Fumio Hirata[Date of Birth]
March 17, 1947

[Sex] Male[Nationality] Japan[Degrees]
March, 1969

Bachelors degree in chemistry (Hokkaido University)

March, 1971

Master of Science, Theoretical Chemistry (Hokkaido University)

March, 1977

Doctor of Science, Theoretical Chemistry (Hokkaido University)[Employment]
2016-

Toyota Physical & Chemical Research Institute, Fellow

2012- 2015

Ritsumeikan University, visiting Professor.

2012-

Institute for Molecular Science, Professor Emeritus

1995-2012

Institute for Molecular Science, Professor

1989-1995

Kyoto University, Associate Professor

1988-1989

Ruttgers University (USA), Research Asistant Professor

1985-1988

Rurgers University (USA), Lecturer

1981-1985

NASAC Co., Senior Scies University (USA),1979-1980

Texas University (USA), Postdoctoral Fellow

Statistical mechanics of molecular liquid and its
application to life phenomena
It is common understanding that living systems cannot live without water. The structureand function of all biomolecules, responsible for keeping our life, have been designed in
the process of evolution, so that they fit best the environment of water. In that sense, itwill not be an overstatement that life on the earth has been born and evolved due tocollaboration between water and biomolecules.
In my career as a researcher, which started from a graduate course, I have developed
the integral equation theory of liquid, a field of the statistical mechanics, to elucidate
structure of water and its role for biomolecular function and structure. Among thetheories I have developed with my collaborators, the extended RISM and 3D-RISM/KH
theories have proved themselves quite useful in analyses of the molecular recognition
that plays crucial role in expression of biomolecular functions. Those theories, whichhave been derived by us as a generalization of the RISM theory proposed by D.
Chandler and H. C. Andersen to aqueous solution of biomolecules, have been
implemented in commercial softwares such as AMBER, and have been utilized atindustrial sites as a powerful tool of drug discovery.
This review is devoted to describe author’s main contribution in the field of solution
chemistry and life science. [1]I.	
 Extended RISM (XRISM) theory and its application tochemistry	 	 	 - What is liquid structure ?	
  The author used the words “structure of liquid” in the introduction above, but what is“structure of liquid?” For example, the structure of a water molecule can be defined bygiving the length of three edges of the triangle, two O-H bond lengths and one H-H
distance. Crystal structure of solid can also be defined readily by providing lattice
constants. (Fig. 1.1)

Fig. 1.1 Structure of a molecule and crystal
However, in liquids, the mutual configuration (or structure) of molecules cannot be
defined uniquely, because molecules are moving around randomly due to thermal
motion. In such a situation, we use a concept of probability density distribution at a
position in space, and correlation of the distribution between two positions. Let ρ(r)and ρ(r’) be the probabilities density to find a molecule at positions r and r’, andρ(2)(r,r’) be the probability density to find two molecuels simultaneously at positions r
and r’. Such a situation can be expressed with the correlation function g ( r, r ') by thefollowing relation.

ρ (2) (r, r ') = ρ(r)ρ(r ')g(r, r ')If the two positions r, r’ are far dsitant, ρ (2) ( r, r ′ ) becomes a simple product of ρ(r)and ρ(r’), since the probability at two positions are independent, that is,ρ (2) (r, r ') → ρ(r)ρ(r ') or g(r, r ') = 1 ( r − r ' → ∞)On the other hand, it vanishes when the positions are so close that molecules at thepostions overlap each other, orρ (2) (r, r ') → 0 or g(r, r ') = 0( r − r ' → 0)

