating its behavior there [47]. Some 
modeling studies suggested that American factories might not be the main source of 
mercury in the US [48], but they are certainly important here as well as in other 
countries, such as China [49].   In countries with dry seasons and dust storms, 
mercury can also reenter the atmosphere seasonally as well [50].
Mercury poisoning wouldn?t be so bad if treatment methods existed which were more 
effective.  The body has difficulty removing mercury from its system, leading to 
individuals ending up continuing to be damaged mentally a long period of time after 
an initial exposure.  Studies on farmers involved with the Iraq event indicated that 
mercury has a half-life in the body ranging from between forty to one hundred days 
[38], and the concentrations in the brain are much higher than in other organs. 
35
Unfortunately, although treatment with current known chelating agents can show an 
increase in excretion by a factor of a thousand (observed in the patient at Dartmouth 
College), this isn?t as helpful as we might like, since the mercury remaining in the 
body continues to do damage until it is extracted.  In the studies in Iraq, they found 
that multiple treatments with the chelating agents were less effective after the first 
round.  The main obstacle to treating patients with mercury poisoning effectively is 
that they show a long asymptomatic period, during which the brain concentrates the 
poison and is continuously being damaged.  This span of time is often long enough 
that the additional length of time necessary to remove the mercury from the patient is 
great enough that serious permanent damage can occur before the treatment is 
complete.
Better and less dangerous chelating agents would therefore be a good product to 
develop, since they could be used to better remove mercury from the body than the 
current chemicals.  In the Iraqi disaster, they used D-penicillamine, N-acetyle-DL-
penicillamine, and a thiol resin containing -CH3SH groups to bind mercury [38]. A 
better understanding of how mercury interacts with the enzymes in cells might 
provide much additional impetus towards intelligent medicine design.  To date, there 
have been a number of studies on different sorts of mercury-sulfur complexes. 
Mercury is suspected to interfere with proper enzyme behavior primarily by binding 
itself to sulfur atoms.
36
2.2 Previous Work
So far, there have been the many studies published in the literature that used 
computers to simulate mercury compounds in different situations.  The following are 
a summary of a few additional related mercury papers which were not referred to 
previously.
The first paper includes calculations on mercury has an analysis based in molecular 
orbital theory and analyzes many complexes, including tetrahedral HgS46- and linear 
HgS2- mercury complexes.  It was published in the early eighties before 
computational capabilities were strong enough to include relativistic effects and notes 
that those ?may even be quite important? when considering mercury complexes [51].
There were also several later papers by a different laboratory that included early 
relativistic calculations on mercury: [52], [53], [54], [55], and [56].  In our case we 
did some calculations with Core Effective Potential basis sets, which include 
relativistic effects for the core electrons in the basis set.
A later study calculates stretching frequencies and hydrated stabilities using a 
relativistic effective core potential with additional polarization functions and finds 
that, as expected, CH3HgOH is one of the most important species involved in 
photodecomposition of aqueous methylmercury compounds [31].  A future paper 
37
computes water solvation energies for a variety of divalent complexes, then goes on 
to determine the energy required to dissolve cinnabar by various species using that 
same model [57]. 
Revisiting one of the earlier topics, another paper analyzes the stabilities of HgS-
based species in water solution, and concludes that it exists as a strongly hydrated 
HgSH(OH) molecule when it is in solution instead [58].
Another study manages to reproduce the known spectroscopic properties of gaseous 
mercury(II) chlorides and bromides successfully [59], and the same group continues 
by calculating reactions relevant to oxidation of atmospheric elemental mercury [60]. 
A more recent ab-initio study of mercury-sulfur and other group sixteen ligands 
calculated  results  which  would  seem  to  imply  that  previous  experimental 
measurements of the stability of HgS and other similar compounds were greatly 
overestimated, perhaps because the experiments were being conducted on dimers or 
mixtures of larger molecules [61].  
Preliminary calculations conducted at the beginning of the research suggest that the 
most stable mercury-sulfur complexes have near-linear angles around the mercury 
atom, and an approximately 120 degree angle between the sulfurs.  It is possible to 
form ring structures with more stability than the linear open forms so long as the 
38
number of sulfur atoms involved is greater than six, and a bare mercury atom will 
easily approach and break open a sulfur ring when placed within 4 angstroms of its 
center when using B3LYP with an extended CEP-31G basis set.  Further examination 
of this phenomenon is indicated for the future.
Suggested future directions that this research should take would also include studies 
on isotopic fractionation in mercury-sulfur species in both aqueous and solid phases, 
theoretical studies on where mercury would stably bind to some common well-
characterized enzymes, and attempts to run some ab-initio calculations on crystal 
formations of mercury and sulfur compounds.
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45
51. Tossell, J.A. and D.J. Vaughan,  Relationships between Valence Orbital 
Binding-Energies and Crystal-Structures in Compounds of Copper, Silver, 
Gold, Zinc, Cadmium, and Mercury. Inorganic Chemistry, 1981. 20(10): p. 
3333-3340.
52. Stromberg, D., O. Gropen, and U. Wahlgren, Non-Relativistic and Relativistic 
Calculations on Some Zn, Cd and Hg Complexes. Chemical Physics, 1989. 
133(2): p. 207-219.
53. Stromberg, D., M. Sandstrom, and U. Wahlgren, Theoretical Calculations on 
the Structure of the Hexahydrated Divalent Zinc, Cadmium and Mercury Ions. 
Chemical Physics Letters, 1990. 172(1): p. 49-54.
54. Stromberg, D. and U. Wahlgren, 1st-Order Relativistic Calculations on Au2 
and Hg-2(2+). Chemical Physics Letters, 1990. 169(1-2): p. 109-115.
55. Stromberg, D., A. Stromberg, and U. Wahlgren,  Relativistic Quantum 
Calculations on Some Mercury Sulfide Molecules. Water Air and Soil 
Pollution, 1991. 56: p. 681-695.
56. Xiao, Z.F., D. Stromberg, and O. Lindqvist, Influence of Humic Substances 
on Photolysis of Divalent Mercury in Aqueous-Solution. Water Air and Soil 
Pollution, 1995. 80(1-4): p. 789-798.
57. Tossell, J.A., Theoretical studies on the formation of mercury complexes in 
solution  and  the  dissolution  and  reactions  of  cinnabar. American 
Mineralogist, 1999. 84(5-6): p. 877-883.
46
58. Tossell, J.A.,  Calculation of the structures, stabilities, and properties of 
mercury sulfide species in aqueous solution. Journal of Physical Chemistry A, 
2001. 105(5): p. 935-941.
59. Balabanov, N.B. and K.A. Peterson,  A systematic ab initio study of the 
structure and vibrational spectroscopy of HgCl2, HgBr2, and HgBrCl. 
Journal of Chemical Physics, 2003. 119(23): p. 12271-12278.
60. Balabanov, N.B. and K.A. Peterson, Mercury and reactive halogens: The 
thermochemistry of Hg+{Cl-2, Br-2, BrCl, ClO, and BrO}. Journal of 
Physical Chemistry A, 2003. 107(38): p. 7465-7470.
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Unusual types of mercury bonding. Chemphyschem, 2004. 5(10): p. 1547-1557.
47
Chapter 3: An Overview of Computational Chemistry 
Techniques
Computational Chemistry is the study of chemical compounds via computer 
simulations.  As we use it here, it is the application of quantum mechanics and 
theories based thereupon.
The purpose of this chapter is to provide a bit of background and an easy reference to 
the terminology and basic methods used in our calculations, aimed towards the 
physical chemist who has not yet become a specialist in applied theoretical chemistry, 
beginning with an introduction to the Schrodinger equation used in quantum 
mechanics and a tour through a low level ab initio method, Hartree-Fock theory 
before going on to discuss the other levels of theory and approaches which we shall 
be using.
3.1 Introduction
In quantum mechanics, the Schrodinger equation[1] can be used to predict the 
electronic stability of atoms and small molecules, but solving it is another matter. 
While it is possible to get precise solutions for smaller systems, such as the H 
atom[2], which was solved exactly in 1926, there are many chemical problems which 
involve larger molecules, such as H2, which remain a work in progress[3, 4].  Heavier 
48
elements also call for attention and are currently beyond direct exact solution of the 
Schrodinger equation due to electron overlap integrals which combine multiple basis 
functions in a nonintegrable (analytically) way.  It is these cases that we take 
measures to approximate the correct solution with a sufficiently accurate estimate to 
proceed.
3.2 ? Key Basics
Approximations.  Hartree-Fock.  Basis Sets (from Linear Algebra). Self-
consistency.
Thus we are forced to accept different approximations in order to make calculations 
on the larger systems feasible.
The approximations which are essential and widely used in our case include the 
Hartree-Fock self-consistent field method and basis functions.  Before discussing 
these at length, we will provide a quick overview of the two techniques for dealing 
with the problem of representing physical chemicals for computational study.
3.2.1 ? An overview of the Hartree-Fock self-consistent field method
An Overview of the Hartree-Fock self-consistent field method and basis 
functions.
49
The geometry of the electron cloud is solved for iteratively in this implementation of 
the  Hartree-Fock approach[5].  As the Hartree-Fock method forms the basis from 
which we build much of the other methods used in our computational chemistry 
calculations, we will discuss it at length below.  Popular methods for conducting this 
solution include approaches where the electron cloud geometries are kept track of 
numerically, and approaches where the cloud is divided into smaller, simpler to 
manipulate functions.  These functions are called basis functions and are combined 
linearly and their total approximates the wavefunction for the electrons.
Applied linear algebra: representing the electron cloud geometry with a basis 
set.
By combining the functions linearly, we can take advantage of properties from Linear 
Algebra.  It is easily proved by linear algebra that if enough functions are combined, 
they can not just approximate, but equal precisely any arbitrary function of the same 
variables.  Therefore, given a large enough number of basis functions (called all 
together a ?basis set?), we can represent any arbitrary geometry.
However, this is somewhat of an overkill, because at a certain point (which has to be 
determined via calculations) adding additional basis functions does not significantly 
improve the final results.  When computationally limited resources are in play, such 
50
as higher-level methods which become rapidly expensive as N, the problem size 
(where N = number of basis functions) increases, it is important to strike a balance 
between the basis set chosen and the quality of the method, so determining what basis 
set is required for stable results in a calculation is essential.
3.2.2 ? The Hartree Fock Method (explained in detail)
How Hartree-Fock works: Iterating the electron cloud geometry to find a self-
consistent geometry.
The Hartree-Fock method works[5] by iteratively solving for the electron probability 
wavefunction using a variational method.  At each step, the current geometries of the 
electron wave functions are used to calculate updated energies and new geometry of 
the electrons across the basis set.  As the field is brought to self-consistency, the 
electron cloud which the basis set and coefficients describe becomes the solution to 
the method.  Further discussion of the mechanisms of Hartree-Fock are described 
below based on the 1970 textbook exposition by Ira N. Levine [58].
We begin by considering a situation where we are calculating the energetics of a 
single atom, and after explaining the Hartree-Fock process under those conditions 
extend it to the molecular situation.
51
Assuming that the total charge of the nucleus is Z, the mass of the electron is m, and 
the unit charge is e', then the following Equation 3.1 represents the Hamiltonian 
needed to calculate the energy of a particular electronic arrangement of n electrons.
(3.1) ?H=? ?
2
2m?i=1
n
?i2??
i=1
n Ze'2
ri ??i=1
n ?
j?i
e'2
rij
The terms are as follows, with the first term being the total kinetic energy of the 
electrons, the second being the nuclear attraction that each electron feels towards the 
nucleus of charge Z, and the third term electron-electron repulsion.
This Hamiltonian is applied to the wavefunction representing the electron geometry 
using the Schrodinger equation as shown Equation 3.2 below.
(3.2) ?H?=E?
This gives the total energy E as an eigenvalue of the wavefunction ?.
However, the correct ? is unknown.  The Hartree-Fock approach is to start out with a 
guess or trial wavefunction, ?, which is a product of eigenfunctions si of the Hartree-
Fock atomic Hamiltonian in polar coordinates ri, ?i, and ?i.
52
(3.3) ?=?i si?ri,?i,?i?
These eigenfunctions si can be represented as a linear combination of basis functions 
bk within the same coordinate system as shown in Equation 3.3a below.  The 
coefficients cik are varied to make the basis set approximate the exact si to the an 
arbitrarily good precision.
(3.3a) si=?k cikbk?ri,?i,?i?
In the atomic case, si can be further simplified and written as a product of a radial and 
angular portion to reduce the complexity of the calculation with little loss in accuracy, 
but as this method does not apply to the molecular calculations which we are 
primarily interested in explaining, we will omit it for now.
We then begin a repeating process called the Self-Consistent Field method.
The self-consistent field method works by fixing all of the electrons except for one in 
place, then optimize the remaining free electron's wavefunction to minimize the total 
energy.  This process is repeated for each electron until an equilibrium is reached.
53
When the electrons are all fixed in place, the electron-electron repulsion term 
becomes the repulsion between a single electron and the field generated by the other 
electrons.
We can divide this into a sum of interactions between the single electrons in the field, 
and can treat them separately.
An individual electron-electron repulsion between an arbitrary electron i and j is 
therefore written as Vij, shown in Equation 3.4, where e' is the charge on an electron 
and the integral over all space is done on the expectation value of sj over rij, which is 
the distance between the two charges:
(3.4) Vij=e' 2??sj?
2
rij dvj
And the total electrostatic interaction for electron i is the sum of Vij over all of the 
other electrons, which appears as the first term in Equation 3.5 below, minus the 
nuclear attraction term for that electron, which is a single term in the case of :
(3.5) Vi?ri,?i,?i?=?
j?i
e'2??sj?
2
rij dvj?
Ze'2
ri
As mentioned before, in the atomic case here the nuclear attraction term includes only 
54
the contribution for the one point nucleus present.  In the molecular system there will 
be a sum of attractions as the second term in Equation 3.5 to account for nuclear 
attraction to each individual nucleus.
We also mentioned that in the atomic case we have a spherical symmetry we can take 
advantage of by applying the Central Field Approximation.  This is done by 
averaging out the two angles in the spherical coordinate system to produce a potential 
which only depends on ri as shown in Equation 3.6.  In the polyatomic case this 
approximation would not apply for the possibly bonding valence electrons (those in 
the outermost orbitals of each atom), but would remain relatively valid for inner shell 
electrons.
(3.6) V?ri?=
?
0
2??
0
?
V?ri,?,??sin?d?d?
?
0
2?
?
0
?
sin?d?d?
This V(ri) is then substituted into the one electron Schrodinger Equation Equation 3.2, 
as the potential energy in the one electron Hamiltonian, making it appear as follows 
in Equation 3.7, where ti is the unknown optimized eigenfunction with the minimum 
energy ?i.
55
(3.7) [? ?
2
2m ?i?V?ri?]ti?1?=?iti?1?
Where the Hamiltonian appears in brackets on the left and the eigenfunction ti yields 
the minimum energy ?i.  This can be solved for by rearranging it as follows in 
Equation 3.8:
(3.8) [? ?
2
2m ?i?V?ri?]ti?1???iti?1?=0
Presuming that ti(1) is made from a linear combination of the basis functions bk in our 
basis set as shown in Equation 3.3a, this is equivalent to a system of linear equations 
which can be solved for their individual coefficients to determine both the new 
electron wavefunction ti(1) for the free electron and the corresponding minimum 
energy state.  The new electron wavefunction for electron i, ti, replaces the original si, 
and the process is then repeated for the next electron present on the atom, until a 
stable configuration is found for all the electrons individually.
At this point, the overall wavefunction ?, is a product of optimized eigenfunctions si 
of the Hartree-Fock atomic Hamiltonian in polar coordinates ri, ?i, and ?i, and our 
calculation is complete.
The total energy is then closely related to the sum of the individual electron energies 
56
calculated during the cyclic solution on Equation 3.8, less the double-counted 
electron repulsion integral which is then subtracted as the second term of the full 
energy shown as Equation 3.9 below:
(3.9) Eatomic=?
i=1
n
?i??
i
?
j?i
??e'2?si?i??2?sj? j??2r
ij
dvidvj
However, the above atomic Hartree-Fock only covers situations where there is only 
one point nucleus present.  We can extend it to multiple atoms in a molecule with 
multiple nuclei with an extended Hamiltonian as shown in Equation 3.10 below:
(3.10) ?H=? ?
2
2m?i ?i
2??
?
?
i=1
n Z
?e
'2
ri ??i=1
n ?
j?i
e'2
rij ?
?2
2m??? ??
2??
?
?
???
Z?Z?
r??
It is instructive to compare this to our original one-nucleus Hamiltonian shown in 
Equation 3.1.
The differences are a sum appearing in the second term of the original equation, 
which now covers all of the positive nuclei Z? present where previously in the atomic 
version we only were concerned with a single positive nucleus of charge Z.  There are 
also two new terms on the right which cover the kinetic energy of each nuclei and a 
nuclear-nuclear repulsion interaction VNN which does not involve the electron cloud 
wavefunction which we shall show in Equation 3.11.
57
(3.11) VNN=?
?
?
???
Z?Z?
r??
Before demonstrating the molecular Hartree-Fock system, we shall apply another 
assumption: the Born-Oppenheimer Approximation, where we assume that the 
positions of the nuclei are fixed compared to the mobile electron cloud, thereby 
removing the fourth term from Equation 3.10 which measures the kinetic energy of 
the nuclei.  The remainder is divisible into two parts, the first three terms, which are 
the electronic Hamiltonian shown in Equation 3.12 below:
(3.12) ?Hel=? ?
2
2m?i ?i
2??
?
?
i=1
n Z
?e
'2
ri ??i=1
n ?
j?i
e'2
rij
The Fock Operator is then the total energy found from the sum of the electronic 
Hamiltonian and the nuclear repulsion energy, as presented in Equation 3.13:
(3.13) ?F= ?Hel?VNN=? ?
2
2m?i ?i
2??
?
?
i=1
n Z
?e
' 2
ri ??i=1
n ?
j?i
e'2
rij ??? ????
Z?Z?
r??
Our expected Hartree-Fock energy, EHF is then the expectation value of these two 
elements over the electronic wavefunction.  Presuming a doubly occupied 
wavefunction with closed shells D, it appears as shown below in Equation 3.14, with 
the different parts of the expectation values factored out into separate units:
58
(3.14) EHF=?D??F?D?=?D? ?Hel?VNN?D?=2?
i=1
n/2
hi??
i=1
n/2 ?
j=1
n/2
?2Jij?Kij??VNN
On the right, we introduce some notation to separate out the different calculation 
types necessary to calculate the energy of the system.  The first term,  hi , has the parts 
of the energy which only depend on one electron, seen below in Equation 3.15 for the 
first electron (1).
(3.15) hi=??i?1???12?i2??
?
Z?
r1???i?1??
Then Jij is the repulsion between the a pair of arbitrary electons (1) and (2), and the Kij 
is the exchange stabilization gained from switching the same two electrons with each 
other.   Jij, and Kij as shown below in Equations 3.16, and 3.17 respectively.
(3.16) Jij=??i?1??j?2?? 1r
12
??i?1??j?2??
(3.17) Kij=??i?1??j?2?? 1r
12
??j?1??k?2??
This system of equations is now solved in the same way as the original atomic 
Hartree-Fock system which we previously showed, with the exception of the 
additional complexity introduced by the presence of the exchange energies.
59
Now we fix the wavefunctions of all but one of the electrons in our trial wavefunction 
?, and beginning with the first electron minimize the energy ? of that single electron 
with the one-electron Fock operator in a single electron Schrodinger equation (shown 
below as Equation 3.18) formatted in the same pattern as the complete Schrodinger 
equation shown in Equation 3.2.
(3.18) ?F?1??i?1?=?i?1??i?1?
When we expand the trial single electron wavefunction ?i under a linear basis set of 
eigenfunctions of the Fock operator ?, as shown in Equation 3.19,
(3.19) ?i=?k cki?k
Then we can substitute this in the Fock Schrodinger equation, Equation 3.18, to gain 
the following system of linear equations as shown in Equation 3.20, which simplifies 
because the Fock operator is linear to the Fock operator applied to the basis set 
underneath the original trial wavefunction while remaining equal to the energy 
eigenvalue.
(3.20) ?F?i= ?F?k cki?k=?k cki ?F?k=?i?k cki?k
This can then be rearranged by subtracting the right side of Equation 3.20 from the 
final simplification of the left, which appears in the same form, as Equation 3.21, 
creating a system of linear equations:
60
(3.21) ?k cki?F jk??iS jk?=0
Where Fjk and Sjk are the Fock operator applied to basis functions ?j and ?k, and Sjk is 
the overlap integral between the two basis functions ?j and ?k, as shown below in 
Equations 3.22 and 3.23.
(3.22) F jk=??j??F??k?
(3.23) Sjk=??j??k?
This system of equations can then be written compactly as Equation 3.24, shown for 
the first two basis functions explicitly:
(3.24) det?F jk??iS jk?=?
F11??iS11 F21??iS21 ?
F12??iS12 F22??iS22 ?
? ? ??
=0
The solution of this system of linear equations for the minimum ?i yields the 
individual coefficients cij for a particular electron I, and the self-consistent field 
process can be repeated in the manner presented previously until the electron 
geometries are no longer changing, leaving them at the energy minima and the energy 
at a minimum as well. 
At this point, if the nuclear geometry is at the equilibrium geometry for the system, 
our work is done and we have the Hartree-Fock energy.
To do a geometry optimization procedure, we need to take the derivative of the final 
61
energy with respect to the nuclear coordinates and update the nuclear geometies in a 
fixed average electron cloud, using the assumption that the electrons move fast 
enough that the nuclei only see their average positions.  The cycle of calculating an 
updated electron wavefunction then repeats using the same process until both sets of 
geometries have reached stable final coordinates, at which point our Hartree-Fock 
energy calculation is complete.
3.2.3 ? Background on Basis Set Selection
Choice of Basis Functions, Slater-Type Orbitals versus Gaussian-Type Basis-
Sets
Initial calculations used Slater orbitals[6], which corresponded closely to the expected 
shape of the electron distribution.  This allowed for small and very quickly 
converging basis sets, but also caused another problem.
Because of the form of a Slater orbital (Equation 3.25 below), it is difficult or 
impossible to do analytical integration for part of the Hartree-Fock solution (as the 
orbital overlap integral has a product of two of these functions and is integrated over 
the distance between the two centers)[7].
(3.25) R(r) = rn-1 e-? r (r = radial distance to the nucleus)
62
This means that for models using Slater orbitals in their basis, although the number of 
actual integrals needed may be small, the amount of work needed to evaluate the 
functions would be quite sizable, because the two-electron overlap integrals are 
impossible to solve analytically with the Slater basis functions. However, this 
problem was overcome by a clever trick:
Using a less efficient for representing the geometry but more efficient for 
calculation Gaussian basis set rather than one with basis functions more similar to 
actual electron cloud geometries.
Initially, S. F. Boys (b.1911-d.1972) suggested and worked on forming a groundwork 
of analytical work that showed a Gaussian approach would be effective in doing 
calculations on molecular systems[57].  Later, John Pople (b.1925-d.2004) was 
integral in implementing a system which used Gaussian functions to form its Slater 
orbital basis set as well[8].  As Gaussian functions do not have the correct kind of 
radial dropoff this meant that many more basis functions were required to achieve the 
same quality of basis functions.  But at the same time, because the overlap integral 
could be done analytically, the problem was overall much simpler computationally 
overall. 
Because of the linear algebra methods used in the basis set solution, their properties 
apply whenever the methods are used, so the difference in function types used in the 
63
expansions would not make any difference if the basis sets were large enough that the 
set could represent the solutions to the Schrodinger equation.  As things turned out, 
the larger Gaussian basis sets were both more efficient (due to the analytical 
integration possible) even though more functions were required to reach the same 
level of quality in the results.
However, the current path of research has come full circle, as the use of higher level 
methods which scale rapidly towards impossibility as the basis set is increased in size, 
now the ease of computing numerical integrals is looking like it may eventually be 
more efficient at attaining accuracy than doing analytical analysis on a Gaussian 
basis.
3.3 ? An Overview of Computational Chemistry Methods
Methods which we used included the following:
? Hartree Fock (HF) (previously discussed)
? Moller-Plesset Perturbation Theory (MP2)
? CCSD (coupled cluster single and double excitations)
? CCSD(T) (single, double, and some triple excitations)
? Density-functional Theory (used with ADF), and
? Hybrid-Density Functional Theory (B3LYP)
64
? And Model Chemistries such as CBS-QB3 (G2 and G3 are other examples)
? Solvation Methods
We did a number of calculations with Gaussian 03[9] implementing the methods of 
Hartree-Fock (HF)[5], Moller-Plesset perturbation theory (MP2)[10, 11], CCSD[12] 
and CCSD(T)[13], B3LYP[14], and a number of model chemistry calculations using 
CBS-QB3[15, 16].  We also did a series of density-functional theory calculations 
using ADF[17-19] to find NMR chemical shifts[20-24].  We will discuss each of the 
methods below.
Hartree-Fock (HF)
As previously discussed, the Hartree-Fock method (HF)[5] is a variational theory 
solution of the Schrodinger equation[1].  It originally was implemented with Slater-
type orbitals[6] but was later improved by Pople et al. with a Gaussian basis set 
implementation[8].  The change in basis set allowed for an analytical solution to the 
overlap integrals between the orbitals.
HF is a computationally light method that scales proportional to the fourth power of 
the number of basis functions in the calculation, or N4.  A doubling in the number of 
basis functions would increase the length of the calculation by a factor of 16.  Other 
65
methods scale at different rates, which can make the computational cost too 
expensive for a typical group as the size of the system grows.
Although it is faster than the soon-to-be discussed higher level methods, the Hartree-
Fock method leaves somewhat to be desired when dealing with hydrogen-bonding 
interactions, and the bonds it models are generally stiffer than experimentally 
measured.  The cause for this can easily be seen when considering the HF molecular 
orbitals involved in a bond dissociation, where the model's results are completely 
incorrect.  The dissociation of HF has an electron which ends up divided equally 
between the atoms after separation, which is nonphysical.
