Table Of ContentMOLECULAR THEORY OF SOLVATION
Understanding Chemical Reactivity
Volume 24
Series Editor
Paul G.Mezey, University of Saskatchewan, Saskatoon, Canada
Editorial Advisory Board
R.Stephen Berry, University of Chicago, IL, USA
John I.Brauman, Stanford University, CA, USA
A.Welford Castleman, Jr., Pennsylvania State University, PA, USA
Enrico Clementi, Université Louis Pasteur, Strasbourg, France
Stephen R.Langhoff, NASA Ames Research Center, Moffett Field, CA, USA
K.Morokuma, Emory University, Atlanta, GA, USA
Peter J.Rossky, University of Texas at Austin, TX, USA
Zdenek Slanina, Czech Academy of Sciences, Prague, Czech Republic
Donald G.Truhlar, University of Minnesota, Minneapolis, MN, USA
Ivar Ugi, Technische Universität, München, Germany
Molecular Theory of Solvation
edited by
Fumio Hirata
Institute for Molecular Science,
Okazaki, Japan
KLUWER ACADEMIC PUBLISHERS
NEW YORK,BOSTON, DORDRECHT, LONDON, MOSCOW
eBookISBN: 1-4020-2590-4
Print ISBN: 1-4020-1562-3
©2004 Springer Science + Business Media, Inc.
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Contents
Preface vii
1
Theory of molecular liquids 1
Fumio Hirata
1 Introduction 1
2 Density Fluctuation in Liquids 3
3 Ornstein-Zernike (OZ) Equations 6
4 Site-SiteOZ (RISM) Equations 15
5 Solute-Solvent System 20
6 Some applications of RISM Theory 23
2
Electronic structure and chemical reaction in solution 61
Hirofumi Sato
1 Introduction 61
2 ab initio Molecular Orbital Theory and the Solvation Effect 63
3 RISM-SCF/MCSCF Theory 72
4 Acid–base Equilibria in Aqueous Solution 75
5 Solvent Effects on Conformational Change of Chemical Com-
pounds 80
6 Solvent Effect on Chemical Reactions 83
7 The NMR Chemical Shift 88
8 Summary 91
Appendix: Appendix 92
1 Partial Charge Treatment in RISM-SCF/MCSCF 92
2 Variational Principle in the RISM-SCF/MCSCF method 94
3
Conformational stability of biomolecules in solution 101
Masahiro Kinoshita
1 CombinedRISM-MCapproachforpredictingpeptideconform-
ations 101
2 Alcohol effects on peptide conformations 122
3 Salt effects on solvation properties of peptides 135
4 Partial molar volume of amino acids and pressure effects 147
v
vi
Appendix 155
1 Algorithms for solving RISM equations 155
4
Three-dimensional RISM theory for molecular liquids and solid-liquid 169
interfaces
Andriy Kovalenko
1 Introduction 169
2 3D-RISM integral equation 175
3 Closures for the 3D-RISM theory 178
4 Hydrophobic hydration 184
5 Potential of mean force between molecular species in solution 190
6 Solvation chemical potential of an ionic cluster in electrolyte
solution 202
7 Self-consistent 3D-RISM approach 226
8 CombinedKohn-ShamDFTand3D-RISMapproachforametal-
liquid interface 240
9 Hybrid 3D-RISM-SCF and ab initio MO method for solvated
molecules 251
Appendix 257
1 Free energy functions in the KH approximation 257
2 Solvation chemical potential in the SC-3D-RISM approach 258
3 SolventeffectivepotentialcouplingtheKS-DFTand3D-RISM
equations 260
4 Algorithms for solving the RISM equation 261
5
Dynamical processes in solution 277
Song-Ho Chong
1 Introductory remarks on the theory for dynamics of simple
liquids 277
2 Interaction-site-model description of molecular-liquid dynam-
ics 296
3 Collective excitations in diatomic liquids 306
4 Ion dynamics in diatomic liquids 314
5 Collective excitations and dynamics of ions in water 331
6 Concluding remarks 344
Index 351
Preface
In most of the past century, the study of solvent effect on chemical
processes in solution has been dominated by continuum models which
hasbeenestablishedduringthe19thcentury. TheOnsagerreactionfield
and the Born model of ion hydration are good examples. The Onsager
reaction field has been widely employed in the interpretation of solvato-
chromism. The Born model of ion hydration has been incorporated in
the Marcus theory for electron-transfer reactions to realize the solvent
reorganization energy. It has been recently generalized to explain the
solvent effect on the electronic structure in solution. The generalized
version of the Born model and the Poisson-Boltzmann equation have
been applied also to biomolecules, i.e., protein as well as nucleic acids,
in water. The model and theory are enjoying the status of standard ma-
chinery for evaluating the electrostatics which play an essential role in
chemical reactions andtheconformational stability ofprotein, which are