At an intermediate distance between the two cases, the behavior of g(r,r’) becomescomplicated, reflecting the correlation of probability between the two positions. Due tothe physical sense, g(r,r’) is called “density pair correlation function.” Average
structure of liquids can be inferred by the pair correlation functions, since the function
contains information of distance between two positions. The correlation functions canbe probed experimentaly by means of the X-ray and/or the neutron diffraction
measurements. The light or particle beam scattered from atoms at two positions interfers

each other, and create a characteristic interference fringe, which can be measured by thediffraction methods. As an example, the pair correlation functions （gαγ）between a pairof atoms in water, which were obtained from the XRISM theory described later, aredepicted in Fig. 2.（Overall behavior of the results is in qualitative agreement with thatobtained from the X-ray and neutron diffraction measurements.）As is well regarded,water structure is characterized with a three-dimensional hydrogen-bond network.
(cartoon below) In the figure, the sharp first peak seen in gOH (marked by b1) is amanifestation of the hydrogen-bond. Due to the hydrogen-bond, water takes atetrahedral coordination, characteristic in ice, which gives rise to the second peak in the
O-O correlation function, which apppears around 〜1.63σ (σ : diameter of a watermolecule) , marked by a2. The postion of a peak includes information of distance
between atoms, from which one can deduce a three dimensional structure of liquid, withan aid of trigonometry. The cartoon of hydrogen-bond network in Fig. 2 was drawn insuch a way from the pair correlation functions.

	
  	
  	
  	
  	
  	
 
	
 
	
 

Fig. 1.2 Pair correlation functions in water and the hydrogen-bondnetwork.

-Basic

theoryofstatisticalmechanics

ofliquids(Ornstein-Zernike equation)An equation to govern the pair correlation function in liquid was proposed by two
Dutch scientists, L. S. Ornstein and F. Zernike, in the beginning of the last century. [2]They have written down the following equation in intuitive basis in order to explain thecritical behavior of the structure factor, obtained from the X-ray and/or neutron
diffraction measurment.

h(r, r ') = c(r, r ') + ∫ c(r, r '')ρ(r '')h(r '', r ')dr ''
V

(1.1)

In the equation, h(r,r’) (= g(r,r’) - 1) is called the total correlation function. Later,
derivation of the equation has been worked out by many scientists based on thestatistical mechanics, and it is now appreciated as the most fundamental equation todescribe liquid structure.
In the mean time, the equation contains another unknown function, c(r,r’). Thisfunction is referred to as “direct correlation function.” In order to solve theOrnstein-Zernike (O-Z) equation, we need another equation that relates c(r,r’) to h(r,r’).
(The equation is called “closure” relation, since it closes the O-Z equation.) Therefore,
it has become one of main themes for the statistical mechanics of liquid to find a closure
relation. The most important closure relation derived so far is called HNC (HyperNetted
Chain)-closure, which reads, [1]c(r, r ') = exp [ −u(r, r ') / kT + t(r, r ')] − 1 − t(r, r ')(1.2)

（ t(r, r ') ≡ h(r, r ') − c(r, r ') ）The O-Z as well as HNC equations can be derived from the partition fucntion of liquid
systems, by means of the functional derivative and/or the diagramatic expansion. The
derivation is skipped in this review. Instead, a concept called “renormalization” used tosolve this type of an integral equation is explained. Let us substitue the entire
right-hand-side of (1.1) into h(r ′′, r ') , iteratively, that will produce an infinite series
illustrated by the following diagram.

In the equation, a black circle denotes an interal over the entire space as follows.

C[c|ρ] is a book-keeping notation to represent the infinite series consisting of
many-body integrals. Each term in the infinite series has a form of the convolution
integral, the Fourier transform of which becomes a simple product of the Fouriertransform of functions consisting the integrand, and the infinite series becomes ageometric series. The sum of geometric series can be readily calculated as + ρc(k) 2 + ρ 2 c(k)
 3 +h(k)= c(k)c(k)=
1 − ρc(k) , c(k)where h(k)are, respectively, the Fourier transform of h(r) and c(r). In Fig. 1.3,
shown is a standard method to solve the integral equation by means of an iterative
procedure.
Although Fig. 1.3 shows a standard alogorithm to solve an integral equation
appearing in the liquid state theory, more important is that it represents a typicalexample for a general concept in physics of many-body problem, referred to as“Renormalization.” In this alogorithm, the functional form of c(r,r’), orc(r, r ') = exp [ − β u(r, r ') + t(r, r ')] − 1 + t(r, r ')stays unchanged, as the iteration progresses. However, the more complicatedmany-body interactions are renormalized into c(r,r’) as the iteration proceeds. Since
each black cicle corresponds to an integral in the coordinate space, the sum of thegeometric series involves multiple integrals, multiplicity of which extends to infinity. Itmeans that this procedure corresponds to sampling of the phase space that is infinitely
large. Nevertheless, actual integration we should perform in this alogorithm is just asingle integral associated with the Fourier transform.