Moller-Plesset Perturbation Theory (MP2)
Moller-Plesset Perturbation Theory[10] is an approach which uses perturbation theory 
to improve the Hartree-Fock results.  A first order Moller-Plesset calculation is 
equivalent to a Hartree-Fock calculation.  MP2[11] consists of a base Hartree-Fock 
calculation with an additional term which adds some of the correlation energy.  There 
are a series of MP methods which include successively more correlation energy 
terms.  MP2 contains one term beyond HF, while MP3[25] and MP4[26] contain third 
and fourth order terms as well.  The MP2 method is slower than HF, scaling at N5 
with the complexity of the calculation.
66
Density-functional Theory (used here with ADF)
Density-functional theory[27] is an alternate way of treating the bonding problem. 
As opposed to the HF approach of modeling inter-electron interactions directly, DFT 
operates by modeling the energy directly based upon the spatial electron distribution. 
This method while being much more efficient (scaling directly with the volume of the 
system being investigated) also has some shortcomings because, in that one electron 
density coordinate system, means of finding the precise correlation energy does not 
yet exist.
The implementation of DFT which we used in ADF works by filling a predefined 
space with electron probability to a specific resolution instead of placing basis 
functions on the atoms in the molecules.  This approach allows for a lot of parallelism 
in the calculations, which can take increasing advantages of current computer 
development trends.
We have used DFT directly in a few cases, in particular in calculating NMR 
shielding[21, 22, 24] trends for HgCl compounds with the ADF computational 
package[19].
Hybrid-Density Functional Theory (B3LYP)
67
B3LYP[14] is a combination of a DFT and HF based model which has a similar 
accuracy as the MP2 method, but at much less computational cost.  It works by 
adding the exchange energy component of the Hartree Fock system to an energy 
calculated by a DFT method.  Enough data has been collected from the B3LYP 
method to confirm this, but our observed errors in the B3LYP method's energies have 
a tendency not to have an obvious trend of being either low or high, appearing instead 
more randomly distributed.
CCSD (coupled cluster single and double excitations)
and  CCSD(T) (single, double, and some triple excitations)
Coupled Cluster theory is another higher level method.
In CCSD[12] the calculation includes contributions from both single and double 
excitations of the electrons in the system.  The energies calculated with CCSD are 
generally higher in accuracy than MP2 calculations, but the computational cost is 
much  greater.   CCSD(T)[13] also includes  some  triple  excitations,  but is 
computationally expensive enough (it scales at N7 with problem size) that it is 
difficult to calculate geometries under the method, although single point CCSD(T) 
calculations are good for confirming that the CCSD results are stable, or adding 
energy corrections to other calculations.  We often use CCSD and CCSD(T) 
68
calculations to demonstrate that our results at lower levels such as MP2 or B3LYP are 
stable.
So to summarize, Hartree Fock theory (HF) scales at N4, MP2 at N5, and CCSD at N7.
Model Chemistries: CBS-QB3 (G2 and G3 are other examples)
Model chemistry methods such as Gaussian-2 (G2)[28], G3[29], or the Complete 
Basis Set method (we used CBS-QB3[15, 16]) are intended to provide the chemist 
with a general-purpose method for computational assistance.  Each method is 
comprised of a series of calculations with fixed basis sets and methods which, when 
combined,  yield  results  with  well-characterized  properties  across  a  set  of 
experimental reference data.  Though often computationally expensive, they are very 
useful in the practical arena as they are designed to provide high quality results in a 
large variety of situations.
The G2 and G3 methods were developed by Gaussian and were tested on various 
reference sets of compounds[30-34] which were well known experimentally to 
confirm that the results have an very good average error ? on the order of one or two 
kcal/mol.
69
The CBS-QB3 method was designed in particular to tackle the problem of limited 
basis sets by doing a series of calculations starting with an B3LYP geometry 
optimization and frequency calculation using the CBSB7 basis set.  After this, a series 
of single point calculations are done at the final geometry, starting with the highest 
level used, a CCSD(T) calculation, with the smallest electron basis set, a 6-31+G(d') 
basis.  This calculation is followed by a more calculations at lower levels under larger 
basis sets, starting with an MP4SDQ/CBSB4 calculation and ending with an 
MP2/CBSB3 calculation.  Finally, the results are combined to yield the model 
chemistry result.
The CBS-QB3 method is in common use today, and has been assessed as similar in 
quality to the Gaussian model chemistry methods (G2 and G3)[15, 35, 36] with less 
computational cost.  For this reason, and because of its ease of use, we made certain 
to use the CBS-QB3 method extensively in our acidity calculations discussed in 
Chapters 5 through 7, so that reproducing similar calculations would be accessible to 
the novice computational chemist.
Solvation Methods
There are a variety of ways to model solvation effects in theoretical chemistry.
70
In this work, we concentrated on two main ones: explicit hydration, where additional 
H2O molecules are added to the calculation and optimized along with the rest of the 
system, and CPCM hydration[37-39], a method where the molecule or system of 
interest is placed in a spherical cavity surrounded by a dielectric to model bulk 
solvation. 
The main difference between these two methods is that in the former case, 
computational costs grow very rapidly, and solving for reasonable and reproducible 
final geometries can become a consideration.  With the second method, there is no 
opportunity for solute-solvent interactions such as hydrogen-bonding, which often 
affects results such as spectra (see Chapter 10, on myo-inositol hexakis phosphate, for 
an example of this).
3.4 ? An Overview of Basis Sets
Key information about basis sets are:
? Basis set essentials
? Diffuse and Polarization functions[40]
? 6-31G[41, 42] and 6-311G(d,p)[43]
? CEP-type basis sets[44-46] 
? cc-pVxZ basis sets[47-49] and complete basis set extrapolation
71
? CBSB7 basis set[16]
? custom basis set functions
? basis set overlap corrections (counterpoise corrections)
Basis set essentials
As we mentioned before, basis sets are used to approximate the ideal of a continuous 
probability distribution functions which would give the geometry of the electron 
cloud surrounding our nuclei.  An infinite or complete basis set would allow the 
representation of any probability distribution, but due to computational limits we are 
restricted to calculating energetics with finite basis sets.  Some methods, like the 
CBS-QB3 model chemistry method, contain a complete basis set extrapolation 
(although this can also be done separate from the model chemistry; we did a complete 
basis set extrapolation in another calculations by hand) that attempts to take care of 
the problems that a limited basis set introduces.
Diffuse and Polarization functions
Most small-scale basis sets suffer from a problem where they become dramatically 
worse when dealing with situations with polarized bonds (between atoms of different 
electronegativity, the electron geometry is distorted towards the more electronegative 
atom) or with ionic compounds (with negatively charged ones especially, because the 
72
extra electrons make the cloud much larger than normal).  This is where diffuse and 
polarization functions can help an inadequate basis set become adequate.
Diffuse functions are basis functions with small exponents, making the functions very 
large.  They are most useful in the case of the anionic compounds[50, 51], because 
they allow the basis set to better represent electron probability distributions that range 
farther from the nuclei in the system than expected by the basis sets, which were 
mostly developed for neutral species.
A different problem exists for cations, where the basis functions have a similar error 
in estimation, only the amount of electron cloud contraction in the cation is less 
because of repulsion from the inner electrons and can be dealt with in gaussian bases 
by slewing the electrons towards the inner gaussian functions used to form the basis. 
This cannot be done for the anions because the size change is much more dramatic.
Polarization functions cover the other case, where the electron cloud is distorted 
further from spherical symmetry around a nucleus than is usual for the basis set.  By 
adding polarization functions, systems which have polar or ionic internal interactions 
(such as when we calculate the properties of ion/counterion pairs), can be more 
accurately calculated.
6-31G and 6-311G(d,p)
73
This type of basis set, currently called a Pople basis set, was based on concepts 
originally developed by Boys and presented in 1950[59].  The set names list the 
number of Gaussian basis functions used to form each orbital in the basis set, with 6 
Gaussians combined to form each core orbital basis function and multiple basis 
functions for the valence electrons.
For 6-31G[41, 42] there are two basis functions per valence electron, one made of 3 
Gaussian distributions added together and one made with a single Gaussian function. 
This type of basis set is called a split-valence basis set because the valence orbital's 
shape can be optimized by adjusting the relative weights of the multiple basis 
functions in the valence orbitals during the ab-initio step.
The additional (d,p) in the second example, 6-311G(d,p) has 3 functions per valence 
electron rather than two as in 6-31G.  It also adds polarization functions to the s and p 
orbitals to further improve the quality of the basis.  The s type orbital receives an 
additional p-type basis function and the p orbital receives a d-type orbital.
CEP basis sets
The CEP basis sets, CEP-31G and CEP-121G[44-46], are Relativistic Compact 
Effective Potential basis sets.  They replace central core electrons by a single 
potential which includes relativistic effects, leaving the valence electrons to be 
74
calculated normally by the theory chosen in the calculation.  The basis sets were 
developed to use a reduced number of basis functions but provide the same accuracy 
as previously developed numerical basis sets.  We used these basis sets extensively in 
our calculations with mercury to save calculation time and allow us to examine larger 
systems which would otherwise be computationally out of reach.
cc-pVxZ basis sets and complete basis set extrapolation
The cc- basis sets, concieved by Dunning, T.H. and later Petersen et al.[47-49], were 
designed specifically to be correlation-consistent across the different basis set sizes, 
which means that the energies calculated with each one would be proportional to the 
energy as calculated with a complete basis set (or with numerical methods to 
sufficient accuracy).  This property allows calculations with a series of cc-pV*Z basis 
sets (they appear in a series from cc-pVDZ, cc-pVTZ, cc-pVQZ, cc-pV5Z) on the 
same system to be combined to easily estimate the results which would appear from 
the complete basis set in a reproducible manner.
An extrapolation function[52] is shown in Equation 3.26 below, and an example of its 
use appears in Chapter 4 applied to an HgCl2 calculation.
(3.26) En = ECBS + An-3
75
CBSB7 basis sets
Similarly, a basis set was customized by Petersen's group for a model chemistry 
which they designed called CBS-QB3[15, 16], which does a basis set extrapolation as 
part of its procedure.  The CBSB7[16] basis sets are not necessarily needed outside of 
the CBS-QB3 method, but they are useful when finding system geometries especially 
in solvated systems, where the CBS-QB3 method sometimes has difficulties 
determining a minimum in the potential energy surface for the geometry during its 
B3LYP optimization step.
custom basis set functions
Its quite possible to add custom functions to a basis set, or to define one from scratch 
entirely, but doing so goes beyond the scope of this paper.  In some of our 
calculations, we added additional basis set functions to the basis sets used to assist in 
the quality of the calculations.  This is discussed in the appropriate sections.
basis set overlap corrections (counterpoise corrections)
Inadequate basis sets can introduce an additional error when there are several atoms 
close together.  The additional basis set coverage caused by the presence of the 
additional atoms can is called basis set superposition error[53], and if the basis set 
76
used was too small, the extra functions significantly improve the possible electron 
cloud geometries that the simulation can access, causing an artificial lowering of the 
calculated energy for the system.
This can be corrected in simpler bonding situations (such as diatomic bonding) by 
applying a counterpoise correction: introducing a ?ghost? atom consisting solely of 
basis functions without an actual nucleus instead of one of the bonding atoms.  By 
substituting a ghost atom for an atom in a system, the additional energy stabilization 
caused by its extra basis functions can be determined by comparison with a 
calculation without the ghost atom, and this correction can be applied to the final 
result.  This may introduce its own problems if there are many basis functions which 
would be fully occupied by the ghost atom's omitted electrons, by overestimating the 
correction for artificial stabilization.
This approach is most useful on the edge cases where the size of the calculation 
combined with the choice of method forces the use of a smaller basis set than would 
be ideal.  In normal cases, it is best to increase the basis set size until adding 
additional basis functions does not significantly affect the final energy, and this is 
what we did for the most part.
3.5 ? The Importance of Quality
77
What is important in quality?  Calculations can have varying levels of quality, going 
from answers which provide qualitative answers (H3AsO4 is more acidic than 
H3AsO3) to quantitative predictions (H3AsO4 is 6.9 pKa units (more) acidic than 
H3AsO3).  As the results of most calculations are defined to a high level of precision, 
but may or may not correspond closely with experimental measurements. 
The causes are often unclear, but often fall into several broad categories.
In some cases, the experimental measurements make assumptions which can be 
demonstrated to be incorrect by the theory, such as in a calculation of oxidation 
energetics for gas phase Hg0 [54], where the species that had initially been assumed to 
be the primary mercury compound in the gaseous system was not clearly identified. 
A series of calculations showed that the assumed reaction was not predicted to be 
energetically favorable under gaseous conditions, and set forward another species 
which fit the observed experimental data much better.
Then there are cases where there are large effects which are difficult to treat with 
theory, such as quantitatively modeling the stabilization of ions in bulk water.[55]  In 
these cases, the theory can often produce a lot of quite valuable information about 
spectra and other properties of the system, but can not necessarily be used to predict 
reaction energetics to high accuracy.  Although some of the assumptions which we 
78
make to use our methods are less than perfect, there is still a lot of good data to be 
seen in the results which we calculate.
Finally, there are the cases which fall somewhere in between, where the experimental 
data is unavailable or unclear and, at the same time, we are pushing the theory in 
some fashion.  We shall seek to explore some of these cases in our study of solvated 
mercury compounds.
Model chemistry methods like CBS-QB3, G2, or G3 have been designed in order to 
produce a predictable level of error in normal situations.  The term "Model 
Chemistry" has to do with the fact that the methods can be used as a model for 
predicting experimental chemistry results, in particular, well characterized gas 
dissociation energies from a standardized test set.  In exchange for possibly requiring 
more computation than is necessary for solving some simpler conditions, the methods 
have been tested over a variety of compounds and the approach explained in detail 
and justified for general use.  They also have an advantage over more hands-on 
methods in that they may be used by physical chemists who are not necessarily 
dedicated theoretical chemists.  Therefore, we considered this type of approach, as 
embodied by CBS-QB3, in many cases.
3.6 ? Approaches to Verifying Quality
79
There are a few ways by which we confirm the quality of a calculation.
By using higher level methods which have been observed to provide more stable, 
better and higher quality results we can show by comparison that a lower, more 
computationally easy method has reached a stable answer as well.  This approach 
requires a knowledge of which assumptions are most correct in the tree of methods 
available to the researcher, so assistance from a dedicated theoretician in constructing 
a plan would be invaluable in this part of the process even for a stand-alone lab.
For systems in the sizes which we used here, method wise we usually started with an 
HF or B3LYP calculation to reach initial geometries from starting guesses or 
molecular mechanics models, followed by MP2 and CCSD (or CCSD(T) calculations, 
for the smaller systems) could show that the total energy and our measurements of 
interest had stabilized in one of the lower level steps.
We often do a variety of calculations on each of our compounds of interest at 
differing levels of theory to get a feel for the level of theory required to get accurate 
results.   For example, as seen in Chapters 5 through 7, we used several different 
methods to deal with hydration including CPCM,  counterions, and explicit hydration 
to estimate solvation effects on a series of polyprotic acids, comparing the results.
80
Alternatively, we can use two similar in quality, but different in approach methods to 
check on the other's result.  If both schema yield the same final answer for a 
dissociation, for example, it makes us confident that that level of theory is sufficient 
to treat the problem.  An example of this might be our calculations using B3LYP and 
MP2 methods in parallel to explore the behavior of the HClOx compounds discussed 
in Chapter 7.
We can apply this same approach to our choice of basis set as well.  By doing a set of 
calculations with a normally sized basis, followed by a few with a much larger basis, 
we can confirm that the results with the extra large basis set are equivalent to the 
smaller set, and this gives us confidence that the results have stabilized to the extent 
that our first set was sufficient to represent the situation we are simulating. 
Another factor in our approach is the ordering of the calculations.  While it is not very 
expensive to do hybrid density-functional method calculations such as B3LYP, it is 
often the case that a B3LYP optimization takes much longer on its own than a less 
correct Hartree-Fock optimization followed by a B3LYP optimization from the final 
geometry.  Even if a method has known shortcomings it can be a vital part of a good 
calculation.  It is like the story of the lensgrinder who said that it is faster to make a 
three inch lens then a six inch lens than make a six inch lens right off.
81
We also used a similar approach when doing our CBS-QB3 calculations, which start 
out with a B3LYP optimization.  We have observed that an initial HF or MP2 
optimization of our compound followed by CBS-QB3 requires much less human 
intervention to reach a stable optimized geometry and we would therefore suggest 
that this approach of preliminary optimization may be a more efficient use of time 
and resources than direct application of CBS-QB3.
This method of starting with a medium or small-scale calculation and then 
bootstrapping the results to reach a higher-level answer more efficently is common in 
applied computational chemistry.  Another tool is to do a calculation a few times 
using different methods and compare the differences in the results[9] For example, 
one can, when constructing a spectra, conduct anharmonic and harmonic frequency 
calculations at a lower level of theory, and compute correction factors from those to 
apply to a higher-level, simpler calculation of harmonic frequencies.  This 
bootstrapping approach would yield results with higher quality results with less 
calculation time than attempting a possibly impossible anharmonic calculation under 
the higher-level model[56].
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90
Chapter 4: Mercury Chloride Free energies in solution: 
equilibrium constants from theoretical calculations at the 
CCSD(T) level and above
A series of calculations on HgClx compounds is conducted using CCSD(T) and 
correlation-consistent basis sets in the gas phase, and combined with hydration free 
energies taken at HF/CEP-121G with the CPCM solvation model.  NMR shieldings 
calculated by ADF are also explored for the same series.
4.1 Introduction
As previously discussed, Hg2+ and its compounds, often referred to as Reactive 
Gaseous Mercury (RGM) in atmospherics studies[1], are of interest to us because of 
the hazards seen from methylmercury compounds, which have been observed to be 
converted from other sources of dissolved mercury by sulfur reducing bacteria.
Mercury chloride compounds have been studied before in solution, but the 
experimental data on hand is from many years ago[2].  An important sink for gaseous 
mercury is the world's oceans, and these have a relatively high concentration of salt, 
which could easily interact with any dissolved cationic mercury.
91
Therefore, we began our calculations by investigating the behavior of chlorinated 
mercury compounds (Hg2+, HgCl+, HgCl2, HgCl3-, and HgCl4-2), followed by 
compounds formed from the other halides expected to be in seawater (F-, Br- and, I-).
4.2 Methods
Gaussian 03[3], a computer quantum chemistry package, was used to conduct the 
calculations presented in this chapter.
In each case we attempted to follow a systematic series of steps when conducting our 
calculations.  We shall describe those steps here.  Although in each stage we used 
different quantum chemical theories to do the calculations, the basis sets used most 
often were CEP-31G and CEP-121G.  Because of prior experience, we expected the 
results from CEP-121G to be higher quality than the others, and for both basis sets we 
included additional diffuse functions to improve the modeling of the anionic forms 
after reviewing our initial calculations without them.  These additional functions for 
heavy atoms (Hg, halogens, oxygen, etc.) are described as follows in Table 4.1 for 
each of the atom types:
Atoms Function Type Coefficient
Hg F 0.486
C, S, O D 0.700
F, Cl, Br, I D 0.650
Table 4.1: Extra diffuse functions used in the calculations conducted in this chapter.
92
Initially, Hartree-Fock geometry optimization and vibrational frequency calculations 
(for confirming the final geometries were not at saddle points on the potential energy 
surface) were conducted for each species.  These were for the most part successful. 
As the primary reason for these calculations was to determine geometries for the 
other methods, the results of most of the HF calculations are not reported here except 
as noted below.
B3LYP geometry optimization and vibrational frequency calculations were slightly 
less successful than the HF calculations due to difficulties getting all of the 
geometries to converge successfully in a timely manner.  We observed some 
compounds oscillating in loops on the potential energy surface, and others where the 
geometry changed so slowly that convergence was not attained in a reasonable length 
of time.  In the majority of cases we eventually did reach optimized geometries, 
however, though the occasional troublesome anion remained unsolved.  In particular, 
this optimization problem prevented us from reporting data for reactions involving 
the HgCl42- species.
Finally, CCSD geometry optimization and vibrational frequency calculations were 
taken  from  the  HF  geometries.   Although  the  CCSD  calculations  were 
computationally expensive, these calculations were completed successfully for most 
93
of the compounds and the results are presented below and compared with the B3LYP 
results.
The largest calculations which we ran used the CCSD(T) method, which was 
combined with multiple Correlation Consistent basis sets from the cc-pV*Z series to 
do energetics calculations at the CCSD geometries.
4.2.1 Basis Set Selection
The Gaussian 03 package[3] included these basis sets for the Cl-, and Br- calculations, 
while the Hg and I- basis sets used were obtained from the Extensible Computational 
Chemistry Environment Basis Set Database, Version 02/25/044.
CCSD(T) calculations were completed for the cc-pVDZ basis, and up to the triply 
substituted species for Cl, Br, and I anions.  In the case of the cc-pVTZ basis, the Cl 
calculation was also finished to the triply substituted HgCl3-.  For the heavier systems 
with Br and I, the results were somewhat limited, but included both of the singly 
substituted ions.
The Cl- calculations were also done up to HgCl2 with cc-aug-pVDZ and cc-aug-
pVTZ, correlation consistent basis sets augmented with extra basis functions to 
improve accuracy for the ionic species in the calculation.
4As developed and distributed by the Molecular Science Computing Facility, Environmental and Molecular Sciences Laboratory 
which is part of the Pacific Northwest Laboratory, P.O. Box 999, Richland, Washington 99352, USA, and funded by the U.S. 
Department of Energy. (The Pacific Northwest Laboratory is a multi-program laboratory operated by Battelle Memorial Institute 
for the U.S. Department of Energy under contract DE-AC06-76RLO 1830. Contact Karen Schuchardt for further information.)
94
4.2.2 Complete Basis Set Extrapolation
With the results from the CCSD(T) calculations it was possible to extrapolate from 
the cc-pVDZ and cc-pVTZ results using a complete basis set extrapolation function 
initially  developed by Halkier, et al.[4] and applied to CCSD(T) shortly 
afterwards[5], which appears as Equation (1) below.  As expected, with the more 
extensive aug-cc-pVDZ/aug-cc-pVTZ basis we see a lower raw energy for the Hg2+ 
cation as well as the other species which were looked at with the approach, Cl-, HgCl+ 
and HgCl2.
The complete basis set energy ECBS can be extrapolated from lower level 
calculations with correlation consistent basis sets by the following method shown in 
Equation 4.1, 4.2, and 4.3, where ECBS is the complete basis set energy, En is the 
energy calculated with the corresponding basis set (cc-pVDZ would have n=2, cc-
pVTZ would have n=3), and A is a factor which depends on which basis sets are 
being used in the calculation.
(4.1) En = ECBS + An-3, or
(4.2) ECBS = En ? An-3, and
(substituting n=2 and n=3 for cc-pVDZ and cc-pVTZ, and solving A and then for 
ECBS)
(4.3) ECBS = (27/19)E3 ? (8/19)E2
95
The solvation model used throughout this project was the CPCM polarizable 
continuum method.  The energy of solvation for each compound at its final gas phase 
geometry was calculated, and this stabilizing factor added to the final Gibbs Free 
Energy when calculating the change in Gibbs Free Energy for each formation reaction 
to estimate the solvation energy in the solvated phase.
Also examined a system with explicitly solvated clusters of water molecules, to 
compare the energetics for the following reaction:
Hg2+ + Cl-  ? HgCl+ + H2O
The Hg2+ was solvated with six water molecules, and the HgCl+ with five.  We then 
calculated the energy using both Hartree-Fock and MP2 approaches.
In future chapters, later calculations including ones with hydration energies calculated 
during the optimization phases shall be presented.  The energies determined from that 
direct approach will then be compared to energies which were found (additively as 
described in this chapter) at that point.
4.3 Results and Discussion
96
In each case we see that the CPCM stabilization calculated is dramatically larger for 
the more charged and smaller species.  This is reasonable, because the CPCM method 
makes a sequestered shell in a continuous dielectric around the compound of interest, 
and a smaller shell will lead to a much stronger electronic stabilization because of the 
reduced area that the charge is interacting over.
Therefore, we see that the CPCM hydration energy for Cl- and HgCl3- are 
significantly different; -76.55 kcal/mol for Cl- and only 47.26 kcal/mol for HgCl3-. 
We see a similar, but even larger difference between the calculated hydration energies 
for Hg2+ and HgCl42-.  There, the energy for Hg2+ is -407.17 kcal/mol, but the 
stabilization for HgCl42-, which is much larger of a species, is -160.89 kcal/mol.  This 
is on the same scale as HgCl+, which has a CPCM stabilization energy of -139.85 
kcal/mol.
Comparing the calculations done with CCSD and B3LYP is instructive as well.  The 
CCSD calculations were done with two different basis sets, CEP-31G+ and CEP-
121G+.  The calculation with the larger basis shows a difference on the order of 3 
hundredths of Hartrees for species including the Chlorine atoms.  This difference is 
approximately 19 kcal/mol (627.5 Hartrees are approximately 1 kcal/mol), but it is 
present in all of the cases so the difference doesn't affect the changes in energy for the 
chlorination reactions.
97
For the solvated cluster, we see a more dramatic result from updating the basis set 
used in the calculation.  The total effect on the stability of the clusters is 
approximately 0.1 Hartrees or 62 kcal/mol.  This dramatic change in energy is 
probably due to the additional wavefunctions on the six water molecules.  The 
difference for the single water molecule is approximately 0.01 Hartrees going 
between the CEP-31G+ basis set and the CEP-121G+ basis set.
This accounts for about half of the energy difference between the free Hg2+ and the 
singly solvated group Hg2+ . 6H2O between the two basis sets.  The larger basis has an 
additional stabilization of 0.07 Hartrees, or approximately 44 kcal/mol when the 
system is calculated under HF conditions.  Under the MP2 method, the energy 
difference caused by the change in basis is only 2 kcal/mol, however.
From the previous measurements, we can find the reaction energetics for each of the 
following tabulated reactions, shown below in Table 4.2.  This table shows the 
difference in solvation stabilization between the products and the reactants.  We see 
here that, as we might expect, that multiple smaller and more charged species are 
stabilized more than the single product molecules except in the final case of HgCl42-.