two of the most important topics in theoretical chemistry. The success
of those theories lies on rather general laws of physics: the long-range
natureoftheelectrostatic interaction, whichmakesthemean-field treat-
ment reasonably good, and the central-limiting theorem, which ensures
a Gaussian character for solvent fluctuations. Owing to their general-
ity, such models can be characterized by just a few parameters, such as
dielectricconstantandviscosity. However, thegenerality ofthetheoryis
sometimes of an unwelcome nature for chemistry, which should be able
to distinguish a chemical element from other elements. The continuum
theory may never be able to distinguish ethanol from acetonitrile, which
have similar dielectric constants. A common maneuver to be employed
in such cases to incorporate chemical specificity is to use an adjective,
“effective”, e.g., “effective” radii, as boundary conditions for solving the
continuum equations. Unfortunately, effective quantities so obtained for
differentphysicalprocessesconflictwitheach other,sometimesseriously,
leading to vain a “religious war”. Broadly distributed values assigned
to the size of ions, such as the Stokes radii of hydrodynamic equations
and the Born radii of hydration free energy, are the best examples of
vii
viii
the ambiguity characteristic of the continuum model. An even more
serious drawback of the model shows up in some biological applications.
One of the most dramatic events which proteins exhibit in solutions is
so called ”cold denaturation,” that is, some protein denatures with de-
creasing temperature. The phenomenon is believed to be caused by a
hydrophobic effect. The continuum model will never be able to explain
the phenomenon even in the level of the ”effective” description.
Molecular simulations, i.e., the molecular dynamics and the Monte
Carlo methods, have become an invaluable tool for studying liquids and
solutions during the last few decades. Those methods have been widely
employed to explore the phase-space or the configuration space of the
liquidsystemtoacquireobservablesasanaverage ofmechanicalquantit-
ies over the space. So, it is capable of accounting for chemical specificity
of the system from its most elementary level. However, this merit turns
into a defect in some applications. Exploring the phase-space from the
most elementary process requires a large amount of computation, and it
oftenendsupwithwanderingaroundaratherlimitedregionofthespace,
not to mention the infamous non-Ergodic trap. Naive use of the method
may lead to results which are either entirely wrong or are unscientific.
While the method is expected generally to provide a good account for
quantities related to short wavelength and large frequency, it become
more and more troublesome as the wavelength becomes greater and the
frequency becomes smaller.
In this book we present the third choice for describing the solvation
phenomena in solutions. The method relies on the statistical mechanics
applied to the liquid state of matter, especially on the RISM theory,
an integral equation theory of molecular liquids. As will be described
briefly in Chapter 1, the liquid state theory has been developed over
the period of the past century, and has now reached the point at which
almost the entire spectrum of chemistry in solution can be faithfully
reproduced, at least in a qualitatively reliable manner: from ions to
biomolecules, and from equilibrium to non-equilibrium. The theory is
free from such adjectives as “effective”, since it is thoroughly based on
the first principle, or Hamiltonian, of the system. There is no necessity
for concerns about the limited sampling of the phase space, because it
explores the entire phase-space in principle by means of the statistical
mechanics. Of course, the theory involves some approximations, and
is never be perfect, as is the case in any meaningful theory. The best
part of the theory is that the approximation involved is unambiguous,
which means it can be improved not by waiting for the development of
the computer, but by grinding the human brain. However, the theory,
by itself, is not enough to describe a variety of chemistry occurring in
PREFACE ix
solutions. Ourstrategyforexploringchemistryinsolutionsistocombine
theRISMtheorywithothermethodologieswellestablishedintheoretical
physics and chemistry.