Renormalization

Fig. 1.3 Iterative solution of the O-Z equation: the iteration is initiated by calculating initialvalues of c(r) from the inter-molecular interaction u(r). The function c(r) is Fourier-tranformed
into c(k). The sum of the infinite series is calculated to get t(k). t(k) is inverse transformed to getc(r) in the real space. The process is iterated untill c(r) converges.

Renormalization of Coulomb interactions: The theory described above can be applied
to a liquid system consisting of spherical molecules to calculate the pair correlation
function. However, there is a tumbling block if one tries to apply the theory in a naive
way to an electrolyte soluiton. The problem is the divergence of Coulomb interaction.
The equation descirbed above involves the integration of interactions over the spaceextending to infinity. The integration of the Coulomb interaction over the infinite spacediverges as

φ (r) 1r∞

∫ φ (r)4π r dr → ∞20

J. Mayer, who is famous with the method called “cluster expansion” of non-ideal gas,solved the problem.[3] He found that the sum of the infinite series (chain sum) below
converges, inspite that the integral of the Coulomb interaction by itself diverges.

In the above equation, κ denotes inverse of the Debye screening length that is
proportional to the square root of the ionic strength. Using the function, Mayer
renormalized the clsuter expansion (or virial expansion) of electrolyte solutions. (The
Debye-Huckel limiting law of elctrolyte solutions corresponds to the first order term of
the cluster expansion.) The Ornstein-Zernike equation can also be rewritten in trems of
the “renormalized Coulomb interaction” q(r) as [4]h = C ⎡⎣ c − φ q ⎤⎦ + q
q(r) = ρδ (r) + ρ 2 q(r)The RISM theory: The theory described so far, which is concerned with a system
consisting of spherical molecules, cannot be applied to such liquid systems as water andalcohol that are of chemical interests. It is because the interaction between molecules insuch liquids, referred to as molecular liquids, depends not only on their distance but also
on their mutual orientation. The work to extend the O-Z equation to molecular liquids
was done by D. Chandler and H. C. Andersen.[5] The theory is referred to as RISM
(Reference Interaction Site Model) theory. The most important feature of the RISM
theory is to express the interaction between a pair of molecules by the sum ofinteractions among atoms (or interaction sites) in the molecules asnnu(1, 2) = ∑ ∑ uαγ (r)α =1 γ =1

where 1 and 2 in u(1,2) represent the position (R) and orientation (Ω) of the respective
molecule. On the other hand, uαγ (r) in the right hand side denotes the interaction
between atom α in molecule 1 and atom γ in molecule 2. That is, the left hand side
represents the interaction between two molecules by a fucntion of the center-to-center
distance and the orientaion, while the right hand side by the sum of atom-atominteractions. The latter is the same model used in the molecular simulation. Chandler
and Andersen reformulated the O-Z equation in terms of the interaction-site model. That

is called “RISM equation.” Here, the idea to derive the equation is briefly sketched.
The RISM equation is derived from the general Ornstein-Zernike equation(Molecular OZ equation).

h(1, 2) = c(1, 2) +ρc(1, 2)ρ(3)h(3, 2)d(3)Ω∫Let us substitue the entire right-hand-side of the equation into h(1, 2) , iteratively, thatwill produce an infinite series described by the following equation, similar to the O-Z
equation for spherical molecules.