Reaction CPCM Stabilization Energy (kcal/mol)
Hg2+ + Cl- ?  HgCl+ +343.87
HgCl+ + Cl- ?  HgCl2 +195.72
HgCl2 + Cl- ?  HgCl3- +49.97
HgCl3- + Cl- ?  HgCl42- -37.08
Table 4.2: Stabilization Energies for Successive Cl- addition to Hg2+
98
We see in each case that the solvation stabilization from the gas phase geometries of 
each compound taken together yields a non-favorable result for the reactions except 
in the case of the final one where the effect is favorable due to the high charge of the 
HgCl42-.  
Reaction ?Grxn 
Energy 
(Hartrees
)
?Grxn 
Energy 
(kcal/mol)
CPCM 
Stabilizatio
n  Energy 
(kcal/mol)
Gas  phase 
geom.  + 
stabilizatio
n 
(kcal/mol) 
?Grxn
Hg2+ + Cl- ?  HgCl+ -.630985 -395.94 +343.87 -52.07
HgCl+ + Cl- ?  HgCl2 -.356220 -223.53 +195.72 -27.81
HgCl2 + Cl- ?  HgCl3- -.075280 -47.23 +49.97 +2.74
HgCl3- + Cl- ?  HgCl42- .061599 38.65 -37.08 +1.57
Table 4.3: CCSD CEP-31G Energy Calculations for Successive Cl- addition
We report the results here to two decimal places in kcal/mol units.  The original 
Hartree units are reported to more decimals, but it is important to realize that the 
results of the calculations may be precise to this many decimal places, but we need to 
show their accuracy against known experimental data as these models contain many 
assumptions  which affect the quality of the results.  Care must be taken in assuming 
that reported experimental measurements are applicable to the conditions presumed in 
99
the calculation, as occasionally the interpretations of experimental measurements 
change as further research is conducted.
In the ab initio calculation with the smallest basis set we observe trends that stay in 
place throughout the other more computationally expensive methods.  Although in the 
gas phase all but the last Cl- addition are energetically favorable, the magnitudes of 
the favorability are comparable with the magnitudes of the hydration energy 
contributions.
In the gas phase, the results vary from the favorable -394.94 kcal/mol change in 
energy for the first chlorination to the unfavorable +38.65 kcal/mol energy change for 
the fourth chlorination.  This could be due to the instability of the Cl- ion in the gas 
phase, which makes forming the larger anion automatically favorable because it gives 
the extra electron more room.  This means that without solvation, HgCl3- would be the 
last compound formed with excess Cl- present under normal gas phase conditions. 
Any HgCl42- introduced "bare" into the gas phase would be predicted to dissociate 
into HgCl3- and Cl- ions by these results as well.
With the contributions from CPCM solvation, we see that the stabilization ranges 
from -52.07 kcal/mol favorable for the first chlorination to +2.74 kcal/mol 
unfavorable for the third.  To add an additional Cl- and reach HgCl42- would only 
require another +1.57 kcal/mol of energy.
100
This would presumably mean the most common species in aqueous solutions would 
be HgCl2, although with sufficient presence of Cl- anions one could push through and 
end up with HgCl42-.
Reaction ?Grxn 
Energy 
(Hartrees)
?Grxn 
Energy 
(kcal/mol)
CPCM 
Stabilizatio
n  Energy 
(kcal/mol)
?Grxn  Gas 
phase  geom. 
+ stabilization 
(kcal/mol)
Hg2+ + Cl- ?  HgCl+ -.625995 -392.81 +343.87 -48.94
HgCl+ + Cl- ?  HgCl2 -.352189 -221 +195.72 -25.28
HgCl2 + Cl- ?  HgCl3- -.072343 -45.40 +49.97 +4.57
HgCl3- + Cl- ?  HgCl42- .064210 +40.29 -37.08 +3.21
Table 4.4: CCSD CEP-121G+ Calculations for Successive Cl- addition
Conducting the same calculations with a larger CEP-121G+ basis set, we observe an 
identical trend in the results.  The most favorable step in the solvated system is the 
initial chlorination of Hg2+ to form HgCl+, and the least favorable is the conversion of 
HgCl2 to HgCl3-, and we see the same instance in the gas phase system of the larger 
anion in the HgCl2 to HgCl3- system being more favorable.
The most stable solvated species here is HgCl2.  Looking at the calculated energetics, 
this is where the benefits of chlorination in the gas phase system become significantly 
101
smaller.  While the first chlorination has a benefit of -392.81 kcal/mol, and the second 
has one of -221.00 kcal/mol, a difference about half the magnitude of the larger 
number, the difference in the second case between -221.00 kcal/mol and -45.40 
kcal/mol is one quarter of the magnitude of the larger figure.  At the same time, the 
magnitudes of the CPCM stabilization are shrinking by a similar amount.  It is the 
interaction between these two different rates of change that places the solvated HgCl2 
system in a balancing place, providing for a different most stable species in the gas 
phase and in solution.  In the gas phase, the ionic system would preferentially form 
HgCl3- rather than HgCl2, because the additional third chlorination is favorable by 
-45.40 kcal/mol against keeping the free Cl- ion separate from the cluster.
Reaction Energy 
(Hartrees)
?Grxn
Energy 
(kcal/mol) 
?Grxn
CPCM 
Stabilizatio
n  Energy 
(kcal/mol)
Gas  phase 
geom.  + 
stabilization 
(kcal/mol)
?Grxn
Hg2+ + Cl- ?  HgCl+ -.633918 -397.78 +343.87 -53.91
HgCl+ + Cl- ?  HgCl2 -.344079 -215.91 +195.72 -20.19
HgCl2 + Cl- ?  HgCl3- -.074486 -46.74 +49.97 +3.23
HgCl3- + Cl- ?  HgCl42- .064352 +40.38 -37.08 +3.30
Table 4.5: B3LYP CEP-121G+ Energy Calculations of Successive Cl- addition to 
Hg2+
102
The B3LYP method has previously been shown to provide reasonable results on the 
G2 test set, with average errors of 2.4 kcal/mol across the collection[6].  Its 
performance on this system is similar.  The gas phase results indicate that the HgCl2 
system will be chlorinated once more with the favorable energy -46.74 kcal/mol, but 
that this third chlorination is not favorable in the solvated system.  The energetics 
calculated here differ from the CCSD values by about 5 kcal/mol in the first two 
systems, but the differences between the results in the HgCl2 to HgCl3- chlorination 
and the HgCl3- to HgCl42- chlorination drop to the order of 1 kcal/mol for the former 
and less than 1 kcal/mol for the latter.
Once again in this method we see that the most stable HgClx species in the gas phase 
is HgCl3- and in the hydrated phase HgCl2.  The energies here required to form HgCl3- 
from HgCl2 and HgCl42- from HgCl3- are approximately equal in magnitude, though 
this theory calculates that the HgCl42- reaction is even less favorable (slightly) than 
HgCl3-.
In all three cases, however, the reaction is shown to show the same identical trends. 
As the B3LYP approach is significantly less computationally expensive than CCSD, 
this stability of the results both indicates that B3LYP is sufficient and that it has 
reached a stable answer.  We shall look at some further methods of calculation, 
however, to confirm this.
103
Method Energy (Hartrees) Energy (kcal/mol)
HF CEP-31G -.23827 -149.51
HF CEP-121G -.22884 -143.60
MP2 CEP-31G -.35487 -222.68
MP2 CEP-121G -.35307 -221.55
Table 4.6:  Comparison of methods in calculating the ?Grxn free energy of reaction for 
the explicitly Solvated System:  Hg2+ . 6H2O + Cl- ?  HgCl+ . 5H2O + H2O 
We see here that the change in free energy here is much lower than the gas phase 
reaction energy.  This is because the single solvation layer present in the system can 
account for a good percentage of the energy stabilization which we previously 
modeled with the CPCM method as adjusted to provide a solvation environment 
similar to water.
The cluster calculation done at HF and MP2 levels shows an energy which is in 
between the gas phase + CPCM stabilized energy calculation for the same reaction 
and the gas phase energies as expected.  The presence of even a single solvation layer 
of water molecules in a nanocluster demonstratably brought the total energy about 
180 kcal/mol closer in the MP2 case and 230 kcal/mol closer in the HF case to the 
stabilized energies found with the other approaches.  In the future, more explicit 
cluster calculations are clearly indicated for further exploration.
104
We also conducted a complete basis set extrapolation from CCSD(T) calculated 
energies, the results of which are shown in Table 4.7 and with supporting data in 
Table 4.10(a-e) below.
Reaction Energy 
(Hartrees)
Energy 
(kcal/mol)
CPCM 
Stabilization 
Energy 
(kcal/mol)
Gas Phase geom. 
+ stabilization
Hg2+ + Cl- ? 
HgCl+
-.6166878
-.6291525
-386.97
-394.79
+343.87 -43.10
-50.92
HgCl+ + Cl- 
?  HgCl2
-.34507
-.347219
-216.53
-217.88
+195.72 -20.81
-22.16
HgCl2 +  Cl- 
?  HgCl3-
-.06584 -41.31 +49.97 +8.66
Hg2+ + Br- ? 
HgBr+
-.6223905 -390.55
Table 4.7: Complete Basis Set CCSD(T) CBS model results for successive Cl- 
additions to Hg2+. Values on the first rows are with the standard cc-pV*Z basis sets, 
values beneath them were calculated with the augmented aug-cc-pV*Z basis sets.
This extrapolation lead us to observe the same trends as we did with the limited CEP-
31G and CEP-121G+ basis sets; the theoretical methods show that the formation of 
HgCl3- in the gas phase is a favorable reaction, while in the solvated system the last 
favorable chlorination is converting HgCl+ to HgCl2.  The main differences we see 
105
here when compared to the CCSD CEP-121G+ are that except for the HgCl+ 
formation with the augmented basis set shown on the bottom right of the first line of 
the table, the energetics calculated with this method are uniformly less favorable than 
the ones found with the CCSD CEP-121G+ method by around 4 kcal/mol.
We also have calculations for Hg2+ + Br- forming HgBr+.  This reaction is favorable 
on about the same level as the chlorination reaction.  Though the hydration energy 
stabilization for the HgBr system is not presented here, we would expect it to be a 
similar magnitude as the HgCl system, which would leave the first bromination 
favorable.  Complete basis set calculations on further HgBrx systems remain an open 
area of exploration for the future.
Further discussion of NMR calculations follows after Tables 8-10 below.
TABLES: Energies of Formation
HgCl compound series energy of formation (Gibbs Free Energy)
CCSD
(Hartrees)
B3LYP 
(Hartrees)
CPCM Hyd. ?G
CEP-31G + CEP-121G + CEP-121G+ (kcal/mol)
Cl- -14.873432 -14.887522 -14.987182 -76.55
Hg2+ -152.141721 -152.141721 -152.760699 -407.17
HgCl+ -167.646138 -167.655236 -168.381799 -139.85
HgCl2 -182.87579 -182.894947 -183.71306 -20.68
HgCl3- -197.824502 -197.854812 -198.774728 -47.26
HgCl42- -212.636335 -212.678124 -213.697558 -160.89
Table 4.8: HgCl Compound energies of formation
106
HgCl formation with explicit single water solvation layer
HF MP2
CEP-31G + CEP-121G + CEP-31G + CEP-121G +
Hg2+ 6H2O -253.347388 -253.4749919 -254.722269 -254.803736
Cl- -14.749066 -14.7366582 -14.877519 -14.890205
HgCl+ 5H2O -251.488878 -251.5852034 -252.929499 -253.007683
H2O -16.845846 -16.8552933 -17.025162 -17.039328
Table 4.9: Solvated Cluster Calculation energies of formation for HgCl system.
(These tables were used to calculated the energetics appearing above.)
Tables 4.10(a-e): Complete Basis Set Calculation on HgCl series: (Hg2+, Cl-, HgCl+, 
HgCl2, HgCl3-, HgCl42-) are presented below.
In Table 10a below we can see that the calculated CCSD(T) stabilization energy is 
much greater for Cl- than for Hg2+ with the correlation consistent basis sets used.  This 
is because the valence electrons used in calculating the stabilizations are not present 
in the case of the Hg2+.  The exercise of comparing the calculated energies for the Hg+ 
and Hg0 species to illustrate this effect is left for the reader.
107
CCSD(T) Calculated Energy, Hartrees
Basis set: Cl: cc-pV*Z, Hg: cc-pV*Z-PP
n=2 (pVDZ) n=3 (pVTZ) n=4 (pVQZ) n=5 (pV5Z)
Cl- -459.6895858 -459.7851298 -459.7851298
Hg2+ -151.9714435 -151.9714435 -152.2772938 -152.3289605
HgCl+ -612.2979752 -612.3792635 -612.7282043
HgCl2 -1072.348222 -1072.514083
HgCl3
-
-1532.120548 -1532.37006
HgCl4
2-
-1991.751637
Table 4.10(a): HgCl series cc-pV*Z basis calculated energies
CCSD(T) Calculated Energy, Hartrees
Basis set: Cl: aug-cc-pV*Z, Hg: aug-cc-pV*Z-PP
n=2 (pVDZ) n=3 (pVTZ) n=4 (pVQZ) n=5 (pV5Z)
Cl- -459.7383021 -459.8050418 -
459.8272536
-459.8342742
Hg2+ -151.9948455 -152.0227306 -
152.2823505
HgCl+ -612.351157 -612.4536232
HgCl2 -1072.427855 -1072.603270
HgCl3-
HgCl42-
Table 4.10(b): HgCl series aug-cc-pV*Z basis calculated energies
108
CCSD(T) Calculated Energy, Hartrees
Basis set: Br: cc-pV*Z, Hg: cc-pV*Z-PP
n=2 (pVDZ) n=3 (pVTZ) n=4 (pVQZ) n=5 (pV5Z)
Br- -2572.577998 -2572.771779
Hg2+ -151.9714435 -151.9714435 -152.2772938 -152.3289605
HgBr+ -2725.190374 -2725.371107 -2725.771581
HgBr2 -5298.111298 -5298.476037
HgBr3- -2725.190374
HgBr42
-
Table 4.10(c): HgBr series cc-pV*Z basis calculated energies
CCSD(T) Calculated Energy, Hartrees
Basis set: I: cc-pV*Z-PP, Hg: cc-pV*Z-PP
n=2 (pVDZ) n=3 (pVTZ) n=4 (pVQZ) N=5 (pV5Z)
I- -296.8548199 -296.9832305
Hg2+ -151.9714435 -151.9714435 -152.2772938 -152.3289605
HgI+ -449.4732538 -449.5771151 -450.0288159
HgI2 -746.6435659
HgI3- -1043.566473
HgI42
-
Table 4.10(d): HgI series calculated energies with cc-pV*Z-PP basis
109
Extrapolated Complete Basis Set CCSD(T) Energies, Hartrees
Using above pVDZ/pVTZ data to extrapolate via (Equation 1)
X=Cl,  cc-
pV*Z* basis
X=Cl,  aug-cc-
pV*Z* basis
X=Br,  cc-
pV*Z* basis 
X=I, cc-pV*Z-
PP basis
X- -459.8253589 -459.8331427 -2572.853371 -297.0372981
Hg2+ -151.9714435 -152.0344717 -151.9714435 -151.9714435
HgX+ -612.4134902 -612.4967669 -2725.447205 -449.6208462
HgX2 -1072.58392 -1072.677129 -5298.629611
HgX3- -1532.475118
HgX42-
Table 4.10(e): Reaction Energetics with extrapolated CBS from the above mercury 
halogen compounds HgClx, HgBrx, and HgIx.
110
To offer further characterization for these HgX compounds and possibly to identify 
local structure via NMR measurement, we also conducted a number of NMR 
calculations[7-9] using the ADF software package[10-12].  Although Hg NMR is 
challenging due to generally low concentrations, future techniques and current 
approaches can remedy the sensitivity issues.  We therefore present the following 
results, summarized in Table 4.11 and 4.12 below:
Table 4.11:  ADF NMR calculation results for compounds in HgClx series calculated 
with excitations.
Table 4.12: ADF NMR calculation results for compounds in HgClx series calculated 
without excitations.
111
HgClx with Excitations
NMR Shielding (ppm)
Hg (solvated) Hg (gas phase) Cl (solvated) Cl (gas phase)
Hg atom (solvated only) 9909.5
HgCl 9109.17 10077.44 618.35 -867.59
HgCl2 7444.05 7306.67 894.14 807.37
HgCl3 6639.91 6538.59 924.4 892.1
HgCl4 6483.6 6764.95 967 929
NMR Shielding (ppm)
Hg (gas phase) Cl (gas phase)
Hg atom 9909.71
9109.25 10077.22 618.29 -867.23
8055.78 8198.2 792.71 580.16
HgCl2 7443.37 7306.71 894.22 807.33
HgCl2 - 2H2O 7335.65 7259.04 865 841
HgCl3 6639.9 6538.56 924.4 892.1
HgCl3 - H2O 6715.55 6571.58 937 2x869, 1x895
6651.42 910
HgCl4 6483.76 6764.95 967 929
HgCl4 - 2H2O 6510.32 6702.4 935 914
HgCl4 (flat) 6778.92 927
6971.03 3x960, 2x810
7137.75 890, 905, and 969
HgClx with No Excitations
Hg (solvated) Cl (solvated)
HgCl
HgCl - H2O
HgCl3 - 2H2O (solv. only)
HgCl5 (solv. only)
HgCl6 (solv. only)
The calculations made with excitations took a significantly longer length of time to 
complete than the calculations with no excitations, which limited the size of the 
systems which we could examine in the former case.  This allowed us in the latter 
case, however, to do calculations with both explicit hydration and more Cl atoms in 
the cluster.
Examining the sections of each table in turn, we see the following trends.
When we consider the solvated HgCl series calculated with excitations as shown in 
Table 4.11, there is a consistent decrease in NMR shielding for HgClx with increasing 
x in the solvated case, as shown in Figure 4.1 below:
Figure 4.1: HgClx series Hg calculated ADF NMR shielding (ppm) (with excitations)
112
Hg atom (solvated only) HgCl HgCl2 HgCl3 HgCl4
6000
6500
7000
7500
8000
8500
9000
9500
10000
10500
11000
Hg NMR shielding with increasing chlorination
Hg (solvated)
Hg (gas phase)
Compound (increasing number of additional Cl- atoms)
Ca
lcu
lat
ed
 N
MR
 sh
iel
din
g (
pp
m
)
In the gas phase calculations, the trend worked for the first two additional Cl atoms, 
but after that the shielding stabilized around 6600 ppm.
If we consider the Cl NMR shielding instead, as charted in Figure 4.2 below, we see 
that there is a similar trend of increasing shielding (ppm) with increasing numbers of 
Cl atoms present in both the solvated and gas phase cases, although the most major 
differences appear between HgCl+ and HgCl2.
Figure 4.2: HgClx series Cl calculated ADF NMR shielding (ppm) (with excitations)
Moving on to the calculations which were done without excitations, we have a greater 
variety of species which we examined, including all of the ones which we looked at in 
113
HgCl HgCl2 HgCl3 HgCl4
600
650
700
750
800
850
900
950
1000
Cl NMR Shielding with increasing Hg chlorination
Cl (solvated)
Cl (gas phase)
Compound (increasing number of additional Cl- atoms)
Ca
lcu
lat
ed
 N
MR
 S
hie
ldi
ng
 (p
pm
)
the system with excitations and explicitly solvated ones.  These are shown in Table 
4.12 and Figure 4.3 and 4.4.
Looking at Figure 4.3 first, where we have a chart of the Hg NMR shielding with 
increasing chlorination, we see that the general trend we observed previously is still 
present.  As more Cl atoms are added to the cluster, the shielding decreases until we 
have HgCl3-, where it apparently bottoms out, having similar shieldings through 
HgCl64-.  We can also see that the presence of water molecules explicitly hydrating 
the system only has a significant effect on the Hg shielding before the mercury has 
two Hg-Cl bonds present; the explicitly solvated HgCl+ shows a lower calculated 
shielding than the plain HgCl+, but otherwise differences are quite minimal.  When 
the Hg has more than 4 Cl atoms attached, the shielding increases again in the 
solvated calculations which included 5 and 6 Cl atoms.
114
Figure 4.3: HgClx series Hg calculated ADF NMR shielding (ppm) (no excitations)
If we examine the Cl shieldings calculated by ADF without excitations, we see less of 
a pattern, although the tetrahedral HgCl3 . H2O system can be distinguished from the 
normal HgCl3 by virtue of an additional NMR peak which appears for Cl.  The trend 
of increasing shielding with increasing substitution holds through HgCl3, but as 
previously seen in the calculations with excitations, the relative differences between 
species shrink drastically after the 3rd Cl atom is added to the group.  The shielding 
conditions for HgCl53- and HgCl64- also do not continue the trend of increasing 
shielding with increasing substitution.
115
Hg 
atom
HgCl HgCl - 
H2O
HgCl2 HgCl2 
- 
2H2O
HgCl3 HgCl3 
- H2O
HgCl3 
- 
2H2O 
(solv. 
only)
HgCl4 HgCl4 
- 
2H2O
HgCl4 
(flat)
HgCl5 
(solv. 
only)
HgCl6 
(solv. 
only)
6000
6500
7000
7500
8000
8500
9000
9500
10000
10500
11000
Hg NMR shielding with increasing chlorination
Hg (solvated)
Hg (gas phase)Compound Reviewed (increasing number of Cl- atoms)
Ca
lcu
lat
ed
 N
MR
 sh
iel
din
g (
pp
m
)
Figure 4.4: HgClx series Cl calculated ADF NMR shielding (ppm) (no excitations). 
Because of the different environments for Cl atoms in the calculated geometries for 
HgCl3 ? H2O, HgCl5, and HgCl6, there are multiple calculated shieldings in each case.
Overall, we would say that from these calculations, we would predict that on the basis 
of NMR one could distinguish between species up to HgCl2, and tell them apart from 
HgCl3- and further substituted species, but that the differences between the shieldings 
for  HgCl3- and  HgCl42- would  be  much  less  straightforward  to  tell  apart 
experimentally.
116
HgCl HgCl - 
H2O
HgCl2 HgCl2 - 
2H2O
HgCl3 HgCl3 - 
H2O
HgCl3 - 
2H2O 
(solv. 
only)
HgCl4 HgCl4 - 
2H2O
HgCl4 
(flat)
HgCl5 HgCl6
550
600
650
700
750
800
850
900
950
1000
Cl NMR shielding with increasing chlorination
Compound (increasing number of Cl- atoms)
Ca
lcu
lat
ed
 N
MR
 sh
iel
din
g (
pp
m
)
Cl (solvated)
Cl (gas phase)
4.4 Conclusions
Through these calculations we demonstrated that the HgClx system can be represented 
with a B3LYP / CEP-121G+ approach with the same overall results as CCSD / CEP-
121G+ or the CCSD(T) complete basis set extrapolation.
This is good news, because the relatively low computational cost of B3LYP 
calculations will allow us to look at larger systems which would be inaccessible with 
the more computationally expensive CCSD and CCSD(T) calculations.
Through our NMR calculations, we showed that a trend of decreasing shielding with 
increasing substitution exists for HgClx compounds, but that the differences become 
progressively smaller and might not be useful for telling apart HgCl3- and above.
4.5 Acknowledgements
We would like to acknowledge the invaluable assistance of Parallel Quantum 
Solutions for both kindly and excellent after-market technical support of their 
QuantumCubeTM chemistry cluster used to calculate the NMR data presented in this 
chapter.
117
4.6 References
1. Sheu, G.R. and R.P. Mason, An examination of methods for the measurements 
of reactive gaseous mercury in the atmosphere. Environmental Science & 
Technology, 2001. 35(6): p. 1209-1216.
2. Sillen, L.G., Electrometric Investigation of Equilibria between Mercury and 
Halogen Ions .8. Survey and Conclusions. Acta Chemica Scandinavica, 1949. 
3(5): p. 539-553.
3. M. J. Frisch, G.W.T., H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. 
Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. 
M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. 
Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. 
Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, 
H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. 
Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, 
A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. 
Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. 
Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. 
Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, 
S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. 
Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. 
Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. 
118
Wong, C. Gonzalez, and J. A. Pople, Gaussian 03, Revision C.02, 2004, 
Gaussian, Inc., Wallingford CT.
4. Halkier, A., et al., Basis-set convergence of the energy in molecular Hartree-
Fock calculations. Chemical Physics Letters, 1999. 302(5-6): p. 437-446.
5. Feller, D. and J.A. Sordo, A CCSDT study of the effects of higher order 
correlation on spectroscopic constants. I. First row diatomic hydrides. The 
Journal of Chemical Physics, 2000. 112(13): p. 5604-5610.
6. Becke, A.D.,  Density-functional thermochemistry. III. The role of exact 
exchange. The Journal of Chemical Physics, 1993. 98(7): p. 5648-5652.
7. Wolff, S.K., et al.,  Density functional calculations of  nuclear magnetic 
shieldings using the  zeroth-order regular approximation (ZORA) for 
relativistic effects: ZORA nuclear magnetic  resonance. Journal of Chemical 
Physics, 1999. 110: p. 7689 
8. Schreckenbach, G. and T. Ziegler, The calculation  of NMR shielding tensors 
based on density  functional theory and the frozen-core  approximation. 
International Journal of Quantum  Chemistry, 1996. 60.
9. Schreckenbach, G. and T. Ziegler, The calculation  of NMR shielding tensors 
using GIAO's and modern  density functional theory. Journal of Physical 
Chemistry, 1995. 99.
10. Guerra, C.F., et al., Towards an order-N DFT method. Theoretical Chemistry 
Accounts, 1998. 99.
119
11. Velde, G.t., et al.,  Chemistry with  ADF. Journal of Compututational 
Chemistry, 2001. 22: p. 931.
12. Baerends, E.J., et al., ADF2004.01, SCM, Theoretical Chemistry, Vrije 
Universiteit, Amsterdam, The Netherlands,  http://www.scm.com. 2004.
120
Chapter 5:  Ab Initio Phosphoric acid pKa calculations using 
CBS-QB3 and MP2 methods
In this chapter we discuss several approaches to calculating the pKas of phosphoric 
acid (H3PO4), a common polyprotic acid which forms several different species in 
aqueous solution, using the MP2[1] and CBS-QB3[2] methods and applying an 
explicit counterion correction to see if the reduction in total ionic charge improves 
accuracy significantly.