Understanding chemical reactions is the main objective of this book
series. The reaction is primarily determined by changes in the electronic
structure of species involved. However, if reactions are occurring in
solutions, the change in the electronic energy is comparable to that of
solvation energy, and the solvent effect can become a determining factor
ofthereaction. Suchastatementcanbephenomenologically understood
from daily observations made by organic chemists that one solvent lets
a reaction proceed, but another solvent does not. It is also important
to realize that the electronic structure itself is largely influenced by a
solvent, especially in polar liquids, which indicates that the electronic
structure and the solvation should not be treated separately. Chapter
2 of the book is devoted to this problem, namely, electronic structure
and chemical reactions in solution. The chapter deals with a theory
referred to as RISM-SCF which combines the RISM theory with the
ab initio molecular orbital theory (SCF). Some applications to selected
topics related to chemical reactions are also presented.
Biomolecules represented by protein and DNA are characterized by
finite, but large, degrees of freedom which they possess, which means
one has to consider a huge number of conformational “isomers”. The
molecules are also distinguished from usual polymers in terms of the
specificity they show in biological activities, which suggests that the
theoretical treatment should be at the atomic level, just as in chem-
ical reactions. In order to meet such a requirement, “solvent effects”
should also be treated at atomic level, not by a continuum model: con-
tinuum models are never able to account for the hydrogen-bonds and
hydrophobicity which are the two important interactions creating spe-
cificityofbiopolymers. Onequestionisthenhowtohandletheeffects on
biomolecules of solvent molecules, the number of which is essentially in-
finite, withoutsacrificing their specificity. Chapter 3is concerned with a
methodology which projects the degrees of freedom of solvent molecules
onto that of a biomolecule in the level of the site-site pair correlation
functions. The method is the same in its spirit as the “influence func-
tional” developed by Feynman. The molecular simulation technique is
combined with the RISM equation to sample the conformational space
of biomolecules, where atomic interactions include not only the direct
intramolecular interactions but also the solvent induced interactions.
The interface between a liquid and other substances or phases is the
place where chemical reactions take place most actively, as is instanced
by catalyses or electrodes. The problem involves the average density
x
which is not constant in space but dependent on position. The interface
can be treated by viewing it as a “solute” with some geometry, im-
mersed in solutions: the “solute”-solvent density pair correlation func-
tions mimic the local density of solvent in the interfacial region. For
such a problem it is highly desired to describe the pair correlation as an
explicitfunctionofpositionratherthanasafunctionprojectedalongthe
radial distance. Chapter 4 is devoted to this subject, namely, to the de-
velopment of the three-dimensional (3D) RISM theory for non-charged,
polar, and ionic molecular species in polar molecular solvents. As a ma-
jor application of the theory an electrode-solution interface is studied in
which both the structures of the solution and of the metal surface are
treated at the atomic level. In order to handle the electronic structure
of electrodes, the 3D-RISM method is coupled in the self-consistent field
loop with the Kohn-Sham type of density functional theory.
The dynamical processes in solution can be treated by combining the
RISM theory with the generalized Langevin theory. The conventional
method of formulating dynamics in molecular liquids is based on the
so called “rot-translational” model, which includes angular coordinates
explicitly. The method relies on the spherical harmonic expansion in or-
der to handle the orientational correlation of molecules, which becomes
intolerably cumbersome as the asphericity of a molecule increases. The
model employed in this book is the interaction-site model (ISM) which
views the dynamics of a molecule as a correlated “translational”-motion
of sites or atoms. Themodellets usincorporatethe RISMtheory natur-
ally into the generalized Langevin equation (GLE) which describes the
timeevolutionofsitedensity. TakingalltheadvantageswhichtheRISM
theory has in dealing molecular liquids, we are now able to evaluate the
dynamic properties such as the velocity auto-correlation functions in
realistic liquids including water. The coupled RISM-GLE treatment of
liquid dynamics is presented in Chapter 5.
On behalf of the authors of the book the editor is grateful to all the
collaborators who have participated enthusiastically in the development
of the molecular theory of solvation presented in each chapter. He also
thanks Dr. T. Yamazaki for careful proof reading as well as technical
help in completing the book, and Ms. R. Kawai for her assistance in
word-processing the manuscript.
FUMIO HIRATA