⎛ ρ⎞h(1, 2) = c(1, 2) + ⎜ ⎟ ∫ d(3)c(1, 3)h(3, 2)
⎝ Ω⎠
⎛ ρ⎞
⎛ ρ⎞
=c(1, 2) + ⎜ ⎟ ∫ d(3)c(1, 3)c(3, 2) + ⎜ ⎟ ∫ d(3) ∫ d(4)c(1, 3)c(3, 4)c(3, 2) + 
⎝ Ω⎠
⎝ Ω⎠
2

The following transformation (“Chandler-Andersen transformation”) is applied to theboth sides of the equation.
fαγ (r) =

(

) (

)

1
f (1, 2)δ R1 + l1α δ R 2 + lγ2 − r d(1)d(2)2 ∫Ω

In the above equation, δ(x) signifies the Dirac delta-function. The transformation
corresponds to an average of the function f(1,2) over the angular space by fixing theposition ( R1 + l1α ) of atom α of the molecule 1 at the origin, while the position（ R 2 + lγ2 ）of the molecule 2 at the postion r.（Fig. 1.4）The RISM equation is obtainedby the transformation, which is expressed in terms of the graphical expansion, similar to
the O-Z equation.

where c denotes the direct correlation function (matrix) c(r,r’) between atoms(interaction sites), the black circles represents the integrals with respect to thecoordinates r and r’. ω is the intra-molecular correlation function (matrix) defined byω αβ ( r ) = δαβδ (r) + (1 − δαβ )sαβ (r)sαβ (r) =(1
δ r − Lαγ
4π L2αγ)In the expressions, Lαγ denotes the distance between atoms α and γ, and δ (r − Lαγ )represents the Dirac delta-function. This corresponds to fixing the distance between
atoms α and γ in a molecule to Lαγ. If one provides all the distance Lαγ between atoms
in a molecule, one can fix the srtucture or geometry of the molecule. (For example, inthe case of a water molecule, LOH, LOH, LHH)

Fig. 1.4 Coordinates for the interaction-site model of liquids—Extended RISM theory and its application [F. Hirata & P. Rossky, Chem. Phys.
Lett., 83, 329 (1981)]—	
 A theory to handle liquids consisting of non-spherical molecules was completed by the
RISM theory. However, it was not yet enough to treat such liquids as water and alcohol
in which molecules are interacting with hydrogen-bonds. It is because thehydrogen-bond is essentally an electrostatic interaction, and the problem associated withdivergence of the Coulomb integral, stated above, stays unsolved. It is the “extended
RISM theory” that solved the divergence problem to be applied to almost any type ofliquids and solutions including water and alcohol.

The extended RISM (XRISM) equation was derived from the RISM theory byrenormalising the Coulomb interaction in a way similar to the case of the O-Z equationfor electrolyte solutions.

where c’, Ω , and Q are defined as follows.

c' = c − φΩ = ω + ρ 2Q

ρ 2Q = C ⎡⎣φ ω ⎤⎦In the equations, Q is a function resulted from applying the renormalization of Coulombinteraction to the RISM theory. It signifies a “renormalized Coulomb interaction
between partial charges bounded by intramolecular constraints.”- Application of the extended RISM theory Structure of water-alcohol mixture	
 [K. Yoshida,A. Kovalenko, T. Yamaguchi, and F.
Hirata, J. Phys. Chem.B, 106, 5042(2002)]	
 Water-alcohol mixtures are the most popular soultion for human beings. However,understanding of their structure and property is still very primitive even in the 21st
century. For examples, water and tertialy butanol make a mixture with any
concentration, and there is no phase separation to water and the alcohol observed.
Nevertheless, it is well documented that the solution shows extremely large
concentration fluctuation at certain temperature and pressure, which is akin to the phaseseparation. Such a large concentration fluctuation has been expressed by words such as“micro-cluster” or “quasi phase separation.” But, what is the structural entity of “microcluster” or “quasi phase separation?” About ten years ago, we have made an analysis of
the solution structure of a water-t-butanol mixture based on the RISM theory. We havealso analysed the thermodynamic stability (or compressibility and concentration
fluctuation) of the solution. From those analyses, we could have clarified the strutctural
origin of the thermodynamic fluctuation.
Shown in Fig. 1.5(A) are the pair correlation functions (or radial distributionfunction: RDF) between aotms of water and alcohol in the solution.	
 The peak position