5.1 Introduction
Phosphoric acid is a common polyprotic inorganic acid which is well-characterized 
experimentally.  Many experimental measurements of its acidities are readily 
available.  However, there are relatively few theoretical studies to date, though 
recently it has been of more interest, perhaps because of its disarming simplicity[3].
Phosphoric acid is a useful model for multiply charged anions because it is light 
enough that it is easy to conduct many different higher-level calculations on it than is 
possible for larger molecules with heavier atoms, which would be considerably more 
computationally expensive to study in a variety of details.
Our goals were to reproduce experimentally measured acid deprotonation constants 
(pKa values) if possible, and to show how future laboratories could follow a 
121
straightforward method which we can demonstrate produces reasonably good results 
of known quality.
Acid deprotonation constants are determined from the deprotonation reactions as 
follows.  For a sample reaction of an acid HA which dissociates in solution to A- and 
H+, shown below as (a):
(a) HA(aq)   ?  H+(aq)  +  A-(aq)
The rate of the forward reaction is called the rate constant K.  As the acidity of the 
HA species varies the rate constant will increase or decrease.  Normal rate constants 
are calculated as a ratio of concentrations of products over reactants at equilibrium, 
which appear as shown below in Equation 5.1 for hypothetical reaction (a).
(5.1) Ka=[H+][A-][HA]
This can then be converted into a pKa by taking the negative logarithm as shown in 
Equation 5.2:
(5.2) pKa=?logKa=?log?[H+][A-][HA] ?
pKa values are especially useful because they can be used with pH measurements to 
predict the form that the acidic chemical HA will take in an aqueous solution of that 
122
acid.  pH measurements are determined based on the concentration of the [H+] ion in 
a solution, as shown in Equation 5.3 below:
(5.3) pH=?log[H+]
The problem of phosphoric acid is an interesting and challenging one in part for two 
main reasons.  Although the protonated form is neutral, it can be deprotonated three 
times, making a significantly negatively charged ion.
Computationally, determining the stability of an ion is generally more difficult than 
the neutral species, especially if it is being stabilized by a solvent.  The electron cloud 
geometry changes in one of two ways when an ion is formed.  If electrons are lost, 
leaving a positive ion, the electron cloud shrinks slightly towards the nucleus after the 
highest energy electrons are removed.  In this situation the shape and geometry does 
not change very much.  When electrons are added to an ion, the cloud becomes much 
larger and the probability of finding any of the electrons further from the nucleus 
becomes much greater.  Representing this latter situation with basis sets can require 
additional basis set functions and other techniques to accurately reproduce the 
optimal electron probability density distribution.
There are many reactions of ions that can be straightforwardly treated with ab initio 
approaches.   In reactions where the total charge on both sides of the reaction is the 
same, and the square of the individual charges are the same, errors in the solvation 
123
model generally cancel out to a great degree if the ions on both sides are similar in 
structure.
However, for deprotonation reactions, this balance is lost.  This may be why previous 
calculations[4] focused mainly on the first deprotonation of phosphoric acid and not 
on further ones.
There are also some technical challenges that crop up because of geometry (B3LYP 
geometry optimizations, such as are found in the initial steps of CBS-QB3, tend to 
have difficulty converging to a minima especially when done with PCM solvation) 
and wavefunction convergence issues (especially in the presence of a strongly 
interacting counterion) which we will discuss later.
As mentioned earlier, phosphoric acid has several well known experimentally 
measured pKa values shown in Table 5.1 below.
pKa Experimentally Measured Value
pKa1 (H3PO4 ? H2PO4- + H+) 2.2
pKa2 (H2PO4- ? HPO42- + H+) 7.1
pKa3 (HPO42- ? PO43- + H+) 12.3
Table 5.1: Experimentally measured pKa values from William L. Jolly, Modern 
Inorganic Chemistry, 2nd edition.[5]
124
These values have been tightly characterized and verified by countless generations of 
undergraduates following their general acceptance in the annals of inorganic 
chemistry research.  The values above were quoted from a standard inorganic 
chemistry textbook,
More recently, we have a few theoretical studies of H3PO4 and deprotonated 
derivatives done by several groups:
D.A. Dixon et al. published a paper on CCSD(T) Complete Basis Set Extrapolations 
with an excellent treatment of the first deprotonation in 2005[4].  In that work, H3PO4 
was calculated to have a heat of formation of -268.8 kcal/mol, a gas acidity of 322.2 
kcal/mol, and a first deprotonation pKa of 2.5.  This particular example required the 
use of several corrections to the energy which would put the approach initially 
outside the purview of the typical physical chemist not specializing in computational 
chemistry.   However, this excellent project shows what will soon be in reach for 
smaller laboratories once common computer technology advances a bit further.
E. Tsuchida's paper from 2006[6] covered molecular dynamics calculations using 
DFT (by way of a PBE functional).  It was concerned with studying liquid phase 
H3PO4 via molecular dynamics (MD) simulation on a supercomputing cluster, and 
successfully reproduced both experimental structures and vibrational properties of the 
125
fully protonated compound, although it noted that the MD simulation observed proton 
exchanges between the H3PO4 groups.
D. B. Chesnut conducted 31P NMR calculations via sB3LYP and GIAO on H3PO4[7], 
and garnered both energetics for hydrogen bonding and absolute NMR shieldings for 
both H3PO4 and its deprotonated anions, noting that there were a variety of 
geometries with multiple H3PO4 atoms associating with each other and with water, 
and these lead to a variety of different possible calculated shieldings around the 
experimental measurement.  The results suggested that H3PO4 . 2 H2O was the best 
model for experimental conditions of 85% H3PO4 31P NMR measurement.
5.2 Methods
Keeping in mind that our goal was to demonstrate a method which would be within 
reach of experimental physical chemistry groups without necessarily access to a 
dedicated theorist, we decided to investigate the following different approaches to 
calculating H3PO4 energetics.
We calculated the change in Gibbs free energies using Gaussian 03[8] with the CBS-
QB3 model chemistry[2] method for each species and MP2/CBSB7[9] free energies 
as well.
126
To estimate solvation stabilization we applied several tools.  Our main one was the 
CPCM polarizable continuum model[10-12].  With it, we did independent Hartree-
Fock calculations[13] using 6-31+G**, 6-31G**, and 6-31G basis sets.  We also 
applied it in conjunction with the CBS-QB3 calculations as well as with the 
MP2/CBSB7 calculations.
After these were done, we added Na+ counterions in association with the negatively 
charged ions in the systems, and did more calculations in the CPCM to determine 
how the presence of the ion reduced dependence on the CPCM model and whether it 
would reduce the error in the calculations.  While it did improve the results, it caused 
trouble with the SCF step of the HF calculation, making several results inaccessible.
 
5.3 Results
The results for the first set of calculations is in Table 5.2.  These are ones done with 
the CBS-QB3 gas phase free energy calculations plus CPCM stabilizations calculated 
under the HF method at those CBS-QB3 geometries (which were found during the 
B3LYP/CBSB7 optimization step of CBS-QB3).  This first estimate approach for 
finding the values tends not to run into difficulties during the geometry optimization
127
CBS-QB3 Gas phase Free Energies + (basis set) 
HF CPCM Stabilization at gas phase geometries
Experimental
Results
H3PO4 6-31+G** 6-31G** 6-31G
pKa1 6.0          _ 5.5 6.5 2.2
pKa2 21.8 18.7 21.5 7.1
pKa3 24.7 14.8 17.9 12.3
Table 5.2: CBS-QB3 Gas Phase Free Energies + CPCM Stabilization (with various 
basis sets) on phosphoric acid.
In this case the extra + in 6-31+G** is a diffuse function and we observe that the 
second  and  third  pKas  with  the  most  negatively  charged  anions  are 
uncharacteristically larger compared to calculation with the smaller basis 6-31G** 
which has only polarization functions.  But though the calculations with 6-31G** 
have results closest to the experimental ones although the reversed trend for the pKa2 
and pKa3 are clearly nonphysical.
Noting the unusually high value for the other pKa2s in this case, one thing to consider 
here might be that the CPCM stabilization in the 6-31G and 6-31G** calculation is 
smaller than it ought to be for the HPO42- species.  This would increase the pKa2 while 
decreasing the pKa3 as was observed here.  In our later calculations we used the
HF/6-31+G** basis for calculating stabilization of gas phase systems for this reason. 
128
H3PO4 CBS-QB3 plus 
HF/6-31+G** 
CPCM energy
CBS-QB3 run in 
CPCM
MP2/CBSB7 
in CPCM
Experimental 
Results
pKa1 6.0       _ 4.9 11.5 2.2
pKa2 21.8 21.1 31.8 7.1
pKa3 24.7 29.8 45.5 12.3
Table 5.3: CBS-QB3 and MP2 Calculations on Phosphoric Acid solvated with CPCM
Adding CPCM to the CBS-QB3 run improved the results slightly for the species with 
lower charges, although the results are still better than the corresponding simple MP2 
geometry optimization and calculation.
However, introducing a counterion improves the results significantly for the second 
and third deprotonation as seen in Table 5.4 below:
129
H3PO4 , NaH2PO4 , 
NaHPO4-, and 
NaPO42- 
CBS-QB3 CPCM 
with Na+ Counterion
CBS-QB3 CPCM 
calculation 
without counterion
Experimental 
Results
pKa1 N/A 4.9 2.2
pKa2 15.6 21.1 7.1
pKa3 24.9 29.8 12.3
Table 5.4: Phosphoric Acid CBS-QB3 calculations with counterion.
There were regrettable failures in calculating the CBS-QB3 energy of the solo Na+ 
ion (?Not enough resources for E2 calculation.?) which prevented us from finding the 
pKa1 using the method.  There were also difficulties with the NaPO42- calculation, 
which experienced several wavefunction convergence failures during the process. 
However, we could find the second and third deprotonation energies, which were 
quite a bit closer to the experimental results, going from a factor of three error to a 
factor of two.
5.4 Discussion and Conclusions
Overall, using CBS-QB3 + CPCM with Na+ counterions yielded results closest to 
experiment.  However, the difficulties with the geometry optimization and the 
130
wavefunction convergence were issues that might not be within reach for a laboratory 
without theoretical assistance.
The results also left a bit to be desired from a quantitative point of view.  Although 
we got much closer to experimental measurements for the second and third 
deprotonation than previous work, there is still a distance remaining before ab inito or 
hybrid ab initio/fitted calculations of pKas can be easily done in experimental labs.
We would conclude that although finding trends in the pKas is possible using CBS-
QB3 along with the CPCM model, easy desktop calculation of quantitative pKa and 
pH values for polyprotic acids remains in the future.
Molecular dynamics calculations should be able to overcome the convergence 
problem we experienced here from the SCF not converging as they use a different 
approach with plane waves to representing the electron cloud.  However, there may 
be drawbacks from the method sampling a solution of a unrealistically high 
concentration of the acid.  In the future it would be interesting to do MD calculations 
on these systems to explore the differences between the two approaches.
More complex solvation models should be able to help as well.  If we add explicit 
water molecules it will increase the cost, but should also take care of some more of 
the chemical interactions between the solvent and the ion which aren't represented by 
131
the CPCM model at all.  In the future, a Car-Parrinello Molecular Dynamics 
calculation[14] might be effective in this case, as the theory is designed to handle a 
fixed volume of space with an effective level of quality, and the direction of 
increasing parallelization in computer design should allow for easy scaling of 
calculations using the method in the future. 
We went on to do calculations with single H2O molecule explicit solvation and with 
some acidic arsenic compounds as we worked to find a better approach to get 
improved results, as detailed in the next section of this chapter.
5.5 Acknowledgements
This work was sponsored by NSF Grant EAR0539109, DOE Grant DE-FG02-
94ER14467, and the NSF-MRSEC at the University of Maryland, College Park 
DMR#0520471.
We would also like to acknowledge D.A. Dixon for references to prior work, J.A. 
Tossell for much advice on the experimental process, and fellow graduate students E. 
Khaskin, and Liang T. for suggestions given on the presentation this work was based 
upon.
132
5.6 References
1. Moller, C. and M.S. Plesset, Note on an Approximation Treatment for Many-
Electron Systems. Physical Review, 1934. 46(7): p. 618.
2. Montgomery, J.A., J.W. Ochterski, and M.J. Frisch, An improved complete 
basis set (CBS) model chemistry. Abstracts of Papers of the American 
Chemical Society, 1996. 211: p. 231-PHYS.
3. Lopez, X., et al.,  Theoretical Evaluation of pKa in Phosphoranes:? 
Implications for Phosphate Ester Hydrolysis. Journal of the American 
Chemical Society, 2002. 124(18): p. 5010-5018.
4. Alexeev, Y., et al., Accurate heats of formation and acidities for H3PO4, 
H2SO4, and H2CO3 from ab initio electronic structure calculations. 
International Journal of Quantum Chemistry, 2005. 102(5): p. 775-784.
5. Jolly, W.L., Modern Inorganic Chemistry. 2nd ed 1991, New York: McGraw 
Hill. 655.
6. Tsuchida, E.,  Ab initio molecular-dynamics simulation of concentrated 
phosphoric acid. Journal of the Physical Society of Japan, 2006. 75(5): p. -.
7. Chesnut, D.B., A Theoretical Study of 31P NMR Chemical Shielding Models 
for Concentrated Phosphoric Acid Solution. The Journal of Physical 
Chemistry A, 2005. 109(51): p. 11962-11966.
8. M. J. Frisch, G.W.T., H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. 
Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. 
133
M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. 
Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. 
Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, 
H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. 
Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, 
A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. 
Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. 
Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. 
Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, 
S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. 
Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. 
Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. 
Wong, C. Gonzalez, and J. A. Pople, Gaussian 03, Revision C.02, 2004, 
Gaussian, Inc., Wallingford CT.
9. Head-Gordon, M., J.A. Pople, and M.J. Frisch, MP2 energy evaluation by 
direct methods. Chemical Physics Letters, 1988. 153(6): p. 503-506.
10. Cossi, M., et al., Energies, structures, and electronic properties of molecules 
in solution with the C-PCM solvation model. Journal of Computational 
Chemistry, 2003. 24(6): p. 669-681.
11. Barone, V., M. Cossi, and J. Tomasi, Geometry optimization of molecular 
structures in solution by the polarizable continuum model. Journal of 
Computational Chemistry, 1998. 19(4): p. 404-417.
134
12. Barone, V. and M. Cossi, Quantum calculation of molecular energies and 
energy gradients in solution by a conductor solvent model. Journal of Physical 
Chemistry A, 1998. 102(11): p. 1995-2001.
13. Roothaan, C.C.J., New Developments in Molecular Orbital Theory. Reviews 
of Modern Physics, 1951. 23(2): p. 69-89.
14. Car, R. and M. Parrinello, Unified Approach for Molecular Dynamics and 
Density-Functional Theory. Physical Review Letters, 1985. 55(22): p. 2471.
135
Chapter 6:  Arsenic and Phosphoric Acid pKa calculations using 
the CBS-QB3 model chemistry and the CPCM SCRF 
solvation method
In this chapter we further discuss several different polyprotic acids, continuing the 
study from the previous chapter and developing an extrapolation which improves the 
accuracy of the results significantly.  Methods used focused on the CBS-QB3 
computational chemistry[1] with the CPCM solvation model[2].
This section based on Zimmermann, M. D. and Tossell, J. A. Acidities of Arsenic(III) 
and Arsenic(V) Thio- and Oxyacids in Aqueous Solution using CBS-QB3.[3] Tables 
and Figures are reproduced from the same.
6.1 Introduction
Arsenic chemistry is important because of its dramatic impact on human welfare as 
well as an element which is widely dispersed around the world.  Arsenic poisoning 
has serious health effects on those exposed to it, causing damage to the immune 
system and dramatically shortening life expectancies.[4]
136
It has previously been shown that high level methods can directly calculate pKa 
values for first deprotonations for small phosphoric acid systems[5], but further 
deprotonations have fewer results available.
This problem will be shown to be easily addressed systematically by the CBS-QB3 
model chemistry[1] and a fitting extrapolation determined from small polyprotic acids 
with the form H3AO4 (with A=P,S,As).  One of the goals of this part of the research 
was to make sure that any procedure developed would be both approachable and 
straightforward enough to be easily accessible to any physical chemist with a 
computer, and this was attained successfully.
The main compounds  analyzed here via ab-initio approaches were H3AsS3, H3AsS4, 
H3PO4, and H2SO4 and their deprotonated derivatives5.  These were done in the gas 
phase and in aqueous solution (either in a PCM modeled uniform dipole system 
approximating water, or the same with an explicit water molecule present to add 
hydrogen bonding interactions).  In each case we calculated the pKas of each 
deprotonation step, then made a linear fit, extrapolating the results against known 
experimentally measured pKa values for H3AsO4 and H3PO4.
5 Although for HAsS32- we were unable to locate a stable equilibrium geometry in our CBS-QB3 
calculation.
137
This approach yielded data which corresponded well with the measured values.  Of 
the methods which were attempted in this experiment, the best fits came for the CBS-
QB3 calculation performed within the CPCM came the closest to a linear relation.
After completing the calculations, several experimental measurements of H2SO3 
which were not used in determining the extrapolation matched the predicted data 
excellently. The values for the extrapolation were within 1 pKa unit of the measured 
experimental values.
6.2 Methods
Each compound was examined with the CBS-QB3 method of calculation[1] as 
implemented in Gaussian 03[6].  CBS-QB3 is a model chemistry like the G2[7] and 
G3[8] methods which aims to provide a universal approach to modeling chemical 
compounds.   CBS-QB3 uses B3LYP[9] for geometry optimization and CCSD(T)
[10], MP4SDQ[11], and MP2 calculations[12] with progressively larger basis sets to 
determine a complete basis set extrapolation for the compounds examined with the 
method.
Like the other model chemistries, CBS-QB3 is an easily conducted calculation for a 
group without a dedicated theoretical support team.
138
A method for accurately determining pKas which could easily be done by a lab 
without dedicated theorists would be useful to chemists in all areas of study. 
Therefore, the approaches which we set forward here were chosen to provide the 
maximum level of quality with a minimum of expertise required for their use.
To verify that the CBS-QB3 model chemistry is a reasonable choice for this system of 
chemicals, we conduct additional calculations with CCSD(T), coupled cluster theory 
with singles, doubles, and some triple excitations, to determine if the results we see 
are reproduced in the same fashion with two representative species, H3AsO4 and 
H3PO4.  The theory is applied with the relativistically corrected CEP-121G basis set 
to include contributions to the calculated pKas from effects in the core electron shells.
CBS-QB3 uses several different basis sets in its calculations to pick up the 
contributions from different levels of theory.  The initial B3LYP step uses a CBSB7 
basis set, while MP2 uses CBSB3, and MP4SDQ CBSB4.    With the CCSD(T) step 
of the calculation, CBS-QB3 uses the 6-31+G(d') basis set, the smallest basis used in 
CBS-QB3.  The progressively smaller basis sets ensure that each step after geometry 
optimization will take a similar amount of time to complete.
CBS-QB3 produces energetics similar to the G2 and G3 model chemistries, with 
energies of the order of 1-2 kcal/mol away from the G2 test set's experimental 
139
measurements[13].  However, the arsenic compounds in the G2 test set are As2, AsH, 
AsH2, and AsH3, while our focus here is arsenic oxides and sulfides.
While conducting the CBS-QB3 calculations we occasionally observed that the initial 
B3LYP optimization did not converge in a reasonable amount of time, requiring 
several restarts of the 30 step optimization sequence to bring the systems to final 
geometries.  We found it helpful in the more difficult cases to optimize under the 
MP2 method, then use that converged geometry as the input for the CBS-QB3 
calculation.  This approach seemed to strike a better balance between theorist 
intervention and CPU time required for the calculations.
CPCM[14] is used to determine the total energy of hydration for each compound. 
The CPCM method is very computationally efficient, and unlike explicit hydration 
does not add a significant computational cost to the overall calculation.  Another 
advantage of using CPCM instead of full explicit solvation is that changes in the 
structure of the solvation cluster of explicit solvent molecules can add noise to the 
data in the results and make it more difficult to easily retrieve useful data from the 
results of calculations.  For example, a change in cluster geometry that adds a 
hydrogen bond to the overall favorable interactions in a group would change the 
energy measured by about 4.3 kcal/mol.  If not accounted for, this could change a 
predicted pKa including the data by about 4 pKa units.
140
One difficulty introduced by using the CPCM method is that converging the B3LYP 
optimizations is even more difficult than in the gas phase without CPCM.  However, 
we feel the additional quality of the results justifies the extra trouble.
Solvation energy is approached in two different ways which have both been used in 
the past.  A gas phase calculation of the species of interest is completed first, 
followed by a calculation of the CPCM solvation stabilization energy at that same 
geometry.  We use a HF/6-31+G** single point calculation with a tight optimization 
of the self consistent field as the basis of our solvation calculation.  The SCFVAC and 
RADII=UAHF tags are also applied to yield direct compatibility with previous 
experiments in our laboratory.  This approach yields a swift, but less accurate 
estimation of the free energy of solvation.
A logical next step here would be to optimize the solvation shell sizes for each 
species analyzed, but this would put reproducing our approach out of reach of groups 
with less theoretical support and was therefore not done in our lab, although it was 
applied with great success in other experiments[5, 15].
A disadvantage of our approach, however, is that it assumes that the stabilization of 
the compounds does not change significantly from changes in their geometry caused 
by placing them in solution.  Also, because the CPCM model represents the solvation 
by a continuous space outside a cavity made to hold the molecule there is no specific 
141
interaction with solvent molecules such as the hydrogen bonding mentioned earlier as 
an occasional problem with explicit solvation.
These two disadvantages, however, can be ameliorated somewhat by our second 
approach, which was to do the entire CBS-QB3 procedure in the CPCM.  This 
yielded different geometries, ones which were optimized under B3LYP/CBSB7 
CPCM conditions.  This approach does not require the assumption that the solvated 
geometry is the same as the unsolvated one ? in fact, it is not ? but  it also makes the 
optimization step even less willing to converge than it was in the gas phase setting. 
This is possibly caused by the much flatter potential energy surface in the latter case.
The total energies of reaction ?Grxn can then be determined through the following 
equation:
(6.1) ?Grxn = ?G(A-gas) ? ?G(AHgas) + ?Gs(AH) ? ?Gs(AH) ? 269.0 kcal/mol
Where ?G (A-gas) ? ?G(AHgas) is the change in energy for deprotonation of the 
compound in the gas phase calculated with the CBS-QB3 method, ?Gs is the free 
energy of solvation (found either through the first method or the second) and -269.0 
kcal/mol is a calculated energy of solvated H+ ion in water as referenced in [16] 
including corrections for the different gas and solvation reference states for the 
142
proton.  In other experiments a value in the neighborhood of -264 kcal/mol has been 
used and the conversations of state dealt with separately[17-21].
The choice of this particular figure, however, is somewhat arbitrary, because during 
the following approach we will be applying a linear correction factor which would 
eliminate any possible errors introduced by a differing constant factor in the free 
energy calculation.
The pKa of deprotonation can be found from the free energy change by dividing it by 
1.3644 kcal/mol.
CCSD(T) calculations from both the final CBS-QB3 gas phase and CPCM CBS-QB3 
solvated geometries for H3AsO4, H2AsO4-, HAsO42-, H3PO4, H2PO4-, HPO42-, and PO43- 
were done with the aforementioned CEP-121G basis set to check for relativistic 
effects, the large standard basis set 6-311G(2d,p) used to measure the effects of 
additional diffuse orbitals, and aug-cc-pVDZ to compare with the CBSB7 and 
CBSB8 basis sets.
The thermal correction to the Gibbs free energy was estimated in these single point 
calculations by assuming  it would be similar  to that calculated  from the 
B3LYP/CBSB7  frequency  calculation  conducted  as  part  of  the  CBS-QB3 
determination and using that figure to correct the single point energy in each case.
143
Following these, a last series of calculations was run with one explicit water molecule 
associated with each species of interest by a hydrogen-bonding interaction.  If there 
was a deprotonated oxygen or sulfur present, the H2O was positioned to form one 
HOH ... -OA hydrogen bond.  In the two cases of saturated systems, H3AsS3 and 
H3AsO3, the water molecule was positioned initially with one hydrogen bond to its 
oxygen from the fully protonated acid: AH ... OH2.  The two different types of 
bonding are illustrated in Figure 6.1 and Figure 6.2 below.
Figure 6.1: H3AsO4 Hydrogen-bonding from explicit water molecule to the 
compound.
144
Figure 6.2: H3AsO3 hydrogen-bonding from acidic hydrogen on arsenic complex to 
the explicit water molecule.
6.3 Results and Discussion
As previously mentioned, we calculated reaction free energy changes with (1).  The 
results from this are tabulated in the Table 6.1 below  for each type of calculation: 
CBS-QB3 gas phase, CPCM stabilization calculated at the gas phase geometries, 
CBS-QB3 calculated in the polarizable continuum, and those three with explicit 
hydration by a single water molecule.
145
We could combine the gas phase and the ?G solvation energies calculated at the gas 
phase to get rapidly estimated solution pKa as well.   From these, we could determine 
pKas for the hydrated systems through division by 1.3644 kcal/mol.   This data is 
summarized in the second table.
Table 6.1: Calculated deprotonation energetics for acid deprotonation reactions.
There was one system, HAsS32-, which we could not locate a converged geometry for 
in the gas phase.  In this case, we found a converged CPCM-optimized geometry, but 
as we did not have a gas phase point we do not have the lowest quality pKas.  During 
146
the optimization processes for HAsS32-, we observed that the compound dissociated 
during optimization into a pair of ions, AsS2- and HS-.  This only occurred in the 
presence of the proton; AsS33- was easily optimized to a stable geometry.  Therefore, 
we were able to calculate the energy required to doubly deprotonate H2AsS3- to AsS33- 
from our results, but pKa2 and pKa3 were unavailable for HxAsS3 species.
In the hydrated neutral systems, where we started with a water molecule in contact 
with the main molecule starting at its optimized gas phase geometry, then conducted 
optimizations both in the gas phase and in the PCM modeled hydration environment, 
the water molecule reached a minima with two hydrogen bonds to the main molecule. 
A typical case is shown in Figure 6.3 of a hydrated H3AsO4 . H2O complex with this 
cyclic style of hydrogen bonding.  Figure 6.4 illustrates the case where hydrogen 
bonding occurs from the water molecule to the anion.  This was true except in rare 
cases such as for H3AsS4 . H2O when optimized in a CPCM reaction field, where the 
water molecule sustained only its initial hydrogen bonding interaction.
147
Figure 6.3: H3AsO4 . H2O complex optimized CBS-QB3 geometry showing typical 
cyclic hydrogen-bonding structure seen in singly solvated systems.
The hydrogen bonding does not show proton transfer either from the explicitly 
solvating water molecule in each calculation to the   molecule or from the compound 
to the water molecule.  However, between the most negatively charged anionic 
species and the least anionic there are differences of about 10% in H-O bond lengths 
in the water when it is hydrogen bonding.  If we compare H3AsO4 and AsO33-, the 
bond length of the hydrogen bonding H atom to the oxygen in its water molecule 
increases from 0.97A to 1.07A.  The length of the hydrogen bond goes from 2.08A to 
148
1.70A between the same two species.  The more negatively charged anions have a 
stronger, shorter hydrogen bond than the neutral species.
There were several different patterns of explicit hydration interaction observed in the 
two kinds of species, neutral and anionic.  When the explicit water molecule interacts 
with the anion, we note that at equilibrium the H2O molecule is positioned so that 
there are one or two hydrogen bonds going from negatively charged oxygen atoms on 
the anion to the hydrogen atoms on the explicit H2O, such as illustrated in Figure 6.4 
below.  Uncharged complexes showed hydrogen bonding arrangements where there 
were both hydrogen bonding interactions going from the uncharged species' protons 
to the explicit water molecule's oxygen atom and interactions going from the water's 
hydrogen atoms to the uncharged complex.
149
Figure 6.4: Hydrated HAsO4-2 . H2O complex CBS-QB3 optimized geometry as 
calculated in the polarizable continuum.
For example, in H3AsO4 optimized under the CPCM via a CBS-QB3 calculation, we 
saw the water molecule oriented with one hydrogen bond from one of the complex's 
protons to the water molecule's oxygen atom while at the same time there was a 
hydrogen bond going from one of the water molecule's hydrogens to the deprotonated 
oxygen atom in the complex as seen in Figure 6.3 above.  H3AsS4 differed, however, 
with an off-axis very long hydrogen bond (see Figure 6.7, below)
The most extensive bonding interaction was seen between the explicit H2O and the 
H3AsS3 cluster.  When optimized in the gas phase using CBS-QB3 the system 
150
optimized into an energy minima with three hydrogen bonding interactions, two H 
atom interactions with the water's oxygen atom, although the third interaction, from a 
hydrogen atom on the H2O back to the third sulfur atom in the cluster was very long 
compared to the other interacting pairs.  This pattern was also seen in the explicitly 
hydrated H3AsO3 complex shown in Figure 6.6, and the long, off-axis style of 
hydrogen bond also appeared in the H3AsS4 . H2O complex shown in Figure 6.7.
Figure 6.5: Illustration of the most hydrogen-bonding pattern seen in the hydrated 
H3AsS3 . H2O complex found from CBS-QB3 geometry optimization in the 
polarizable continuum.
151
Figure 6.6: Similar multiple hydrogen-bonding interaction seen in H3AsO3 . H2O 
complex calculated under CBS-QB3 method with the CPCM present.
152
Figure 6.7: Long hydrogen-bonding interaction seen in the CBS-QB3 calculation with 
the polarizable continuum when optimizing the H3AsS4 . H2O explicitly hydrated 
system.
Having discussed geometries extensively, we move on to examine the acidities 
calculated with our methods.
The pKa data shows several interesting trends, best explored by examining the 
different methods in the case of the H3AsO4 and the H3PO4 compounds, both of which 
are well-characterized experimentally.
153
Table 6.2: pKa values for H3AsO4 and H3PO4 multiple deprotonations with each CBS-
QB3 based method.
Table 6.3: pKa values for H3AsO4 and H3PO4 multiple deprotonations with  the 
CCSD(T) method under 6-311G(2d,p), aug-cc-pVDZ, and CEP-121G basis sets.
In most of the records, we observe that the pKa3 is significantly lower in the CBS-
QB3 / gas phase with CPCM corrections calulations than in the CBS-QB3 CPCM 
calculations.  For the species with sulfur atoms this difference is generally about 5%, 
but with oxides we notice a difference around 15-20%.  This may be a result of the 
difference in electronegativities of the two species; with oxygen's significantly higher 
electronegativity we see a greater effect.  The stabilization is a result of the electronic 
interaction between the self consistent field of electrons arranged around the ion and 
154
the polarizable continuum outside the cavity, so a greater concentration of electron 
probability would cause a much more intense stabilization effect.
The calculations with the CPCM present reduce the total free energy further for each 
species.
It can be noted that the energies calculated with CBS-QB3 in the CPCM the total 
energies are significantly lower for most of the species we studied, except for the 
most negative, strongly charged anions such as AsO43-, AsO33-, and AsO33- . H2O.  In 
these cases the energy difference was on the order of only about 10 kcal/mol, which is 
of the same order of magnitude as our experimental results.
In the case of the fully deprotonated oxide species, including these, AsO43-, AsO33- 
and the hydrated versions of the same two, we suspect the cause is that the CPCM 
stabilization energy for the gas phase species is very large, on the order of 500 
kcal/mol (400 kcal/mol for sulfides and sulfates).  The energies are probably similar 
because of this large contribution to the energy from solvation.  At the same time, the 
geometries of the highly charged anions are at a deep well in the geometry potential 
energy surface and do not change much when placed in the CPCM.  It is likely that 
because there is not much of a difference in geometries the CBS-QB3 energies are 
similar between the different ways of approximating solvation.
155
However, if we compare the results in Table 6.2 and Table 6.3 with the ones that we 
find in experimental references, we see that there are some discrepancies, especially 
for pKa2s and pKa3s.  This is to be expected, as the theory is more strained in these 
cases.  The data, however, does show the proper trends for each of the species.  This 
suggests that we can find a relation of some sort between the two.
We therefore prepared Figures 6.8 and 6.9, which illustrate both sets of data, 
experimental and theoretical.
Figure 6.8: Graphs of experimental versus theoretical pKas for As(V) and P(V) 
systems.
156
When plotting the experimentally and theoretically determined data against each 
other, we can see a clear linear relation between the two, as illustrated in Figure 6.8 
and Figure 6.9.  The difference in these two cases is smallest in magnitude when we 
compare the CBS-QB3 calculations which were prepared in the polarizable 
continuum to the experimental ones.  These points also had the  linear regression 
fitting the two types of data together, with an r2 value of 0.952 for the non explicitly 
solvated system and one of 0.974 for the explicitly solvated one.
Figure 6.9: Linearity in results calculated with CCSD(T) methods compared to the 
results from systems calculated via CBS-QB3 in the CPCM.
157
This linearity was also observed in our high level CCSD(T)/6-311G(2d,p) calculation 
as well as our CCSD(T)/aug-cc-pVDZ results, although the data spectacularly failed 
in the former case when optimized in the CPCM, and in the latter when optimized 
without.  These data are summarized in Table 6.4 below.
Table 6.4: Linear Extrapolations for phosphoric and arsenic acids calculated from 
previous pKa tables.
As we can see, the results from charged couple theory with the relativistically 
corrected core effective potential basis set, CCSD(T)/CEP-121G, also compare 
favorably, although their r2 values are not as good, at 0.923 and 0.907.
Visual observation of the linear extrapolations in Figure 6.8, Figure 6.9 lets us 
observe the error in CBS-QB3 CPCM with explicit hydration with water is the 
method with the smallest evident error, and this is confirmed by the data in Table 6.4, 
where we see that it has an r2 value of 0.974, which is basically equivalent to the 
CCSD(T)/6-311G(2d,p) result, but with a much flatter slope.
158
We can use the extrapolations determined from the known H3PO4 and H3AsO4 data to 
fit pKa1, pKa2, and pKa3 values for each of the two types of solvation, CPCM with 
and without explicit hydration, for H3AsO3, H3AsS4, H3AsS3, and H2SO4.  The results 
for the CBS-QB3 CPCM pKa's with explicit solvation are tabulated in Table 6.5 
below.  This corrective extrapolation would account for any systematic differences 
from other approaches caused by our particular choice of H+ solvated ion energy or 
our choice of method.  This extrapolation therefore appears as Equation 6.2, below:
(6.2) pKaexpt = 0.429 pKaCBS-QB3 CPCM w/H2O ? 0.233
Table 6.5: Fitted pKas for each polyprotic acid species using the linear extrapolation.
159
Of the pKas from the experimental system used to fit the data, we see errors of 0.6, 
0.3, and 0.9 pKa units for H3AsO4, and 0.3, 1.2, and 0.3 pKa units for H3PO4. 
Experimental data which we retrieved after producing the extrapolation fared 
similarly, with errors of 4.5 for the known H3AsO3 point, and 0.7 and 0.9 for H2SO3, 
another polyprotic acid system which is well characterized.  These errors are on the 
order of 5 to 30 percent of the raw values, but if we consider the amount of 
improvement with the fitting than without, the improvement is quite dramatic, with 
errors in the theoretical pKas around double or triple the magnitudes of the data in the 
worst cases.  
Unfortunately, there was a lack of experimental data for similar polyprotic acids to 
compare to the H3AsO3, H3AsS3, and H3AsS3.  We would therefore expect the results 
not to be as good as the chemical environment would be different between both oxy- 
and thio- acids as well as the different oxidation states of arsenic.  However, the small 
polyatomic clusters do have a structural similarity that should allow the extrapolation 
to be of some help.  We see this with our data for H3AsO4, which shows the largest 
error of all the known points.  The results for H2SO3, which were not used in 
constructing the extrapolation are much closer, within one pKa unit of the measured 
experimental values after applying the correcting factor.
160
Although the linear relation for the CCSD(T) calculation with the 6-311G(2d,p) basis 
has a (barely) better r2 value than the explicitly hydrated CBS-QB3 CPCM value we 
settled upon, a visual examination of the data shows that the latter has definite 
advantages over the CCSD(T) data.  As the slope of the correction is much greater, it 
indicates that the CCSD(T) method is less correct in this case.  However, the 
CCSD(T)/aug-cc-pVDZ data also shows almost the same quality of result as the 
CCSD(T)/6-311G(2d,p) one.
6.4 Conclusions
Therefore, we would recommend use of the CBS-QB3 CPCM with explicit hydration 
approach for calculating pKa values in this situation.  The results have been shown to 
be more reliable than calculations done without the correction factor, and though the 
accuracy is definitely lower for trioxides (and presumably the sulfates and sulfides), it 
is sufficient for producing semiquantative predictions of second and third pKas.
From our results, we would predict that H3AsS3 is likely to be deprotonated at least 
twice for species in solution near pH 7, and it is likely that H3AsS4 will be fully 
deprotonated in solutions buffered near the netural point, existing purely as AsS43-. 
H3AsO3 is predicted to exist primarily in singly deprotonated form for most of the 
neutral range up to pH 12.
Further study of H3AsS3  would be a reasonable next step.  Molecular mechanics 
calculations could yield an ensemble of average geometries which might be of aid in 
161
finding a distribution of energies in an explicit solvent.  From our calculations, we 
would expect that the presence of more explicit water molecules would lead towards 
a geometry for the anionic species closer to that of the original, fully protonated 
species, lowering the cost of dissociation.
We would recommend to laboratories without a dedicated theoretician to do an 
HF/6-311G optimization calculation in the gas phase first, then follow that up with 
the CBS-QB3 / CPCM calculation as described in the text.  From our experience, the 
initial Hartree-Fock calculation will quickly yield an optimized geometry sufficiently 
close to the B3LYP / CBSB7 optimized geometry that the CBS-QB3 calculation will 
converge quickly and without undue difficulty.
6.5 Acknowledgements
NSF Grant EAR0539109 supported the research in this chapter, which is based on the 
J. Phys. Chem. A paper by Zimmermann and Tossell[3] which is part of a trio of 
works with G. R. Helz who suggested the arsenic system for study.  We would like to 
also acknowledge G. R. Helz for many interesting afternoon discussions of arsenic 
systems detailed in this work.
162
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165
Chapter 7:  HClOx ab initio calculations in the CPCM with 
previously explored fitting and counterions
In this chapter we examine some properties of different perchloric, chloric, chlorous, 
and hypochlorous acids using the fitting system developed in the previous chapter. 
The fit is also shown with counterions present to reduce the total charges in the 
calculation.
7.1 Introduction
In this case we are interested in the deprotonation of HClOx compounds, with x=1 to 
4.  Perchloric acid, HClO4, is one of the strongest acids, with an experimental pKa of 
-10[1] at 70% concentration in liquid sulfur dioxide, and a gas phase association 
energy of 1180 kJ/mol[2]. Our calculations will explore the dissociation chemistry of 
HClO4, HClO3, HClO2, and HClO from an ab-inito point of view. Chloric acid, 
HClO3, has an experimental pKa of -1[3], chlorous acid has a pKa of 1.96[4], and 
hypochlorous acid a pKa of 7.497[5].
Perchloric Acid deprotonation was also examined by another group in 2008[6], who 
showed that a CBS-QB3 calculation[7-9] was sufficient for calculating pKas for 
HClO4.  In that paper, they use a variety of theoretical approaches, approaching their 
experimental measurement of pH -10 generally within 1 kcal/mol. Chloric and 
166
perchloric acids heats of formation were also previously reviewed[10] using G2 
theory[11], but counter-ions were not used in either case.
7.2 Methods
We calculated both gas phase and solvated geometries and energetics with Gaussian 
03[12] using MP2[13] and B3LYP[14] with the CBSB7 basis[7], and also conducted 
CBS-QB3 calculations[7-9] under the same conditions.  For each gas phase B3LYP 
geometry, we calculated the energy of solvation using CPCM[15-17] with Hartree-
Fock orbitals determined with the 6-31G, 6-31G**, and 6-31+G** basis sets.
The Gibbs Free Energy of reaction is then calculated for each of the methods for each 
of the deprotonation reactions.  The gas phase calculated energies were combined 
with the HF/6-31+G** calculated solvation energies, and an H+ (aq) solvation energy 
of 269.0 kcal/mol was used for the calculations.
No additional basis functions were added to either the CBSB7 basis sets or the 6-31G 
series basis sets in this calculation.
7.3 Results and Discussion 
Calculated energies of solvation and sums of electronic and thermal Free Energies (in 
Hartrees) for each species appears in Table 7.1 below.
167
Table 7.1: Calculated Gas-phase solvation energies and Free Energies for (H/Na)ClOx 
(x=1 to 4).  Systems which were CPCM solvated during the calculation on the right 
are marked SCRF (Self Consistent Reaction Field ? CPCM is the type of SCRF we 
used).
From these data, we can calculate deprotonation energetics for each species with two 
different types of solvation.  Solvation calculated by adding the gas phase solvation 
energy calculated with the HF method, and solvation calculated at the same time. 
The results appear in Table 7.2 below:
Table 7.2: Deprotonation reaction energies in kcal/mol for solvated system calculated 
both at SCRF and gas phase geometry with solvation energy added in.
168
HF Sum of Electronic and thermal Free Energies (Hartrees)
DeltaG (solvation) (kcal/mol) MP2 CBS-QB3 Free Energy B3LYP
6-31+G** 6-31G 6-31G** SCRF (no SCRF) SCRF (no SCRF) SCRF (no SCRF)
NaClO -29.71 -31.23 -28.48 -696.820017 -696.765733
HClO -5.81 -6.73 -5.52 -535.276815 -535.266005 -535.456340 -535.445790 -536.024040 -536.012998
ClO- -70.38 -71.04 -71.62 -534.787752 -534.672064 -534.991375 -534.878292 -535.543241 -535.428596
NaClO2 -22.85 -23.71 -21.44 -771.607165 -771.566866 -771.892604 -771.849173 -772.969062 -772.930156
HClO2 -10.71 -12.28 -9.83 -610.224103 -610.211089 -610.507065 -610.492406 -611.154246 -611.139540
ClO2- -67.47 -68.49 -68.27 -609.752524 -609.644066 -610.064243 -609.958804 -610.691112 -610.583528
NaClO3 -26.76 -29.08 -25.72 -846.619184 -846.568050 -847.002461 -846.940452 -848.149434 -848.104492
HClO3 -9.24 -12.57 -8.76 -685.221764 -685.210979 -685.596667 -685.583420 -686.320960 -686.307633
ClO3- -63.41 -65.98 -64.28 -684.773719 -684.673270 -685.178457 -685.079909 -685.880324 -685.779604
NaClO4 -27.69 -30.55 -27.15 -921.624532 -921.570212 -922.097531 -922.036657 -923.313772 -923.261055
HClO4 -9.69 -13.82 -9.57 -760.213787 -760.199508 -760.676010 -760.659924 -761.472749 -923.261055
ClO4- -56.68 -57.43 -57.51 -759.792178 -759.700054 -760.276303 -760.184317 -761.058762 -760.965657
MP2 CBS-QB3 Free Energy B3LYP
269 SCRF Gas phase + SCRFSCRF Gas phase + SCRFSCRF Gas phase + SCRF
37.89 39.13 22.77 22.53 32.70 33.14
HClO2 ? H+ + ClO2- 26.92 30.05 8.87 9.08 21.62 23.14
HClO3 ? H+ + ClO3- 12.15 14.24 -6.57 -7.22 7.50 8.17
HClO4 ? H+ + ClO4- -4.44 -2.58 -18.18 -17.55 -9.22 -7.52
H+ (aq) kcal/mol
HClO ? H+ + ClO-
As seen in Table 7.2, the calculated energetics are generally one or two kcal/mol less 
favorable when done in the faster Gas Phase + SCRF approach.
The most interesting difference here is perhaps the CBS-QB3 energy calculations 
when compared to the MP2 and B3LYP.  With the complete basis set extrapolation, 
the deprotonation for HClO3 is favorable in solvated conditions.  This is as expected, 
because the experimental pKas are negative as well, although the calculated 
dissociation is more favorable than the experimental measurements indicate. 
Table 7.3: Calculated pKas for each HClOx acid.  pKa is the change in Gibbs Free 
Energy / 1.3644.
The calculated pKas in this case are similar to the others which we found for the 
phosphoric acid in arsenic, and arsenous acids discussed in the previous chapter in 
that both the favorable and unfavorable pKas were overestimated.  However, the 
basic pKas were relatively close to the experimental measurements in both the HClO4 
and HClO cases when using the CBS-QB3 method.
Using the approximation which we calculated for that data set, Equation (7.1) below, 
we have the following adjusted results in Table 7.4.
169
MP2 CBS-QB3 Free Energy B3LYP
SCRF Gas phase + SCRF Gas phase + SCRF Gas phase + SCRF
7.5 27.77 28.68 16.69 16.52 23.97 24.29
1.96 HClO2 ? H+ + ClO2- 19.73 22.02 6.5 6.65 15.84 16.96
-1 HClO3 ? H+ + ClO3- 8.9 10.44 -4.82 -5.29 5.5 5.99
-10 HClO4 ? H+ + ClO4- -3.25 -1.89 -13.33 -12.86 -6.76 -5.51
pKa values
Expt. pKa
HClO ? H+ + ClO-
(7.1) pKafitted = 0.429 pKaCBS-QB3 ? 0.233
 As the fitting was made to be used with CBS-QB3 calculations, and the most 
applicable columns have been bolded in the table below.
Table 7.4: HClOx pKas as fitted by adjustment method.
In all cases except for HClO4  the results show a decided improvement.  The 
percentage errors for each point are reproduced in Table 7.5 and Table 7.6 below.
Table 7.5: Percent error in unfitted HClOx pKas
Table 7.6: Percent error in fitted pKa values
Although the percentage errors increase in the case of the HClO4 values compared 
with experiment, in the other cases the quality of the answer improved to well within 
170
MP2 CBS-QB3 Free Energy B3LYP
SCRF Gas phase + SCRF Gas phase + SCRFSCRF Gas phase + SCRF
7.5 11.66 12.05 6.9 6.83 10.03 10.16
1.96 HClO2 ? H+ + ClO2- 8.21 9.19 2.53 2.6 6.54 7.02
-1 HClO3 ? H+ + ClO3- 3.56 4.22 -2.33 -2.53 2.1 2.31
-10 HClO4 ? H+ + ClO4- -1.66 -1.07 -5.98 -5.78 -3.16 -2.62
Fitted pKa values
Expt. pKa
HClO ? H+ + ClO-
MP2 CBS-QB3 Free Energy B3LYP
SCRF Gas phase + SCRFSCRF Gas phase + SCRFSCRF Gas phase + SCRF
-55% -61% 8% 9% -34% -36%
HClO2 ? H+ + ClO2- -319% -369% -29% -32% -234% -258%
HClO3 ? H+ + ClO3- 456% 522% -133% -153% 310% 331%
HClO4 ? H+ + ClO4- 83% 89% 40% 42% 68% 74%
Fitted pKa value % Error Calculations
HClO ? H+ + ClO-
MP2 CBS-QB3 Free Energy B3LYP
SCRF Gas phase + SCRFSCRF Gas phase + SCRFSC F Gas phase + SCRF
270% 283% 123% 120% 220% 224%
HClO2 ? H+ + ClO2- 906% 1024% 232% 239% 708% 765%
HClO3 ? H+ + ClO3- -990% -1144% 382% 429% -650% -699%
HClO4 ? H+ + ClO4- -67% -81% 33% 29% -32% -45%
pKa% Error Calculated Values
HClO ? H+ + ClO-
an order of magnitude of the correct result.  Keeping in mind that the extrapolation 
was made for CBS-QB3 SCRF calculations, these results are quite satisfactory.
Examining the CBS-QB3 results, with the fitting the error ranges from an absolute 
value of 8% to 133% in the case of the explicitly solvated calculation, and 9% to 
153% for the calculation done separate from the solvation stabilization calculation. 
At the same time, when the calculations were not fitted the errors went from 33% to 
382% for the SCRF stabilized CBS-QB3 calculation, and with the stabilization 
calculation done separately the absolute error ranged from 29% to 429%.  In each 
case, the maximum error appeared in the HClO3 calculation, although the smallest 
error was in the HClO4 in the non fitted case and in the HClO calculation in the fitted 
case (thought the HClO4 results were slightly worse after fitting).
Comparing the different methods, we can easily see from Table 7.5 that the greatest 
errors occurred in the MP2 calculation, and while the B3LYP calculations were off by 
less, they were still not as good as the CBS-QB3 calculations.
As an alternative to the equation with unbalanced charges, we also did the same 
calculations with Na+ counterions.  This allowed us to balance the charge difference 
on each side of the deprotonation equilibrium as follows:
Na+ + HClOx ? H+ + NaClOx
171
This structural change makes the sum of squares of charges on both sides equal, 
which should make it easier for the models to handle the reaction energies more 
effectively, thereby reducing errors in the calculation by a large amount.
Table 7.7: ?Grxn Reaction energies (kcal/mol) for counterion-assisted calculations.
One of the first things which we notice here is that the additional Na+ ion is causing 
something to go wrong with our B3LYP calculations.  The reaction energetics all 
appear to have approximately 270 kcal/mol more stability for the products predicted 
than the other calculations.  This extra energy seems to be appearing in the raw 
energy calculations for the NaClOx compounds listed in Table 7.1 (1 Hartree is 
approximately 627.5 kcal/mol), although direct comparison between B3LYP and 
HF/MP2 methods is not possible.
However, the energetics from the MP2 and CBS-QB3 calculations appear similar to 
the ones done without the counterion, so we shall focus on those results below.
Next, we will examine the data represented in pKa form both with and without the 
extrapolation constructed previously for the CBS-QB3 SCRF calculations.
172
Reaction Energies MP2 CBS-QB3 Free Energy B3LYP
269 SCRF Gas phase + SCRF Gas phase + SCRF Gas phase + SCRF
437162.94 437132.25 21.03 24.57 437631.82 437600.99
Na+ + HClO2 ? NaClO2 + H+ 8.86 13.84 7.31 13.22 -262.06 -259.02
Na+ + HClO3 ? NaClO3 + H+ -0.15 7.65 -5.40 7.68 -270.63 -268.31
Na+ + HClO4 ? NaClO4 + H+ -8.51 -1.38 -15.27 -5.17 -278.51 -273.16
H+ (aq) kcal/mol
Na+ + HClO ? NaClO + H+
Table 7.8: Calculated and experimental pKa values for each counterion-assisted 
HClOx calculation.
Table 7.9: HClOx pKa values fitted by the previously developed linear extrapolation.
The best data is clearly the uncorrected CBS-QB3 predicted pKas.  While the trends 
are reproduced in the MP2 calculation as well, the results aren't as close to the correct 
answers.  The easiest way to compare the results is by examining the percentage 
errors on each.
Table 7.10: % error in directly calculated HClOx pKa values versus experimental 
measurements.
The errors for the MP2 and CBS-QB3 calculations are quite good when done in the 
SCRF.  The uncorrected absolute errors compiled in Table 7.10 range from 231% to 
173
MP2 CBS-QB3 Free Energy
SCRF Gas phase + SCRFSCRF Gas phase + SCRF
7.5 320406.73 320384.24 15.41 18.01
1.96 Na+ + HClO2 ? NaClO2 + H+ 6.5 10.15 5.36 9.69
-1 Na+ + HClO3 ? NaClO3 + H+ -0.11 5.61 -3.96 5.63
-10 Na+ + HClO4 ? NaClO4 + H+ -6.24 -1.01 -11.19 -3.79
pKa values
Expt. pKa
Na+ + HClO ? NaClO + H+
MP2 CBS-QB3 Free Energy
SCRF Gas phase + SCRF SCRF Gas phase + SCRF
7.5 137476.65 137467.01 6.35 7.47
1.96 Na+ + HClO2 ? NaClO2 + H+ 2.53 4.1 2.04 3.9
-1 Na+ + HClO3 ? NaClO3 + H+ -0.3 2.15 -1.96 2.16
-10 Na+ + HClO4 ? NaClO4 + H+ -2.93 -0.69 -5.06 -1.88
Fitted pKa values
Expt. pKa
Na+ + HClO ? NaClO + H+
MP2 CBS-QB3 Free Energy
SCRF Gas phase + SCRF SCRF Gas phase + SCRF
4273699% 4273399% 106% 140%
Na+ + HClO2 ? NaClO2 + H+ 231% 418% 173% 394%
Na+ + HClO3 ? NaClO3 + H+ -89% -661% 296% -663%
Na+ + HClO4 ? NaClO4 + H+ -38% -90% 12% -62%
pKa% Error Calculated Values
Na+ + HClO ? NaClO + H+
38% for the MP2 calculation done in the SCRF, while the uncorrected error for CBS-
QB3 in the SCRF ranges from 296% to 12%.  This is less than the corresponding 
error for the unfitted data calculated without the Na+ counterion shown in Table 7.5; 
in the MP2 case it ranged from 990% to 67%, and for the CBS-QB3 calculation it 
went from 382% to 33%.