of RDF provides information concerning the distance between a pair of atoms forwater-water, water-alcohol, and alcohol-alcohol. Three-dimensional structure of thesolution can be deduced from the distance information based on an idea of thetrigonometry. Illustrative picture deduced in such a way from RDF is shown in Fig.
1.5(B). In case of the infinitely dilute alcohol in water, the hydrogen-bond network ofwater makes the main frame of the solution structure, and a t-butanol molecule isincorporated in the main frame by making hydrgen-bonds with water molecules. In thecase of low concentration of butanol in water, butanol molecules are incorporated in thehydrogen-bond network of water again so that their butyl groups are in contact eachother. It looks as if a small “micelle” is formed. We believe this is the identity of“micro-cluster” or “quasi phase separation.” On the other hand, in the infinite dilutionof water in butanol, a water molecule is incorporated in the hydrogen-bond chain of
butanol by making hydrogen–bonds with the alcohol. Those results reveal the
microscopic structure of water-alcohol mixture in an unequivocal manner.
	
 
	
 
	
 
	
 
	
 
	
 
	
 
	
 
	
 
	
 
	
 
	
 
	
 
	
 
	
 
	
 
	
 
	
 

Fig. 1.5(A)The atom-atom pair correlation functions in water-butanol mixture.

	
 
	
 
	
 
	
 
	
 
	
 
	
 

Fig. 1.5(B) Solution structure of water-butanol mixture inferred-Thermodynamic property of a water-alcohol mixture ( I. Omelyan, A. Kovalenko,
F. Hirata,

J. Theo. Comp. Chem., 2 (2), 193-- 203 (2003) )-We have revealed the microscopic strucure of water-alcohol mixture in the peceding
section. The next question to be asked is “how the structure is manifested inthermodynamic properties?” Since the words such as “micro-cluster” and/or “quasi
phase separation” are terminologies expressing the density and/or concentration
fluctuations in solution, it is natural to analyse the compressibility of the solution. It has
been well documented that the compressibility is a measure of the density and/or
concentrtion fluctuation. Shown in Fig. 1.6 is the isothermal compressibility calculated
from the equation. The isothermal compressibility can be calculated from the site-site
direct correlation functions using the following equation which can be derived from the
RISM/KH and Kirkwood-Buff thoeries.
	
 
	
 
	
 

kBT χ T0 =1m⎛⎞ρv ⎜ 1 − ρv ∑ ∑ cγ v γ v ' (0)⎟⎝⎠γ =1 γ '=1m

It will be clear that the RISM/KH theory reproduees the experimenntal results,
concentration and temperature dependence of the compressibility, faithfully. From theresults, the following picture concerning the anomalous behavior of water-alcohol
mixture can be drawn.
	 	
 Fig. 1.6

Isothermal compressibility for water-butanol mixtureA) In pure water, the compressibility reduces with increasing temperature in thistemperature range. The behavior can be explained in terms of the ice-like structure orhydrogen-bond network which is bulkier and more compressible than the
non-hydrogen-bonded structure. The ice-like structure “melts” with risingtemperature, which makes water less compressible. 	
 B) The compressibility of pure butanol increases with rising temperature. This behavior
is a common feature shared by many other liquids but water and gallium. The behavior
can be explained in terms of the thermal expansion that increases with rising temprature,that is, the compressible space increases as temperature increases.
C) Concentration dependence of the compressibility shows characteristic minima in thetemperature range investigated. The existence of mina demonstrates that there are twocompeting effects in the concentration dependence which balances at someconcentration. One of those effects is the increase of compressibility with increasingconcentration of butanol, which can be explained in terms of a model of ideal mixing.
Suppose the compressibility of the mixture is expressed by a simple superposition of thecompressibility of the component liquids, weighted by repspective concentration or mol
fraction in such a way that χ T = ( x − 1) χ water + x χ butanol . Then, the contribution of
butanol to the compressibility, which is greater than water, becomes more dominative as
the concentration increases, thereby the compressibility increases with increasing
concentration at the butanol-rich region. On the other hand, such a simple picture does
not apply any more at the lower concentration or the water rich region. The structure ofwater-butanol mixture, deduced from the pair correlation functions exhibited in Fig. 1.5,
is quite useful and instructive for explaining the anormalous behavior. Butanol
molecules in the low concentraion regime are incorporated in the hydrogen-bondnetwork of water through their OH-group, and their alkyl groups fill the void space ofthe hydrogen-bond network, as is shown in Fig. 1.5B (b). That is, the alkyl gorups
reduces the compressibility by filling the compressible space of water.
	 - RISM-SCF theory and its application [S. Tenno, F. Hirata, and S. Kato, Chem. Phys.
Lett., 214, 391 (1993)]−
Most of chemical reactions (especially biomolecular reaction) on the earth aretaking place in the environment of solution. On the other hand, the quantum chemistryor the electronic-structure calculation that is a major tool to explore the reaction, waspracticed without solution environment for long time. One of author’s contribution to
the science is to propose a theory to explore the electronic structure of a molecule (orsolute) in solutions by hybridizing an electronic-structure theory with the RISM theory.
The new theory is referred to as “RISM-SCF.” Essential point of the theory is to add theelectrostatic potential energy (or “reaction field”) due to solvent to the Hamiltonian (orFock operator) of the Schrodinger equation concering the electronic structure. The
reaction field can be expressed in terms of the pair correlation function byVλ ∈solute (rλ ) =∑ ∫ r − r ρg ( r − r ) drqαα ∈solvent