Unfortunately, for the gas phase ion + stabilization energy calculations the results tell 
a different story.  Although in both cases the counterion calculations showed 
improvement in overall accuracy, the change isn't as pronounced.
In the direct calculation of the pKa the percent errors from Table 7.5 are similar or a 
little worse for both of the methods, with an absolute error in the MP2 method of 
1144% to 81%, and the CBS-QB3 calculation from 429% to 29%.  The results with 
the counterion are not this good, with absolute errors ranging from 661% to 90% for 
the MP2 calculation, and 663% to 62% for the CBS-QB3 calculation as shown in 
Table 7.10.
Table 7.11: % error in fitted pKa values compared to experimental measurements.
174
MP2 CBS-QB3 Free Energy
SCRF Gas phase + SCRF SCRF Gas phase + SCRF
1833658% 1833529% 15% 0%
Na+ + HClO2 ? NaClO2 + H+ -29% -109% -4% -99%
Na+ + HClO3 ? NaClO3 + H+ 70% 315% -96% 316%
Na+ + HClO4 ? NaClO4 + H+ 71% 93% 49% 81%
Fitted pKa value % Error Calculations
Na+ + HClO ? NaClO + H+
Although the fitting was not developed with counterions, it performs well in most 
cases except for the CBS-QB3 gas phase + SCRF energy calculation for this series. 
The results for the fitted data is in Table 7.11.
Notably, the quality of the results improved slightly with the fit, but not to the extent 
of the previous calculations.  In Table 7.11 the MP2 SCRF results had absolute errors 
ranging from 29% to 70%, whereas previously the fitted error went from 58% to 
472% in Table 7.6, a decided improvement.  The CBS-QB3 results were similarly 
improved, with errors ranging from 6% to 117% in Table 7.6, while the errors with 
the counterion present went from an absolute error of 4% to 96%.
The calculations done in the gas phase with the SCRF stabilization were not quite as 
good.  The percentage error in the results for MP2 was reduced from 63% to 538% in 
Table 7.6 to 95% to 331% in Table 7.11.  However, the CBS-QB3 calculated results 
had absolute errors of only 7% to 137% previously in Table 7.6, but when the 
counterion was introduced the errors on average increased; although the minimum 
error was reduced to 0% the other errors ranged from 81% to 316%.  In the 
calculation without the counterion the errors were around 40% for the HClO4 and 
HClO2 pKa calculations, but with the counterion they went from 50% to above 90%.
175
Figure 7.1: pKas for each method (including both direct and counterion assisted 
calculation results).
In an ideal case, the points would fall on the diagonal of Figure 7.1 if they were equal 
to the experimental measurements, but we can see that the data is relatively linear in 
all cases.  This is why it is unsurprising that a linear fitting function such as the one 
we developed is effective.
7.4 Conclusions
As we saw, the best results appear in the CBS-QB3 results calculated in the CPCM 
and corrected by the fitting method.  The fitted pKas show the correct trends across 
176
-15 -10 -5 0 5 10
-15
-10
-5
0
5
10
15
20
25
30
MP2 SCRF
Gas phase + SCRF
CBS-QB3 Free Energy 
SCRF
Gas phase + SCRF
B3LYP SCRF
Gas phase + SCRF
the systems and, except for the HClO4 deprotonation, are within 1 pKa unit of the 
experimentally measured values.
The addition of Na+ counterions to balance total charge on either side of the reaction, 
the direct results without fitting showed improvement over the CBS-QB3 CPCM 
calculated values, with pKas which were closer to the experimental measurements 
except for the Na+ + HClO4 ? NaClO4 + H+ reaction.  The experimental trends across 
the series are also reproduced.
The fitting, while not developed with counterions, improved the counterion calculated 
results except for the case of the HClO4 deprotonation.  However, the extreme acidity 
of HClO4 and the difference in experimental conditions (the commonly cited pKa 
was measured in liquid sulfur dioxide[1]) may account for some of the difference in 
our calculated value.
Calculations with explicit solvation would be an interesting topic to explore in this 
area in the future.  It would also be interesting to consider other counterions besides 
Na+, to see if a different one would improve the accuracy of that approach.
7.5 References
177
1. Brownstein, S. and A.E. Stillman, Proton Resonance Shifts of Acids in Liquid 
Sulfur Dioxide. The Journal of Physical Chemistry, 1959. 63(12): p. 2061-
2062.
2. Marcus, Y., The thermodynamics of solvation of ions. Part 2.-The enthalpy of 
hydration at 298.15 K. Journal of the Chemical Society, Faraday Transactions 
1: Physical Chemistry in Condensed Phases, 1987. 83(2): p. 339-349.
3. Kolthoff,  ed.  Treatise  on  Analytical  Chemistry.  1959,  Interscience 
Encyclopedia, Inc.
4. Atkins, P.W. and J.A. Beran, General Chemistry. 2nd ed1990, New York: 
Scientific American Books.
5. Morris, J.C., The Acid Ionization Constant of HOCl from 5 to 35?. The 
Journal of Physical Chemistry, 1966. 70(12): p. 3798-3805.
6. Zhang, J., et al., Theoretical study of pKa for perchloric acid. Journal of 
Molecular Structure: THEOCHEM, 2009. 906(1-3): p. 46-49.
7. Montgomery, J.A., et al., A complete basis set model chemistry. VI. Use of 
density functional geometries and frequencies. Journal of Chemical Physics, 
1999. 110(6): p. 2822-2827.
8. Montgomery, J.A., et al., A complete basis set model chemistry. VII. Use of 
the minimum population localization method. Journal of Chemical Physics, 
2000. 112(15): p. 6532-6542.
178
9. Montgomery, J.A., J.W. Ochterski, and M.J. Frisch, An improved complete 
basis set (CBS) model chemistry. Abstracts of Papers of the American 
Chemical Society, 1996. 211: p. 231-PHYS.
10. Francisco, J.S.,  Ab Initio Characterization of HOClO3 and HO4Cl: 
Implications for Atmospheric Chemistry. The Journal of Physical Chemistry, 
1995. 99(36): p. 13422-13425.
11. Curtiss, L.A., et al., Gaussian-2 Theory for Molecular-Energies of 1st-Row 
and 2nd-Row Compounds. Journal of Chemical Physics, 1991. 94(11): p. 
7221-7230.
12. M. J. Frisch, G.W.T., H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. 
Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. 
M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. 
Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. 
Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, 
H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. 
Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, 
A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. 
Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. 
Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. 
Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, 
S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. 
Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. 
179
Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. 
Wong, C. Gonzalez, and J. A. Pople, Gaussian 03, Revision C.02, 2004, 
Gaussian, Inc., Wallingford CT.
13. Head-Gordon, M., J.A. Pople, and M.J. Frisch, MP2 energy evaluation by 
direct methods. Chemical Physics Letters, 1988. 153(6): p. 503-506.
14. Becke, A.D.,  Density-functional thermochemistry. III. The role of exact 
exchange. The Journal of Chemical Physics, 1993. 98(7): p. 5648-5652.
15. Barone, V. and M. Cossi, Quantum calculation of molecular energies and 
energy gradients in solution by a conductor solvent model. Journal of Physical 
Chemistry A, 1998. 102(11): p. 1995-2001.
16. Barone, V., M. Cossi, and J. Tomasi, Geometry optimization of molecular 
structures in solution by the polarizable continuum model. Journal of 
Computational Chemistry, 1998. 19(4): p. 404-417.
17. Cossi, M., et al., Energies, structures, and electronic properties of molecules 
in solution with the C-PCM solvation model. Journal of Computational 
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180
Chapter 8:  Hg(SH)2 gas phase formation reactions.
In this short chapter we examine several reactions showing Hg(SH)2 species 
formation in the gas phase with a variety of different methods, B3LYP, MP2, CCSD, 
MP3, and MP4.
8.1 Introduction
With mercury and sulfur compounds being detected at places with volcanic activity[1, 
2], a series of calculations on mercury sulfur compounds seemed like an interesting 
line of research.
We therefore conducted a variety of calculations on MeHgSxH (x=1...4, presented 
with the methylmercury results), Hg(SH)2, and other compounds.  In this section we 
shall discuss the results of our Hg(SH)2 gas phase formation calculations.
8.2 Methods
In this section, we examined reactions of formation for Hg(SH)2.  HgSH+, HgSH-, and 
Hg(SH2), modeled with both B3LYP[3], MP2[4], MP3[5], CCSD[6], and MP4[7] 
with a CEP-121G basis set[8-10] sometimes augmented with an extra basis function 
181
for each atom (see below), with single point calculations under the MP4 and CCSD 
methods.
As previously mentioned, further MeHgSH compounds are also discussed in the 
following chapter on methylmercury chemistry.
The CEP-121G basis set was used with and without an extra diffuse basis function, as 
detailed below in Table 8.1, to verify the effects of the extra function on the results. 
In this calculation we are only dealing with singly charged species with the exception 
of Hg2+, so we would expect that the extra basis function would be less important than 
in the polyprotic acid anions which we examined elsewhere.
Atoms Function Type Coefficient
Hg F 0.486
C, S D 0.700
F, Cl, Br, I D 0.650
Table 8.1: Extra diffuse functions used in the calculations in this chapter.
8.3 Results and Discussion
In some cases, computational limitations prevented the calculations from being 
completed in a timely fashion.  This accounted for the empty entries in Table 8.2(a) 
182
below.  However, with the data on hand, we can calculate the energetics for a number 
of gas phase reactions.
Table 8.2(a): HgSH compound free energies of formation.
As expected, the reactions below were all found to be favorable in the gas phase.  In 
cases where charged species were present, the total charge at the end was either the 
same, but spread over more atoms, or reduced.
183
B3LYP CEP121G MP2 CEP121G CCSD CEP121G MP3 CEP121G MP4 CEP121G
HS- -10.772981 -10.575504 -10.587805 -10.584092 -10.587220
HgS -163.910255
HgSH- -164.627721 -163.620367 -163.641318 -163.628021
HgSH+ -164.220624 -163.253038 -163.269724 -163.258158
HgSH2 -175.305547 -174.145182 -174.171829 -174.156028
HgS2H- -174.791619 -173.636030 -173.657019 -173.640733 -173.667945
B3LYP CEP121G* MP2 CEP121G* CCSD CEP121G* MP3 CEP121G* MP4 CEP121G*
HS- -10.784490 -10.655727 -10.671206
HgS -163.922552 -163.200566 -163.195613 -163.180627
HgSH- -164.642643 -163.886935 -163.873446 -163.911717
HgSH+ -164.244865 -163.508380 -163.516523 -163.500578 -163.536769
HgSH2 -175.348527 -174.505940 -174.522862 -174.505643 -174.549480
HgS2H- -174.821540 -173.985038 -173.993562 -173.976121 -174.025625
B3LYP CEP121G MP2 CEP121G CCSD CEP121G MP3 CEP121G MP4 CEP121G
H + . He -2.982260 -2.941150 -2.946254 -2.944716 -2.945727
He (alone) -2.924981 -2.884755 -2.888371 -2.887456 -2.888122
Hg2+ -152.776064 -152.045051 -152.046850 -152.043552 -152.048519
H+ -0.057279 -0.056395 -0.057883 -0.057260 -0.057605
S0 -10.014929 -9.859813 -9.878254 -9.867174 -9.870064
S-2 -9.932134 -9.740315 -9.748820 -9.745876 -9.748243
B3LYP CEP121G* MP2 CEP121G* CCSD CEP121G* MP3 CEP121G* MP4 CEP121G*
H + . He -2.982260 -2.941150 -2.946254 -2.944716 -2.945727
He -2.924981 -2.884755 -2.888371 -2.887456 -2.888122
Hg2+ -152.778206 -152.161998 -152.159227 -152.153976 -152.168062
H+ -0.057279 -0.056395 -0.057883 -0.057260 -0.057605
S0 -10.016473 -9.922550 -9.954233 -9.940476 -9.946566
S-2 -9.932811 -9.803792 -9.817432 -9.815444 -9.819731
Table 8.2(b): HgSH compound gas phase reaction energies with different basis sets.
We can see from Table 8.2(b) above that the most favorable single additions listed are
Hg2+ + HS- ? HgSH+ with an energy going from -395 to -433 kcal/mol, and the 
HgSH+ + S2- ? HgS2H- reaction which is predicted to be favorable to the order of 
400-422 kcal/mol.
The second addition of HS- to Hg2+, going from HgSH+ to HgSH2, is also extremely 
favorable, approximately 195 to 215 kcal/mol.
From reactions (2) and (3) we can see that HgSH- and S0 are about 30 kcal/mol less 
stable than HgS+ and HS-.  If we examine the Lewis electron dot structures of the 
compounds, we see that this makes sense:
Compare (Hg::SH)- and (S:::)0 vs Hg:::S and H:S:::-.
184
B3LYP CEP121G MP2 CEP121G CCSD CEP121G MP3 CEP121G
-421.42 -396.88 -398.51 -395.65
Hg2+ + 2HS-  -> HgSH2 -617.16 -595.57 -595.73 -592.54
-68.01
-93.48 -97.80 -86.25 -91.33
-195.74 -198.69 -197.22 -196.90
-400.89 -403.28 -400.64 -399.53
Sum of Electronic and Thermal Free Energy Changes for reactions (kcal/mol = 627.5 * Hartrees)
Hg2+ + HS- -> HgSH+
HgS + HS- -> HgS2H-
HgSH- + S -> HgS2H-
HgSH+ + HS-  -> HgSH2
HgSH+ + S2- -> HgS2H-
Sum of Electronic and Thermal Free Energy Changes for reactions (kcal/mol = 627.5 * Hartrees)
B3LYP CEP121G* MP2 CEP121G* CCSD CEP121G* MP3 CEP121G* MP4 CEP121G*
Hg2+ + HS- -> HgSH+ -428.06 -433.39 -423.81
Hg2+ + 2HS-  -> HgSH2 -628.34 -647.89 -633.31
HgS + HS- -> HgS2H- -71.85 -80.79 -77.99
HgSH- + S -> HgS2H- -101.92 -110.16 -101.78 -105.01
HgSH+ + HS-  -> HgSH2 -200.28 -214.50 -209.50
HgSH+ + S2- -> HgS2H- -404.02 -422.22 -413.90 -414.21 -419.88
Generally, S is represented in calculations by ring structures of S5 or S6, which satisfy 
the octet rule for each sulfur atom, so the above calculation on the atomic sulfur atom 
is expected to be less favorable than it might be otherwise.  In a future calculation, we 
might consider calculating the energetics for S5 and S6 with these methods, then have 
the Hg group extract the single atom from the sulfur moiety.
With the reaction calculations done, we can compare the favorability of each reaction 
depending on the presence of the diffuse function, and depending on methods.  The 
figures for this comparison are summarized in Table 8.2(c) below:
Table 8.2(c): Additional energy calculated released with additional diffuse basis 
function present.
We can see that the additional diffuse function makes the largest difference when 
considering the Hg2+ + 2 HS- reaction, which makes sense because the two HS- groups 
would be the most stabilized by the additional function.  The total extra favorability 
when calculated with all three methods that both calculations were conducted with is 
nearly double that of the single HS- addition.
185
Additional favorability with additional diffuse basis function.
B3LYP MP2 CCSD MP3
Hg2+ + HS- -> HgSH+ 6.65 36.5 28.16
Hg2+ + 2HS-  -> HgSH2 11.18 52.31 40.76
HgS + HS- -> HgS2H- 3.84
HgSH- + S -> HgS2H- 8.44 12.36 10.45
HgSH+ + HS-  -> HgSH2 4.54 15.81 12.6
HgSH+ + S2- -> HgS2H- 3.14 18.94 13.26 14.68
We can also compare the energies of reaction for the different methods.  This 
information appears in Figure 8.1 below:
Figure 8.1: Calculated energetics for each reaction using different methods.
From this figure, we see that the energetics for each series of reactions without 
diffuse functions added to the CEP-121G basis set show the same basic trends for 
each method, except for B3LYP, where the reactions of HgS + HS- to form HgS2H- 
and HgSH+ + S2- to make HgS2H- are both a bit less favorable than the HgSH- + S0 ? 
HgS2H- reaction and the Hg2+ + HS- ? HgSH+ reactions respectively.
186
-700.00
-600.00
-500.00
-400.00
-300.00
-200.00
-100.00
0.00
Comparative energies of reaction for CEP-121G calculations using various methods
(kcal/mol)
Hg2+ + HS- -> HgSH+
Hg2+ + 2HS-  -> HgSH2
HgS + HS- -> HgS2H-
HgSH- + S -> HgS2H-
HgSH+ + HS-  -> HgSH2
HgSH+ + S2- -> HgS2H-
Method used
Su
m 
of V
ibr
atio
na
l a
nd
 Th
erm
al F
ree
 En
erg
ies
 (kc
al/m
ol)
B3LYP,                        MP2,                       CCSD,                        MP3
However, considering Figure 8.2 below, which shows the same reaction energetics 
with the extra basis functions present, we now see that the MP2 and MP3 methods 
show the same trend as B3LYP, which retained the same energetic relationships 
between the different considered reactions as it had without the extra basis functions 
augmenting the CBS-QB3 basis.
Figure 8.2: Calculated energies of reaction with diffuse basis functions added to the 
CEP-121G basis used in the previous figure.
In each case the reaction was more favorable with diffuse functions present, although 
the effect was the smallest for the B3LYP method, in the smallest cases it was 3-4 
187
-700.00
-600.00
-500.00
-400.00
-300.00
-200.00
-100.00
.00
Energies of reactions for CEP-121G with diffuse basis functions
(kcal/mol)
Hg2+ + HS- -> HgSH+
Hg2+ + 2HS-  -> HgSH2
HgS + HS- -> HgS2H-
HgSH- + S -> HgS2H-
HgSH+ + HS-  -> HgSH2
HgSH+ + S2- -> HgS2H-
Method Used
En
er
gy
 of
 re
ac
tio
n (
kc
al/
m
ol)
B3LYP,                         MP2,                         CCSD,                      MP3,                        MP4
kcal/mol, but the effect was greatest for Hg2+ + 2 HS- ? Hg(SH)2 for the MP2 and 
MP3 methods, where the difference was 40-50 kcal/mol. 
8.4   Conclusions  
An interesting future calculation would be to see if the relationships between the 
different levels of favorability are reproduced in different solvation environments.  As 
higher-charged anions and cations are stabilized to different degrees by solvation, the 
most favorable reactions are often different depending on the solvent.  This would 
also allow us to examine how the reactions behavior changes in undersea conditions 
as might be observed at volcanic vents.
Further calculations involving methylmercury sulfur compounds are also important, 
because the pathways that sulfur-reducing bacteria use to deal with sulfur in their 
environments  have been observed to methylate  elemental  mercury in their 
neighborhoods[11].   We  previously  discussed  in  the  introduction  how  the 
methylmercury compounds were one of the most hazardous for mankind.
8.5 References
1. Cox, M.E.,  Summit outgassing as indicated by radon, mercury and pH 
mapping, Kilauea volcano, Hawaii. Journal of Volcanology and Geothermal 
Research, 1983. 16(1-2): p. 131-151.
188
2. Ferrara, R., et al.,  Atmospheric mercury emission at Solfatara volcano 
(Pozzuoli, Phlegraean Fields - Italy). Chemosphere, 1994. 29(7): p. 1421-
1428.
3. Becke, A.D.,  Density-functional thermochemistry. III. The role of exact 
exchange. J. Chem. Phys., 1993. 98: p. 5648-52.
4. Head-Gordon, M., J.A. Pople, and M.J. Frisch, MP2 energy evaluation by 
direct methods. Chemical Physics Letters, 1988. 153(6): p. 503-506.
5. J. A. Pople, J.S.B., and R. Seeger, Theoretical Models Incorporating Electron 
Correlation. Int. J. Quant. Chem, 1976. S10.
6. ???ek, J.,  On the Use of the Cluster Expansion and the Technique of 
Diagrams in Calculations of Correlation Effects in Atoms and Molecules. 
Advances in Chemical Physics1969: John Wiley & Sons, Inc. 35-89.
7. K. Raghavachari and J. A. Pople, Approximate 4th-order perturbation-theory 
of electron correlation energy. Int. J. Quant. Chem, 1978. 14: p. 91-100.
8. Cundari, T.R. and W.J. Stevens, Effective Core Potential Methods for the 
Lanthanides. Journal of Chemical Physics, 1993. 98(7): p. 5555-5565.
9. Stevens, W.J., H. Basch, and M. Krauss, Compact Effective Potentials and 
Efficient Shared-Exponent Basis-Sets for the 1st-Row and 2nd-Row Atoms. 
Journal of Chemical Physics, 1984. 81(12): p. 6026-6033.
10. Stevens, W.J., et al., Relativistic Compact Effective Potentials and Efficient, 
Shared-Exponent Basis-Sets for the 3rd-Row, 4th-Row, and 5th-Row Atoms. 
189
Canadian Journal of Chemistry-Revue Canadienne De Chimie, 1992. 70(2): p. 
612-630.
11. Baldi, F., Microbial transformation of mercury species and their importance 
in the biogeochemical cycle of mercury. Metal Ions in Biological Systems, 
1997. 34(34): p. 213-257.
190
Chapter 9:  Methylmercury compound chemistry in Aqueous 
Solution
In this chapter we examine a variety of methylmercury chloride and methylmercury 
thiol compounds, comparing relative energetics over several different methods from 
Hartree-Fock to CCSD, and both gas phase and CPCM water solvated conditions, 
and going on to discuss calculated spectra of the species.
9.1 Introduction
Methylmercury compounds offer a distinct interest for us, as they are dramatically 
poisonous, acting as a persistent oxidizer which is concentrated in fatty cells such as 
neural ones, causing permanent and persistent damage to organisms exposed. 
Methylmercury has been blamed in several severe ecological accidents, including one 
in Japan[1, 2] and an incident in Iraq[3].  Current and continuing use of coal burning 
power ensures that the world will have plenty of human-sourced[4] mercury 
compounds floating around for the foreseeable future.
Therefore, further understanding of these compounds would be quite beneficial.
Using theoretical modeling to study methylmercury compounds via computer 
software has a dramatic advantage of safety to the researcher over experimental 
191
laboratory studies.  By using computational chemistry in this way, we can shortcut 
the possibility of an unfortunate laboratory accident abruptly ending our line of 
research[5], and at the same time benefit scientific knowledge.
Our ab initio approach has the advantage of safety over more intimate experimental 
studies, but at the same time it has disadvantages as well.  As we can only focus on 
specific compounds and structures that we have fixed upon in advance, our 
applicability to experimental results can be affected both by the accuracy of 
experimental understanding (of which species are important and present during 
possibly ambiguous measurements) as well as the accuracy of the models.
As previously shown with H3PO4 and H3AsO4 calculations in Chapters 5 and 6, the 
simple and direct use of a CPCM solvation model[6-8], while very useful, has some 
shortcomings as well.  While the pKas calculated for single deprotonations were not 
too far from the experimentally measured pKas, the raw results for further 
deprotonations left somewhat to be desired, although the trends were generally good, 
and we showed how they could be improved.  Also, using CPCM solvation prevents 
any accounting for the interactions that may occur between our compounds of interest 
and the solvent molecules.
Our results here will address both of these possible possible shortcomings as follows.
192
We have some initial support for the qualitative quality of these calculations from the 
results in the previous H3PO4 and H3AsO4 series' results, which solidly reproduced 
trends of the pKas of those species.  By focusing on the differences in energetics 
between the solvated and unsolvated systems, and the relative stabilities of the 
different compounds, we can avoid the problems which we faced in the acidity 
calculations where we depended on precise raw energies.
As previously discussed in the mercury chloride NMR calculations in Chapter 4, in 
HgCl2 and above the effects of explicit hydration on the mercury compounds' NMR 
shieldings were minimal.  This would imply that there are few interactions between 
the solvent molecules and the mercury proper, so the use of CPCM here instead of 
explicit solvation should be acceptable.  Of course in the future, explict solvation of 
these compounds would be a reasonable item to investigate as well.
9.2 Methods
We conducted calculations on MeHgBr, MeHgCl, MeHgF, MeHgI, MeHgSH, 
MeHgS2H, MeHgS3H, and MeHgS4H compounds with four different levels of theory: 
HF[9], MP2[10], B3LYP[11], and CCSD[12], using the CEP-121G Compact 
Effective Potential basis set[13-16] with extra diffuse functions (shown in Table 9.1, 
below):
193
Atoms Function Type Coefficient
Hg F 0.486
C, S D 0.700
F, Cl, Br, I D 0.650
Table 9.1: Extra diffuse functions used in the calculations in this chapter.
194
9.3 Results and Discussion
Compound HF MP2 B3LYP CCSD
MeHgF -183.904536 -184.559852 -185.440527 -184.560058
MeHgCl -174.768980 -175.393869 -176.208113 -175.405348
MeHgBr -173.233131 -173.814946 -174.671765 -173.824920
MeHgI -171.307600 -171.850547 -172.735523 -171.858900
MeHgSH -170.571453 -171.183413 -172.003599 -171.199811
MeHgS2H -180.503454 -181.234340 -182.149031 -181.263312
MeHgS3H -190.443152 -191.295474 -192.303537 -191.336711
MeHgS4H -200.381167 -201.355578 -202.457404 -201.407340
Table 9.2: Sum of Electronic and Thermal Free Energies at 298K  (in Hartrees) 
calculated for each methylmercury species with HF, MP2, B3LYP, and CCSD, 
calculated with the CEP-121G basis set augmented with our additional functions.