λα

λ

λ

In the above expression, λ and α are symbols to distinguish solute and solvent atoms,respectively, and qα partial charge on solvent atom α, gλα(|rλ - r|) the pair correlation
functions (or radial distribution functions) of solvent atom α around solute atom λ. The
Fock opertor which takes the solvent effect into consideration can be expressed byF̂i solv = F̂i − fi ∑ Vλ b̂λλ ∈solutewhere Fi is the Fock operator of solute in vacuum, and the second term expresses thecontribution from the reaction field. We solve the Schrodinger equation for theelectronic structure of solute with the solvated Fock operator, while we solve the RISM
equation to get the solvent distribution aorund solute with the partial charge obtained
from the quantum calculation.
There is a point to be made in actual applications of the theory to a molecule insolution, that is, solvent and solute give influence each other. The distribution of solvent
around solute, g(r), depends on the electronic structure or the effective charges of solute.
On the other hand, the electronic structure (or wave function; Ψ ) is influenced by thereaction field from solvent. Therefore, our strategy to attack the problem is to solve the
Schrodinger equation and the RISM equation iteratively untill the electronic structure
and the solvent distribution become self-consistent each other. Scheme of the iterative
calculation is illustrated in Fig. 1.7.

Fig. 1.7 Algorism for self-consistent solution of the RISM-SCF theory.

Menschutkin reaction: As an illustrative example of applications of the RISM-SCF
theory, we describe an application to the Menshutkin reaction. [K. Naka, H. Sato, A.
Morita, F. Hirata, and S. Kato, Theor. Chem. Acc. 102,165 (2000) ]H3N + CH3Cl <=> H3N+–CH3 + Cl–
Shown in Fig. 1.8 is the free energy profile along a reaction coordinate.

The

difference （dC-N - dC-Cl）between the C-Cl distance (dC-Cl) and the C-N distance (dC-N)
is chosen as the reaction coordinate. (E or F=0 at dC-Cl=∞) The reaction does notproceed in vacuum, because the energy keeps increasing after the reaction crosses theactivation barrier. On the other hand, in water, the free energy decreases dramticallyafter crossing the activation barrier, indicating that the reaction takes placespontaneously. The solvent effect for this reaction turns out to be nearly 100 kcal/mol.
Physical origin of the solvent effect can be understood by examining the solvent
distribution around the solute. The solvent distribution around the solute is shown in Fig.
1.9. The solvent distribution around Cl- ion after the reaction shows a sharp peak aorund
R=3.0A, which can be asigned to the hydrogen-bond between Cl- and H of water. Thishydrogen-bond between solute and solvent is contributing to the free energy to drive thereaction.

Fig. 1.8 Energy and free enegy profile
along the reaction coordinate.

Fig. 1.9 Solvent distribution around solute along the reaction
coordinate.