Examination of Table 9.2 results in a graphed form allows us to see the following 
trends quite easily as shown in Figure 9.1 below.
195
Figure 9.1: Energies calculated from Table 9.2.
We can see the general trend here that the Hartree-Fock raw energies are the highest, 
while the higher level MP2 and CCSD calculations are slightly lower.  This is as 
expected, because HF is a lower level method that does not take into account some 
sources of additional stabilization that MP2 and CCSD do.
Note that with this basis, CEP-121G, the energies for the different methylmercury 
halides are not in order of mass as would be true for other basis sets.  This is because 
the compact effective potential basis only directly models electrons in the valence 
shell of each atom.
196
HF MP2 B3LYP CCSD
-200
-195
-190
-185
-180
-175
-170
MeHg compound raw energy trends
MeHgF
MeHgCl
MeHgBr
MeHgI
MeHgSH
MeHgS2H
MeHgS3H
MeHgS4H
Method
Ca
lcu
lat
ed
 E
ne
rg
y (
Ha
rtr
ee
s)
CEP basis sets have advantages because they can account for some relativistic effects 
which take place in the inner shells of electrons, but as a side effect the energetics 
cannot be compared directly between different compounds.  However, the differences 
between a variety of compounds can (and shall here) be used to calculate dissociation 
and reaction energetics for a number of reactions.
With just the data in Table 9.2, we can also look at the results fo the MeHgSxH series 
in more detail.    Let's examine the differences in each of the MeHgSxH energies as 
we add more sulfur atoms.
Table 9.3: Energy differences (Hatrees) in adding additional S atoms to the MeHgSxH 
chain.
Examination of Table 9.3 indicate that each addition after the first changed the energy 
by about 6 kcal/mol favorably through going from the 2nd to 3rd addition was a lot less 
of a cumulative difference, having changed by only 1 kcal/mol on average.  We 
would therefore expect that the change in stabilization for additional sulfur atoms in 
197
Difference in adding another S to the S-chain (Hartrees)
HF MP2 B3LYP CCSD
A MeHgSH to MeHgS2H -9.93200100E+000 -1.00509270E+001 -1.01454320E+001 -1.00635010E+001
B MeHgS2H to MeHgS3H -9.93969800E+000 -1.00611340E+001 -1.01545060E+001 -1.00733990E+001
C MeHgS3H to MeHgS4H -9.93801500E+000 -1.00601040E+001 -1.01538670E+001 -1.00706290E+001
Change in that difference in adding an S atom(Hartrees)
A -> B -7.697E-03 -1.021E-02 -9.074E-03 -9.898E-03
B -> C 1.683E-03 1.030E-03 6.390E-04 2.770E-03
Change in difference (kcal/mol   1 Hartree = 627.5 kcal/mol)
A -> B -4.83 -6.4 -5.69 -6.21
B -> C 1.06 0.65 0.4 1.74
the chain would remain small.  The most additional stabilization is gained when going 
from 2 to 3 sulfurs in the Hg-S-SH chain.
We next turn our attention to some calculations on the same systems in a CPCM 
solvated environment.  CPCM solvation models additional stabilization on polar 
systems by placing them in a cavity inside a polarizable continuum.  The results of 
these calculations appear in Table 9.4, below.
HF/CEP-121G CPCM
(Hartrees)
B3LYP/CEP-121G CPCM 
(Hartrees)
MeHgF -183.941568 -185.467233
MeHgCl -174.798515 -176.228814
MeHgBr -173.256549 -174.691642
MeHgI -164.086258 -172.749289
MeHgSH -170.593184 -172.018513
MeHgS2H -180.527589 -182.163634
MeHgS3H -190.467892 -192.320485
MeHgS4H -200.405402 incomplete
Table 9.4: CPCM Solvated HF and B3LYP energies for MeHgX and MeHgSxH 
(X=F, Cl, Br, I,), (x=1...4).
Comparing these results in Table 9.4 calculated under CPCM solvated conditions to 
the ones calculated in the gas phase, the MeHgF and MeHgCl species are calculated 
to be lower energy in the solvated conditions, but the MeHgBr and MeHgI 
compounds are higher energy overall under solvated conditions.  This is probably 
198
because the larger Br and I ions are not electronegative enough to overcome the 
nonpolar methyl group attached to the mercury atom.  This would lead to these 
species preferring solvents which are less polar than water, such as the nonpolar 
environment of the phospholipid bilayers of cells.  This difference in solubility would 
lead us to predict that MeHgF and MeHgCl would be much safer compounds than 
MeHgBr and MeHgI.
The methylmercury linked to the sulfur chains show a similar trend as the less polar 
MeHgBr and MeHgI, with the total free energies of the species pointing to more 
stability in the gas phase than under solvated conditions.  We would therefore predict 
that these would also prefer nonpolar environments such as found in fatty tissue.
To continue, we shall consider the spectra of the above compounds, reproduced 
below in Figures 9.2-9.5.  Discussion follows.
199
Figure 9.2: B3LYP/CEP-121G CPCM IR Spectrum for MeHgF
Figure 9.3: B3LYP/CEP-121G CPCM IR Spectrum for MeHgCl
200
Figure 9.4: B3LYP/CEP-121G CPCM IR Spectrum for MeHgBr
Figure 9.5: B3LYP/CEP-121G CPCM IR Spectrum for MeHgI
These spectra show that the geometry for MeHgI is at a saddle point, and therefore 
the calculated energy is not the minimum for the species.  However, from examining 
the structure it is clear that the cause of this is the eclipsed geometry between the 
halogen atom and the H of the methyl group attached to the central mercury atom, as 
the bond angle between MeHgI is slightly less than 180 degrees, and the I is aligned 
201
to the methyl hydrogen.  The vibrational mode is reproduced below in Figure 9.6, and 
bears out this hypothesis:
Figure 9.6: B3LYP/CEP-121G CPCM Imaginary Mode for MeHgI.
Several of the MeHgSxH geometries suffer from the same issue, as seen in the 
following Figures 9.7 and 9.8.  These peaks appear as negative ones in the solvated 
spectra shown in Figures 9.9 through 9.11 below:
202
Figure 9.7: Typical imaginary mode for eclipsed conformation of MeHgSxH as seen 
in MeHgSH (B3LYP/CEP-121G CPCM)
Figure 9.8: Typical imaginary mode for MeHgS2H
203
Figure 9.9: MeHgSH IR Spectra (B3LYP/CEP-121G CPCM)
Figure 9.10: MeHgS2H IR Spectra (B3LYP/CEP-121G CPCM)
Figure 9.11: MeHgS3H IR Spectra (B3LYP/CEP-121G CPCM)
204
Now, let us consider the calculations on the gas-phase species.  Having calculated 
spectra under B3LYP/CEP-121G in the gas phase as well, we see the following in 
Figures 9.12-9.19:
Figure 9.12: MeHgF IR Spectra (B3LYP/CEP-121G)
Figure 9.13: MeHgCl IR Spectra (B3LYP/CEP-121G)
Figure 9.14: MeHgBr IR Spectra (B3LYP/CEP-121G)
205
Figure 9.15: MeHgI IR Spectra (B3LYP/CEP-121G)
Figure 9.16: MeHgSH Spectra (B3LYP/CEP-121G)
Figure 9.17: MeHgS2H Spectra (B3LYP/CEP-121G)
206
Figure 9.18: MeHgS3H Spectra (B3LYP/CEP-121G)
Figure 9.19: MeHgS4H Spectra (B3LYP/CEP-121G)
Comparing the gas phase and CPCM calculated MeHgF systems in turn in Figure 9.2 
and 9.12, we see the most dramatic differences in the stretching mode (see Figure 
9.20 below) that appears at 518 cm-1 in the gas phase system and at 460 cm-1 in the 
solvated calculation.
207
The relative intensity of this stretching mode is dramatically larger in the solvated 
system, with a normalized intensity slightly more than five times larger in the 
solvated case.  This would make sense because as F is very electronegative, we would 
expect that the stabilization from solvation would make changing the bond length not 
as expensive, because the Hg-F dipole would be exposed to more of the stabilizing 
(modeled) solvent.
The asymmetric stretching mode which appeared at 583 cm-1 in the gas phase 
calculation and 536 cm-1 in the solvated system was comparatively half as intense in 
the normalized solvated IR spectrum as the peak was in the gas phase calculation.
Figure 9.20: MeHgF Symmetric Stretching Mode displacement vectors from 
B3LYP/CEP-121G CPCM calculation
208
The other modes of interest involving the Hg atom are the two bending modes, which 
appear at 158 cm-1 in the gas phase and around 140 cm-1 in the solvated system.  The 
CPCM solvated system has a relative intensity which is about four times greater than 
the gas phase calculation's intensity.
Moving on to the MeHgCl calculations shown in Figure 9.3 and 9.13, we see the 
differences between the solvated and unsolvated gas phase systems are a lot less 
pronounced.  The symmetric stretch which appears at 332 cm-1 in the gas phase 
moves to 278 cm-1 in the CPCM solvated system, but the relative intensity is only 
twice as much in the solvated system compared to the gas phase calculation's 
normalized intensity.  In the MeHgF calculation the difference was a factor of five.
The asymmetric stretch for MeHgCl has nearly the same intensity in both cases, 
appearing at 520 cm-1 in the gas phase calculation and 503 cm-1 in the CPCM solvated 
calculation.  Intensities differ by only about 15%.
The bending modes are also much closer together, appearing at 118.5 cm-1 in the gas 
phase calculation and 105 cm-1 in the solvated calculation.  Here there is a significant 
intensity difference; in the gas phase the relative normalized intensity is about seven 
times smaller than the solvated system.
209
For the MeHgBr system shown in Figure 9.4 and 9.14, the differences are similar to 
those observed in the MeHgCl calculation.  For the symmetric stretch, we see that the 
expected difference in intensities and base frequencies, with the solvated symmetric 
stretch at 178 cm-1 having just about twice the normalized intensity of the gas phase 
symmetric stretch that appears at 223 cm-1.
The asymmetric stretch, which appears at 511 cm-1 in the gas phase and 488 cm-1 in 
the solvated system, is almost entirely the vibration of the -CH3 methyl group towards 
the central Hg atom, continuing the trend we saw start with the MeHgCl calculation, 
where as the vibrational modes became more distilled towards the two separate 
vibrations as opposed to symmetric and asymmetric we saw the difference between 
the frequencies grow from its initial difference of 65 cm-1 for MeHgF to 188 cm-1 for 
MeHgCl and 288 cm-1 for MeHgBr.
The bending modes appear for MeHgBr at 106 cm-1 in the gas phase, but in the 
solvated system the modes are at 64 and 79 cm-1, although their intensities are 
significantly greater as well, with the normalized intensities about 60 times larger 
than the bending mode intensities in the gas phase.
For the MeHgI system which appears in Figure 9.5 and 9.15, we see the former 
symmetric stretch, which is now almost completely an Hg-I stretch, at 173 cm-1 in the 
gas phase and at 139 cm-1 in the solvated system.  In this case, the solvated system 
210
was at a saddle point, and the stretching mode for Hg-I also contains a slight amount 
of I-Hg-Me bending as well.  The intensities differ by slightly more than a factor of 
two, with the mode more intense in the solvated system.
The Hg-Me stretch appears at 501 cm-1 in the gas phase calculation and at 465 cm-1 in 
the solvated B3LYP/CEP-121G calculation, with normalized intensities which are 
basically the same, differing by about 10% (with the solvated system being more 
intense).
Due to the saddle point in the solvated MeHgI calculation, one of the bending 
frequencies is not calculated.  The remaining one, however, appears at 92 cm-1, while 
in the gas phase the bending appears at 98 cm-1.  The difference in intensities is even 
greater here, with the normalized CPCM-solvated aqueous phase intensity being 
about 65 times greater than the corresponding gas phase intensity.
Turning our attention to the MeHgSxH series of compounds, we would expect to see a 
similar trend as the sulfur chain lengthens.
Starting with MeHgSH, and comparing Figure 9.9 and Figure 9.16 we observe that 
the symmetric and asymmetric stretches appear at about the same places as they did 
for the MeHgCl system.  This makes reasonable sense because the Cl has a molar 
mass of about 35 g/mol and the -SH group has a similar molar mass of 33 g/mol. 
211
With a bond of similar strength, one would expect that the vibrational modes would 
be calculated to be the same.
The symmetric stretch for MeHgSH, which mostly consists of the Hg-SH bond 
stretching, appears at 321 cm-1 in the gas phase calculation and 271 cm-1 in the 
solvated calculation.  The normalized intensity is about twice as much in the solvated 
system as it is in the gas phase calculation.
The asymmetric stretch appears at 508 cm-1 in the gas phase calculation for MeHgSH, 
and at 478 cm-1 in the solvated calculation.  The intensity is about 1.6 times larger in 
the solvated system than the non-solvated one.
With these MeHgSxH calculations, there were often minor saddle points that did not 
significantly affect the overall energy.  However, these did affect the predicted 
vibrational frequencies, leaving us with only one solid bending mode in the predicted 
spectrum for solvated MeHgSH.  This appears at 66 cm-1, where in the gas phase the 
bending modes appear at 117 cm-1.  The relative intensities are dramatically different, 
with the solvated system having about 18 times as intense a bending peak on its 
spectrum as the normalized gas phase calculation's.
In the MeHgSH calculation, there is a bending mode between Hg-S-H which appears 
at 652 cm-1 in the gas phase and 616 cm-1 in the solvated calculation.  This mode is 
212
relatively more intense in the gas phase calculation, with an intensity about 1.4 times 
as strong as the normalized solvated bending mode.
Moving on to Figure 9.10 and 9.17, of MeHgS2H, its Hg-S bond stretching mode 
appears at 316 cm-1 in the gas phase and 281 cm-1 in the solvated system.  The 
intensities differ by a factor of 2.
The asymmetric stretch of mostly the Me-Hg bond appears at 506 cm-1 in the gas 
phase and 490 cm-1 in the solvated system.  The relative intensities are similar, with a 
difference of maybe 1.5 times.
Because the MeHgS2H system is not axially symmetric, the two bending modes 
separate quite dramatically, with the gas phase modes appearing at 113 cm-1 and 69 
cm-1, while the solvated ones appear at 106 cm-1 and 68 cm-1.  The relative intensities 
differ by a factor of slightly more than 5 in each case.  The bending mode 
perpendicular to the Hg-S-S plane at 69 cm-1 and 68 cm-1 is about 4 times as intense 
as the in-plane mode (at 113 cm-1 and 106 cm-1) in both cases.
The S-H bending mode perpendicular to the S-S bond appears at 262 cm-1 in the gas 
phase and 221 cm-1 in the solvated system, with a normalized intensity about double 
the gas phase intensity in the B3LYP/CEP-121G CPCM case.  This dramatically 
lower frequency is probably due to the stabilizing effect of the H atom's interactions 
213
with the previous sulfur in the chain, which was not present in MeHgSH.  The S-H 
bending mode parallel to the S-S bond appears at 866 cm-1 in the gas phase 
calculation and 857 cm-1 in the solvated system, confirming this evaluation.  It's 
intensity is half that of the parallel mode in the gas phase case, and a third of the 
parallel mode in the solvated case.
The S-S stretching mode appears at 463 cm-1 in the gas phase calculation and 466 cm-
1 in the solvated calculation.  Although the normalized bond stretching intensities are 
small, they differ by a factor of two as well.
For the MeHgS3H calculated spectra, which appear in Figure 9.11 and 9.18, the Hg-S 
bond stretching mode appears at 299 cm-1 in the gas phase and 263 cm-1 in the 
solvated system.  In both cases the mode includes vibrations of the H atom attached to 
the sulfer chain tail as well.  The relative normalized intensity for the solvated system 
is approximately double that of the non-solvated system.
The Me-Hg bond stretching mode appears at 506 cm-1 in the gas phase calculation 
and at 486 cm-1 in the solvated calculation.  The intensity differs by a factor of about 
1.3, with the solvated system having a greater intensity.  This mode as it appears here 
was pretty much unaffected by the additional S atoms in MeHgS2H and MeHgS3H 
compared to MeHgSH, which is somewhat expected, as there should not be much 
interaction between the Me group and the sulfur chain.
214
The bending modes for MeHgS more-or-less perpendicular to the first S-S bond 
appear at 107 cm-1 in both the gas phase and the solvated case.  For the parallel 
bending mode, the Me-Hg-S bend appears at 71 cm-1 in the gas phase and at 96.5 cm-1 
in the solvated system.  In the perpendicular mode, the difference in intensities is 
about 17 times, but in the parallel mode the difference is only a factor of two.
The S-H bending mode perpendicular to the S-S bond appears at 342 cm-1 in the gas 
phase calculation and at 325 cm-1 in the solvated calculation, with a difference in 
intensities of a factor of about 1.8 times.  This mode appears to have mixed with the 
Hg-S asymmetric stretching mode which appears at 299 cm-1 in the gas phase and 263 
cm-1 in the solvated system, as that mode also has H motion perpendicular to its 
immediate S-S bond. The bending modes for S-H parallel to the final S-S bond 
appear at 861 cm-1 and 853 cm-1 in the gas phase and solvated systems respectively, 
with a difference in intensity of about 1.6.
The S-S-S stretching modes become increasingly complex as the S chain lengthens, 
now appearing similar to the traditional stretching modes of H2O.  The S-S-S group 
has an asymmetric mode appearing at 433 cm-1 in the gas phase and 430 cm-1 in the 
solvated calculation's IR spectra.  The normalized intensity in the solvated case is 
approximately double the gas phase intensity.  This mode is shown in Figure 9.21 
below.
215
Figure 9.21: MeHgS3H asymmetric stretching mode calculated in the gas phase under 
B3LYP/CEP-121G.
For MeHgS3H's symmetric S3 stretch, shown below in Figure 9.22, which appears at 
449 cm-1 in the gas phase calculation and at 453 cm-1 in the solvated calculation, the 
intensities differ by a factor of almost ten, with the solvated intensity being the 
greater.
216
Figure 9.22: MeHgS3H symmetric stretching mode calculated in the gas phase under 
B3LYP/CEP-121G.
As the MeHgS4H calculation ran into difficulties for the solvated system, we will 
compare the results of the gas phase spectrum in Figure 9.19 to the corresponding gas 
phase spectrum for MeHgS3H appearing in Figure 9.18 above.
Hg-S bond stretching appears at 313 cm-1, and Me-Hg stretching appears at 506 cm-1 
with a similar intensity to the Hg-S stretch.
For MeHgS4H in our gas phase calculation, we observe Me-Hg-S bending modes at 
108 cm-1 and 121 cm-1.  The mode bending the molecule perpendicular to the first S-S 
bond has a normalized gas phase intensity about twice as large as the parallel mode.
217
The S-H bending modes appear at 328 cm-1 for the perpendicular mode which keeps 
the H distance approximately constant to the second sulfur atom, and at 865 cm-1 for 
the mode parallel to the first S-S bond.  Interestingly, the relative intensities of these 
two gas-phase modes are almost the same, differing by only a factor of 1.3 (though in 
favor of the perpendicular bending mode as we would expect).  The intensities are on 
the same scale as the Hg-Me stretching peak at 506 cm-1.
The S-S bond modes appear at 408 cm-1, 444 cm-1, and 451 cm-1.  The mode at 408 
cm-1 is mostly a stretch of the central two sulfur atoms, and has an intensity about ? 
as large as the two modes involving the outer S atoms.  The largest peak , at 444 cm-1, 
is about 1.3 times the intensity of the Hg-Me stretching peak at 506 cm-1.
9.4   Conclusions  
Overall,  the  key  observations  here  were  the  differing  solubilities  for  the 
methylmercury halides.  Only MeHgF and MeHgCl were polar enough to be 
calculated more stable in CPCM solvation, indicating that these species would 
perhaps be less dangerous than -Br or -I substituted analogues.  All of the MeHgSH 
compounds were less stable in water than in the gas phase, so we would predict that 
they would also prefer nonpolar environments, such as are found in phospholipid 
bilayers of cells.
218
In the future, it would be interesting to conduct more calculations with energies of 
formation in other, less polar solvents, to see at which points the compounds which 
were destabilized by simulated water were most stabilized.  This would shed some 
light on the types of environments which they would gravitate towards.
9.5 References
1. Harada, M., Minimata Disease - Methylmercury Poisoning in Japan Caused 
by Environmental-Pollution. Critical Reviews in Toxicology, 1995. 25(1): p. 
1-24.
2. Takizawa, Y., Understanding minamata disease and strategies to prevent 
further environmental contamination by methylmercury. Water Science and 
Technology, 2000. 42(7-8): p. 139-146.
3. Bakir, F. and e. al., Methylmercury Poisoning in Iraq - Interuniversity Report. 
Science, 1973. 181(4096): p. 230-241.
4. Yan, R., D.T. Liang, and J.H. Tay, Control of mercury vapor emissions from 
combustion flue gas. Environmental Science and Pollution Research, 2003. 
10(6): p. 399-407.
5. Nierenberg, D.W., et al.,  Delayed cerebellar disease and death after 
accidental exposure to dimethylmercury. New England Journal of Medicine, 
1998. 338(23): p. 1672-1676.
219
6. Barone, V. and M. Cossi, Quantum calculation of molecular energies and 
energy gradients in solution by a conductor solvent model. Journal of Physical 
Chemistry A, 1998. 102(11): p. 1995-2001.
7. Barone, V., M. Cossi, and J. Tomasi, Geometry optimization of molecular 
structures in solution by the polarizable continuum model. Journal of 
Computational Chemistry, 1998. 19(4): p. 404-417.
8. Cossi, M., et al., Energies, structures, and electronic properties of molecules 
in solution with the C-PCM solvation model. Journal of Computational 
Chemistry, 2003. 24(6): p. 669-681.
9. Roothaan, C.C.J., New Developments in Molecular Orbital Theory. Reviews 
of Modern Physics, 1951. 23(2): p. 69-89.
10. Head-Gordon, M., J.A. Pople, and M.J. Frisch, MP2 energy evaluation by 
direct methods. Chemical Physics Letters, 1988. 153(6): p. 503-506.
11. Becke, A.D.,  Density-functional thermochemistry. III. The role of exact 
exchange. The Journal of Chemical Physics, 1993. 98(7): p. 5648-5652.
12. ???ek, J.,  On the Use of the Cluster Expansion and the Technique of 
Diagrams in Calculations of Correlation Effects in Atoms and Molecules. 
Advances in Chemical Physics1969: John Wiley & Sons, Inc. 35-89.
13. Stevens, W.J., H. Basch, and M. Krauss, Compact Effective Potentials and 
Efficient Shared-Exponent Basis-Sets for the 1st-Row and 2nd-Row Atoms. 
Journal of Chemical Physics, 1984. 81(12): p. 6026-6033.
220
14. Krauss, M., W.J. Stevens, and H. Basch, Relativistic Effective Potential Scf 
Calculations of Agh and Auh. Journal of Computational Chemistry, 1985. 
6(4): p. 287-295.
15. Stevens, W.J., et al., Relativistic Compact Effective Potentials and Efficient, 
Shared-Exponent Basis-Sets for the 3rd-Row, 4th-Row, and 5th-Row Atoms. 
Canadian Journal of Chemistry-Revue Canadienne De Chimie, 1992. 70(2): p. 
612-630.
16. Cundari, T.R. and W.J. Stevens, Effective Core Potential Methods for the 
Lanthanides. Journal of Chemical Physics, 1993. 98(7): p. 5555-5565.
221
Chapter 10:  Ab-Initio modeling of pH dependant Raman 
Spectra of Myo-Inositol Hexakis Phosphate
Experimental data from Heighton, L.
This chapter discusses calculated Raman spectra of a collection of myo-inositol 
hexakis phosphates in various states of deprotonation and how this compares to the 
experimental spectra.  The calculated Raman spectra are then dissected, with key 
peaks examined and the corresponding vibrational modes matched to the features on 
the experimental spectra.  Changes observed in the experimental spectra upon 
changes in pH are then explained.
10.1 Introduction
An item of interest in environmental and agricultural chemistry is the behavior of 
organic and inorganic phosphates in biological systems, as both organic (determined 
to primarily exist as myo-inositol hexakis phosphate (IHP)) and inorganic phosphates 
are important environmentally.  IHP has been shown to be the a very important, but 
not well understood form of organic phosphate which is the most common source of 
phosphate in the enviornment[1].  It is essential to be able to distingush the organic 
and inorganic forms of phosphates, because plants are unable to use IHP without 
digestion to remove the phosphate groups from the central carbon ring.
222
The various species have been studied previously with NMR[2], Mass Spectral[3], 
and Raman[4, 5]  techniques.  Although Raman spectra of the different forms of IHP 
have been demonstrated experimentally to be quite different, prior treatments of the 
system did not include detailed theoretical studies[4] which could shed additional 
light on the behavior resulting in the observed experimental changes in the spectra 
with pH.
The structure of IHP, shown below in Figure 10.1, has twelve acidic protons present 
that can be removed.  In the interest of explaining the experimentally observed 
Raman spectra[5], this focused our attention to the three main species which would 
show distinct and different spectral characteristics.  We therefore set forward the 
following calculations to explore the possibilities.
223
Figure 10.1: IHP structure without stereochemistry.  Around a single bonded C6H6 
ring are six H2PO3 groups.
10.2 Methods
As the IHP system was relatively large, we started with a Hartree Fock[6] calculation 
with a smaller basis set, 6-31G, than we used in previous calculations.  Because we 
were more interested in the spectral and vibrational information rather than 
energetics, we expected the lower level of theory to be acceptable.  We also 
224
performed B3LYP[7] calculations on the same systems to confirm the stability of the 
HF spectral results.  Calculations were conducted with Gaussian 03[8].
The main three compounds which we examined were H12IHP (fully protonated), 
H6IHP6- (half deprotonated), and IHP12- (fully deprotonated). These three were chosen 
to cover the three main states of the phosphonic acid groups, fully protonated 
[H2PO3-]0, [HPO3-]-, and [PO3-]2-.  As these particular species show the most 
differentiation in their experimental spectra as well as populations in vivo systems, 
they should allow us to cast the most light on the experimental results.
Initial calculations were gas phase only, followed by explicit hydration with 6 water 
molecules in each system.  This was done successfully for H6IHP6- . 6 H2O.
Although CPCM solvation calculations were initially considered, because the 
phosphate groups were expected to exhibit hydrogen bonding interactions which 
would affect the spectra, conducting a CPCM investigation was left to a future date.
10.3 Results and Discussion
Below appear the optimized geometries: HF/6-31G first, as shown in Figure 10.2, 
then B3LYP/6-31G, in Figure 10.3.  As the species are complex, the figures appear as 
crosseyed stereograms for ease of examination.
225
Figure 10.2: H12IHP HF optimized structure (3d, crosseyed stereogram)
Figure 10.3: H12IHP B3LYP re-optimized structure (3d, crosseyed stereogram)
In each case, an initial optimization was first conducted  from our structure with 
simple molecular mechanics methods (not reproduced here), then using that geometry 
as our first guess, with HF/6-31G.  After a stable geometry was found, B3LYP was 
used to re-optimize and calculate vibrational frequencies as well.  This gave us IR 
peaks for both methods for comparison, and Raman peaks for the HF calculations. 
226
The optimized geometries for the half-deprotonated species appear below in Figure 
10.4 and Figure 10.5.
Figure 10.4: H6IHP6- HF structure (3d, crosseyed stereogram)
Figure 10.5: H6IHP6- B3LYP structure (3d, crosseyed stereogram)
We then calculated the structure of an explicitly hydrated system, the half-
deprotonated H6IHP6- , with water molecules positioned to hydrogen bond with each 
227
of the phosphonic acid groups present.  The stable minima which we found appears in 
Figure 10.6, below.  
Figure 10.6: H6IHP6- HF structure, explicitly solvated explicitly by 6 H2O molecules 
(3d, crosseyed stereogram)
As the anions became progressively more negatively charged, the optimization steps 
began taking increasing lengths of time to reach a stable energy minima.  The last set 
of calculations on the fully deprotonated IHP12- system was, as expected, the most 
difficult to stabilize; pure gas phase calculations upon it are still in progress, as well 
explictly solvated calculations for H12IHP.
Let's look at the spectra of each species in turn.  First, we shall examine the synthetic 
HF spectra of the fully protonated, neutral species H12IHP, which includes both IR 
and Raman peaks, as shown in Figure 10.7.
228
Figure 10.7: HF synthetic IR and Raman spectra for H12IHP calculated with the 6-
31G basis set.
As we can see, with the many IR peaks, the largest seen at 3453 cm-1, 3841 cm-1, 705 
cm-1, 946 cm-1, 3858 cm-1, 919 cm-1, 3709 cm-1, 3772 cm-1, 4019 cm-1, and the primary 
Raman peaks showing around 4015 cm-1, with four peaks at 4021 cm-1, 4030 cm-1, 
and 4019 cm-1, and 3996 cm-1 having the highest intensities overall, with a smaller 
one at 809 cm-1.  The experimental Raman spectra, which we will cover below, run 
from 500 cm-1 to 2000 cm-1, and we shall discuss this area of the spectra in more 
detail later.
Our focus here in telling the differences between the different states of the IHP 
system will be the phosphate groups, as they become deprotonated and behave 
differently in the different cases.   However, before we address those, lets examine 
the spectra overall and look at the differences between the HF and B3LYP 
calculations.
229
In our B3LYP calculation, shown in Figure 10.8, we have the primary IR peaks 
appearing at 2643 cm-1, 3083 cm-1, 3275 cm-1, 772 cm-1, 3325 cm-1, 948 cm-1, 3262 
cm-1, 793 cm-1, and 836 cm-1.  For the higher frequency modes, the frequencies 
changed little, for example the vibrational modes at 948 cm-1 and 946 cm-1 in the HF 
calculation.  These modes correspond with vibrations of hydrogen-bonding H atoms 
between the phosphate groups which are vibrating perpendicular to the O-H-O 
bonding axis.
Figure 10.8: B3LYP synthetic IR spectrum for H12IHP calculated with the 6-31G 
basis set.
A peak at 780 cm-1 corresponds to a stretching distortion of the C6 ring in the B3LYP 
calculation also appears in the HF calculation, although the additional bond stiffness 
seen in HF makes the intensity of the peak much weaker.
The largest difference here is in the vibration at 2643 cm-1 in the B3LYP calculation, 
which turns out to correspond with the peak at 3453 cm-1 in the HF calculation.  This 
vibrational mode is for an especially well shared hydrogen atom, and is shown in 
Figure 10.9, which illustrates the mode in the B3LYP case.  We would expect that the 
230
hydrogen-bonding H atoms would show lower frequency vibrational modes in the 
B3LYP calculation because it is well known that in HF calculations hydrogen bonds 
are much stiffer and ionic than they are in reality.
Figure 10.9: B3LYP vibrational mode at at 2644 cm-1.  Note the displacement vector 
for the H atom at the top shares it between the two nearby O atoms.
The vibrational spectra for the half-deprotonated system in the gas phase appears 
below in Figure 10.10 for the HF calculation and Figure 10.11 for the B3LYP 
calculation.  We shall discuss both briefly at the same time, as the experimental 
characterization was done in aqueous conditions and the results do not particularly 
apply to our overall discussion.
231
Figure 10.10: HF synthetic IR and Raman spectra for gas phase H6IHP-6 calculated 
with the 6-31G basis set.
Figure 10.11: B3LYP synthetic IR spectrum for gas phase H6IHP-6 calculated with the 
6-31G basis set.
Taking both together, we can see that the general shape of both IR spectra are nearly 
the same, showing that the HF method is sufficient in this case for modeling H6IHP-6 
in the gaseous phase.  However, the Raman spectra has little resemblance to the 
experimental spectra shown later in Figure 10.14, as it was calculated in the gas 
phase, so we shall pass over these results to focus on the explicitly solvated system, 
which goes much farther in explaining the experimental results.
232
Our calculation of the same system with six explicit water molecules using HF, as 
shown in Figure 10.12, shows the expected behavior in its Raman spectra, with peaks 
appearing at 832 cm-1, at 960-970 cm-1, and around 1100 cm-1 and 1162 cm-1.
Figure 10.12: HF synthetic IR and Raman spectra for H6IHP6- . 6H2O calculated with 
the 6-31G basis set.
The primary vibrational mode at 832 cm-1 is the hydrogen-bonding phosphate H 
atoms moving perpendicular to the axis of hydrogen bonding between adjacent 
phosphate groups.  The primary mode at 967 cm-1 appears to be a symmetric stretch 
that appeared when the phosphate was deprotonated as shown in Figure 10.13, while 
the mode at 1100 cm-1 corresponds to an asymmetric stretch of the same groups. The 
peaks near 1500 appear to be H atom bending modes mostly on the central carbon 
atoms.
233
Figure 10.13: Phosphate group symmetric stretch observed in HF/6-31G calculated 
Raman spectrum for H6IHP6- . 6 H2O at 967 cm-1.
The peaks around 1162 cm-1 correspond to various vibrational modes of the C6 ring in 
the center of the compound.
We can now compare our Raman data to experimental spectra[5] taken under various 
pH conditions, as shown in Figure 10.14.
Looking between the peaks seen experimentally at low (acidic) pH 3, where the fully 
protonated H12IHP would be predominant, and the peaks seen in more neutral 
solutions near pH 7, we can first observe in the experimental data that there is a trend 
where the peak at 850 cm-1 shrinks, and a peak appears near 1000 cm-1.  This trend is 
duplicated in our theoretical data for the explicitly solvated H6IHP-6 . 6 H2O anion as 
calculated with the HF/6-31G, which is a good sign.
234
Figure 10.14: Experimentally Measured Raman Spectra under various pH conditions 
as measured by L. Heighton[5].
Let's use our calculations to interpret the Raman peaks seen on the experimental 
spectra, identifying them as follows.
The peak slightly below 1000 cm-1 in the experimental spectra is probably the 
phosphate symmetric stretching mode shown by the singly deprotonated HPO3-R 
groups in our calculation and shown in Figure 10.13.  The peak further down is the 
vibrational modes of the intramolecularly hydrogen bonding protons on the phosphate 
235
groups vibrating perpendicular to the bonds.  This would explain the near 
disappearance of the peak in the most basic conditions, where the acidic groups 
would be fully deprotonated and this kind of mode would no longer be possible.
Finally, the peak just above 1000 cm-1 is related to the vibrational modes of the 
central C6H6 ring, which is why it remains for the most part unchanged regardless of 
the external pH.    The modes between 1450 and 1600 cm-1 on our spectrum appear to 
correspond to different bending modes of nonbonding H atoms, mostly on the central 
C6 ring, although they also include some motion of phosphate H atoms in unfavorable 
directions.  This might explain why the peaks seen on the experimental spectrum in 
this area become subdued under the most basic pH conditions.
10.4 Conclusions
We have shown that the HF/6-31G method is sufficient in this case, with IR spectra 
with similar shapes in the area of interest between 500-2000 cm-1 as the higher level 
B3LYP method.  Although predictive peak positions were not necessarily achieved 
with this approach, the clear trends of where the Raman absorptions are with relation 
to each other correspond closely to the experimental results, confirming the identities 
of the species suspected by the experimenter.  Theoretical vibrational modes provided 
additional insight into the sources of each observed peak in the experimental 
measurement.
236
In the future, it would be interesting to explore energetics calculations on these 
compounds.
The large charges would probably make the calculation difficult, but a clear starting 
point would be to do a single point CCSD(T) calculation at the final B3LYP 
geometry, and possibly some calculations on the anions with larger basis sets.  As we 
observed explicit solvation was essential for the spectra to correspond with 
experimental measurement, either explicit water molecules or a modeled solvent will 
be essential, with all the additional computational costs which that implies.
Currently, further efforts continue to model the solvated, fully deprotonated IHP-12 
system, and this additional information will be presented in a future paper. Future 
calculations on explicitly solvated molecules of the fully deprotonated IHP-12 should 
shed further light on the area of the experimental spectrum in the 1200-1700 cm-1 area 
as well, as changes were observed there compared to the H12IHP and H6IHP-6 systems 
examined here.
Another good future effort would be to do a vibrational calculation including 
anharmonic contributions could provide corrections to the measured frequencies, 
possibly allowing us to predict the experimental spectrum directly.  This type of 
calculation would also still be possible even if full optimization under the higher level 
237
method was inaccessible.  These could be added as corrections to the IR and Raman 
spectral lines of interest to improve the raw accuracy theoretical results.
10.5 Acknowledgements
We would like to acknowledge Heighton, L. for several entertaining afternoons 
discussing IHP and possible applications of theoretical chemistry, for patience while 
the calculations were being conducted, and for assistance in finding good references.
10.6 References
1. Turner, B.L., et al., Inositol phosphates in the environment. Philos Trans R 
Soc Lond B Biol Sci., 2002. 357(1420): p. 449-469.
2. Heighton, L., W.F. Schmidt, and R.L. Siefert,  Kinetic and Equilibrium 
Constants of Phytic Acid and Ferric and Ferrous Phytate Derived from 
Nuclear Magnetic Resonance Spectoscopy. Journal of Agricultural and Food 
Chemistry, 2008. 56: p. 9543-9547.
3. Heighton, L., et al.,  Electrospray ionization mass spectroscopy shows 
speciation of phytate to be pH dependent. Journal of Food, Agriculture & 
Environment, 2008. 6(2): p. 401-407.
238
4. Yang, H.-F., et al., Electrochemical and Surface Enhanced Raman Scattering 
Spectroelectrochemical Study of Phytic Acid on the Silver Electrode. J. Phys. 
Chem. B., 2004. 108: p. 17412-17417.
5. Heighton, L.P. and W.F. Schmidt. Raman spectra of organic (myo-inositol 
hexakis phosphate) and inorganic P sepctra show pH dependence. in 
Proceedings of American Chemical Society National Meeting.  2009. 
Washington, D.C.
6. Roothaan, C.C.J., New Developments in Molecular Orbital Theory. Reviews 
of Modern Physics, 1951. 23(2): p. 69-89.
7. Becke, A.D.,  Density-functional thermochemistry. III. The role of exact 
exchange. The Journal of Chemical Physics, 1993. 98(7): p. 5648-5652.
8. M. J. Frisch, G.W.T., H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. 
Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. 
M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. 
Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. 
Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, 
H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. 
Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, 
A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. 
Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. 
Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. 
Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, 
239
S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. 
Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. 
Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. 
Wong, C. Gonzalez, and J. A. Pople, Gaussian 03, Revision C.02, 2004, 
Gaussian, Inc., Wallingford CT.
240
Chapter 11:  Conclusions and Future Work
In which we summarize the overall results from each section of the research and 
offer suggestions for further study.
11.1 Introduction
In conclusion, we have examined a number of different chemical systems using a 
variety of theoretical methods.
Systems examined included the series of mercury chlorides, methylmercury chlorides 
and other mercuric halides discussed previously, as well as a variety of inorganic 
polyprotic acids, whose acidities were explored in detail.  We also studied the Raman 
spectra of myo-inositol hexakis phosphate (IHP) in a joint project with an 
experimental group.
The theories applied ranged from Hartree-Fock[1] to CCSD(T)[2], CBS-QB3[3, 4], 
and complete basis set extrapolations[5].  Calculations included geometry and 
stability calculations, which were used in both the gas phase and in solvated systems 
(simulated by CPCM solvation[6-8] and explicit hydration with H2O, consisting of 
single and multiple water molecules), and NMR shielding calculations[9-11]  done 
with ADF[12-14] , and infrared spectra calculated with Gaussian 03[15].
241
11.2 Results and Discussion
Results were generally successful.
In the case of the mercury chlorides, we calculated energetics and structures, and 
NMR data for HgCl+ through HgCl64-.  Energetics results were shown to be stable 
between B3LYP / CEP-121G+ and the higher level CCSD and CCSD(T) complete 
basis set extrapolations, so B3LYP is sufficient for calculations on these compounds. 
The overall NMR results showed trends for the NMR with decreasing shielding 
running from approximately 10000 cm-1 to 6700 cm-1 with increasing substitution.
In our polyprotic acid study, we examined the behavior of a set of polyprotic acids 
including H3PO4, H3AsO4, H3PO3, H3AsO3, H3AsS4, H3AsS3, and H2SO3.  Each 
species of these, both unexplicitly and explicitly solvated, was calculated for stable 
geometries and the energetics were predicted using both gas phase CBS-QB3 and 
CPCM solvated CBS-QB3.  We then had graphed the predicted pKa values against 
the experimental measurements, discovering a linear relation between the two.  A 
linear extrapolation was determined to adjust the calculated pKa values, which 
improved the results to theoretical quality, reproduced below as Equation 11.1.
(11.1) pKaexpt = 0.429 pKaCBS-QB3 CPCM w/H2O ? 0.233
242
The acidity calculation results done with CBS-QB3 in the CPCM were uniformly 
reasonable for the first deprotonation, as expected, though the second and third 
deprotonations were not as good (also as expected).  With the extrapolation we 
developed, however, the results became theoretical quality; within 2 kcal/mol of the 
experimental measurements.
The results with the extrapolation were also tested on an H2SO3 system which we did 
not include in the original results used to make the system, and were then used to 
explore a series of HClOx compounds (x=1...4) with counter-ions present (described 
in Chapter 7).  These calculations yielded results that showed the correct trends of 
increasing acidity in the series, although they overestimated the experimental acidity 
of the HClO4 dramatically.
The methylmercury structures, which we previously discussed as being responsible 
for the instances of mercury poisoning in Japan (as Minamata Disease)[16] and in 
Iraq (from repurposed mercury-treated grain)[17] were also explored in detail, 
showing the expected trends of decreasing solubility with the softer halogens Br and 
I.  The IR spectra and differences in them between solvated and unsolvated conditions 
were also examined in detail.
At the suggestion of Lynne Heighton, an experimentalist, we did a series of Raman 
Spectra calculations on partly depronated myo-inositol hexakis phosphate (IHP), the 
243
most common organic phosphate compound seen in nature, to compare and shed 
further light on the experimental data previously presented at ACS[18].  We 
calculated both Raman spectra with HF and IR spectra with HF and B3LYP for both 
the nondeprotonated H12IHP system and the partly deprotonated H6IHP6- systems, the 
latter with explicit hydration, and the spectra showed the expected trends, confirming 
the experimental results and casting light on the vibrational modes responsible for 
several of the observed peaks.
In the future, we can see that its important to check over even unexpected results 
visually to see if an obscured relation exists.  The good results found in the case of the 
polyprotic acids are a clear indication that this approach is effective.  
Throughout our explorations,  we observed that the largest challenge in applied 
theoretical chemistry is probably determination of the geometries corresponding to 
the energy minima.  This was especially true when dealing with edge cases that 
stressed the theory, such as hydrated ionic species.  In many cases, much of the CPU 
time was spent on geometry optimization rather than other parts of the calculations.
We addressed this somewhat by applying a stair-step method, optimizing the 
geometries with a quickly-minimizing HF calculation with a small basis set to get a 
better starting geometry than could be determined by hand, followed by higher level 
calculations.  Although the HF geometries were not very accurate, they provided an 
244
easy to reach geometric springboard for the future calculations which stood closer 
than our initial guesses as to the geometries.
The most difficult conditions  we observed when reaching geometric equilibrium was 
modeling anionic systems with the B3LYP method with CPCM solvation.  Under 
these three conditions, it was often the case that the geometry began oscillating 
slowly around a stable geometry on the multidimensional free energy surface instead 
of straightforwardly reaching a final geometry.  This is because the presence of 
CPCM flattens the potential energy surface and B3LYP tends to be one of the slower 
methods to reach equilibrium.  A strongly charged system will be deeply stabilized 
whatever the geometry by the presence of the CPCM, which makes it more difficult 
to reach a final geometry regardless of the method.
We found that the best thing to do in this case was to solve for a stable geometry in 
the gas phase first, and follow that preliminary calculation with the CPCM 
calculation.  In troublesome cases, a HF calculation in the gas phase followed by an 
MP2 calculation in the CPCM allowed for a starting geometry for B3LYP which was 
effective in a timely fashion.  This was also helpful in our CBS-QB3 calculations 
with anions because of the initial B3LYP optimization step.
Future steps which would correspond with our group's focus on environmental and 
geochemical  applications  of  computational  chemistry  could  likely  include 
245
calculations on other Hg systems.  For example, when we examined our 
methylmercury calculation results, we saw that solvation actually destabilized some 
of the compounds.  It would be exciting to test a variety of different solvents to allow 
us to determine what solvent polarity would be necessary to make MeHgBr more 
stable when solvated, for example.  Of course, another group might set forwards to do 
this same type of calculation on other, better characterized systems, such as 
protonated or ionic clusters where precise physical measurements are already 
available.
We also did a number of calculations which focused on the behavior of HgClx 
compounds, both in the gas phase and in solvation.  Further calculations of this sort 
could be done with other simulated solvents.  With increasing interest in ionic liquids 
for separations because of their environmental friendliness and reusability, for 
example, it would be interesting to explore the possible behaviors of the mercury 
compounds in a more ionic liquid.
11.3 Acknowledgements
We would like to acknowledge S. Vinnikova for her great assistance in preparing this 
section and offering helpful suggestions and encouragement during its writing.
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Glossary
ADF Amsterdam Density-Functional theory software (by Scientific 
Computing and Modeling).
B3LYP Hybrid HF-DFT method with similar quality results as MP2
CBS-QB3 Complete Basis Set Extrapolation Model Chemistry 
computational method
CCSD Coupled Cluster Theory (high level) computational method 
(with single and double excitations)
CCSD(T) Coupled Cluster Theory (very high level) computational 
method (with some triple excitations as well)
CEP-121G Compact Effective Potential basis set with
CEP-31G Compact Effective Potential basis set
CPCM Polarizable Continuum Method computational method for 
simulating solvation (with water or other solvents)
DFT Density-functional Theory
G03 Gaussian 03 computational chemistry software (from Gaussian, 
Inc).
G2 GAUSSIAN-2 Model Chemistry computational method
G3 GAUSSIAN-3 Improved Model Chemistry computational 
method
HF Hartree-Fock (low level) ab initio computational method.  
250
MP2 Moller-Plesset Perturbation Theory (second order) 
computational method.
NMR Nuclear Magnetic Resonance
pH Measure of Acidity (in water solutions, ranges from 0 ? acidic, 
to 14 ? basic, pH = - log([H+]))
pKa Measure of Acid Strength, related to pH
polyprotic acid In this case, acids with more than one acidic proton which can 
be removed in aqueous solution
 
251
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energy gradients in solution by a conductor solvent model. Journal of Physical 
Chemistry A, 1998. 102(11): p. 1995-2001.
16. Barone, V., M. Cossi, and J. Tomasi, Geometry optimization of molecular 
structures in solution by the polarizable continuum model. Journal of 
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17. Cossi, M., et al., Energies, structures, and electronic properties of molecules 
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9. Stevens, W.J., H. Basch, and M. Krauss, Compact Effective Potentials and 
Efficient Shared-Exponent Basis-Sets for the 1st-Row and 2nd-Row Atoms. 
Journal of Chemical Physics, 1984. 81(12): p. 6026-6033.
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2. Takizawa, Y., Understanding minamata disease and strategies to prevent 
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3. Bakir, F. and e. al., Methylmercury Poisoning in Iraq - Interuniversity Report. 
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285
6. Barone, V. and M. Cossi, Quantum calculation of molecular energies and 
energy gradients in solution by a conductor solvent model. Journal of Physical 
Chemistry A, 1998. 102(11): p. 1995-2001.
7. Barone, V., M. Cossi, and J. Tomasi, Geometry optimization of molecular 
structures in solution by the polarizable continuum model. Journal of 
Computational Chemistry, 1998. 19(4): p. 404-417.
8. Cossi, M., et al., Energies, structures, and electronic properties of molecules 
in solution with the C-PCM solvation model. Journal of Computational 
Chemistry, 2003. 24(6): p. 669-681.
9. Roothaan, C.C.J., New Developments in Molecular Orbital Theory. Reviews 
of Modern Physics, 1951. 23(2): p. 69-89.
10. Head-Gordon, M., J.A. Pople, and M.J. Frisch, MP2 energy evaluation by 
direct methods. Chemical Physics Letters, 1988. 153(6): p. 503-506.
11. Becke, A.D.,  Density-functional thermochemistry. III. The role of exact 
exchange. The Journal of Chemical Physics, 1993. 98(7): p. 5648-5652.
12. ???ek, J.,  On the Use of the Cluster Expansion and the Technique of 
Diagrams in Calculations of Correlation Effects in Atoms and Molecules. 
Advances in Chemical Physics1969: John Wiley & Sons, Inc. 35-89.
13. Stevens, W.J., H. Basch, and M. Krauss, Compact Effective Potentials and 
Efficient Shared-Exponent Basis-Sets for the 1st-Row and 2nd-Row Atoms. 
Journal of Chemical Physics, 1984. 81(12): p. 6026-6033.
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Shared-Exponent Basis-Sets for the 3rd-Row, 4th-Row, and 5th-Row Atoms. 
Canadian Journal of Chemistry-Revue Canadienne De Chimie, 1992. 70(2): p. 
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16. Cundari, T.R. and W.J. Stevens, Effective Core Potential Methods for the 
Lanthanides. Journal of Chemical Physics, 1993. 98(7): p. 5555-5565.
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2. Heighton, L., W.F. Schmidt, and R.L. Siefert,  Kinetic and Equilibrium 
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5. Heighton, L.P. and W.F. Schmidt. Raman spectra of organic (myo-inositol 
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Washington, D.C.
6. Roothaan, C.C.J., New Developments in Molecular Orbital Theory. Reviews 
of Modern Physics, 1951. 23(2): p. 69-89.
7. Becke, A.D.,  Density-functional thermochemistry. III. The role of exact 
exchange. The Journal of Chemical Physics, 1993. 98(7): p. 5648-5652.
8. M. J. Frisch, G.W.T., H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. 
Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. 
M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. 
Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. 
Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, 
H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. 
Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, 
A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. 
Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. 
Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. 
Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, 
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2. Pople, J.A., et al., Electron Correlation Theories and Their Application to 
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Chemistry, 1978. 14(5): p. 545-560.
3. Montgomery, J.A., et al., A complete basis set model chemistry. VI. Use of 
density functional geometries and frequencies. Journal of Chemical Physics, 
1999. 110(6): p. 2822-2827.
4. Montgomery, J.A., et al., A complete basis set model chemistry. VII. Use of 
the minimum population localization method. Journal of Chemical Physics, 
2000. 112(15): p. 6532-6542.
5. Halkier, A., et al., Basis-set convergence of the energy in molecular Hartree-
Fock calculations. Chemical Physics Letters, 1999. 302(5-6): p. 437-446.
289
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Chemistry A, 1998. 102(11): p. 1995-2001.
7. Barone, V., M. Cossi, and J. Tomasi, Geometry optimization of molecular 
structures in solution by the polarizable continuum model. Journal of 
Computational Chemistry, 1998. 19(4): p. 404-417.
8. Cossi, M., et al., Energies, structures, and electronic properties of molecules 
in solution with the C-PCM solvation model. Journal of Computational 
Chemistry, 2003. 24(6): p. 669-681.
9. Wolff, S.K., et al.,  Density functional calculations of  nuclear magnetic 
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14. Guerra, C.F., et al., Towards an order-N DFT method. Theoretical Chemistry 
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15. M. J. Frisch, G.W.T., H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. 
Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. 
M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. 
Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. 
Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, 
H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. 
Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, 
A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. 
Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. 
Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. 
Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, 
S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. 
Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. 
Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. 
Wong, C. Gonzalez, and J. A. Pople, Gaussian 03, Revision C.02, 2004, 
Gaussian, Inc., Wallingford CT.
291
16. Takizawa, Y., Understanding minamata disease and strategies to prevent 
further environmental contamination by methylmercury. Water Science and 
Technology, 2000. 42(7-8): p. 139-146.
17. Bakir, F. and e. al., Methylmercury Poisoning in Iraq - Interuniversity Report. 
Science, 1973. 181(4096): p. 230-241.
19. Heighton, L.P. and W.F. Schmidt. Raman spectra of organic (myo-inositol 
hexakis phosphate) and inorganic P sepctra show pH dependence. in 
Proceedings of American Chemical Society National Meeting.  2009. 
Washington, D.C.
292