（References）[1] F. Hirata ed., “Molecular Theory of Solvation,” Springer, 2003.
[2] L. S. Ornstein and F. Zernike, Proc. Acad. Sci., Amsterdam, 17, 793 (1914)[3] J. Mayer, J. Chem. Phys., 18, 1426 (1950)[4] W.D.T. Dale and H. L. Friedman, J. Chem. Phys.,48, 2742 (1968)[5] D. Chandler and H.C. Andersen, J. Chem. Phys., 57, 1930 (1972)

II. Exploring the dynamics of solution based on the generalized
Langevin and RISM theories
In the previous chapter, I have explained the role of “solvent fluctuation” played inchemical reactions, but not it’s time evolution. Time evolution of solvent plays crucial
roles in chemical processes in solution. A typical example of such processes is so called“Solvation Dynamics” or “Dynamic Stokes Shift.” The process is initiated byphoto-exitation of a solute molecule in polar solvent, for example, detaching of anelectron from the solute. Then, the electrostatic field exerted from the solute to solvent
changes abruptly, because the charged state of the solute changes. However, thepolarization of solute cannot follow the abrupt change of the field instantaneously, but
relaxes with a certain relaxation time. The time evolution of the relaxation, which canbe measured by a probe light, reflects the chemical specificity and liquid structure ofsolvent. I have proposed a theoretical method to pursue the solvation dynamics of polar
solvent by combining the two theories in statistical mechanics, the RISM theory
explained in the previous chapter and the generalized Langevin theory.
Let’s start the chapter with a brief introduction of the generalized Langevin equation(GLE), which enables atomistic description of the dynamics of liquids and solutions. A
generalized Langevin equation can be derived by defining a set of dynamic variables asa function of the representive point ( Γ(t) ) in the phase space (Hilbert space), and byprojecting all other degrees of freedom onto those variables. Let C(t)(= C(Γ(t)) be thedynamic varaibles. Time evolution of a variable in the phase space can be described by
the following equation (Liouville equation),dB(t)= iL B(t)
dt

(2.1)

where L is the Liouville operator defined by the following equation.

⎡⎛ ∂H ⎞ ⎛ ∂ ⎞ ⎛ ∂H ⎞ ⎛ ∂ ⎞ ⎤L ≡ i ∑ ⎢⎜⎟ ⋅⎜⎟ − ⎜⎝ ∂p ⎟⎠ ⋅ ⎜⎝ ∂r ⎟⎠ ⎥i ⎣ ⎝ ∂ri ⎠ ⎝ ∂p i ⎠ii ⎦GLE is obtained by projecting B(t) onto C(t) . An operator ( p̂ ) for the projection isdefined by the following equation,p̂B(t) =C ⋅ ( C, B(t))(C,C)

In Eq. (2.3), B(t) is a variable in the phase space, “ • ” means a matrix product,(,) signifies the inner product of two vectors in the Hilbert space, defined by, = dΓf eq (Γ)C(Γ)B(Γ)
(C, B) = CB∫In the equation, f eq (Γ) denotes a probablity distribution function in equilibrium, B
indicates the adjoint vector of B. The generalized Langevin equation can be derived by
operating on the both sides of Eq. (2.1) with p astdC(t)= iΩ ⋅ C(t) − ∫ dτ K(t − τ ) ⋅ C(τ ) + R(t)
0
dt

(2.2)

In the equation, Ω , R(t) , and K(t) are referred to as “corrective frequency”,“random force”, and “friction kernel”, defined respectively by the following equations.

iΩ =(C, C)(C,C)


R(t) = exp [ i(1 − p̂)L t ] (1 − p̂)CK(t) =

 )( R, R(t)(C,C)

Eq. (2.2) looks very similar to the phenomenological Langevin equation, but all thevaribales in the equation, including R(t) and K(t) , have atomic-scale descriptions.
- Generalized Langevin Equation of Molecular Liquid Choice of the dynamic variables bears essential significance to describe molecularliquids. The most important requirement for the variables is how successful they are toaccount for chemical specificity of molecular liquids. The chemical specificity isreflected to the dynamics through the structure of liquids. There are two picturesconceivable for the dynamic of liquids. One of those pictures has been practiced
conventionally in most of the theories of liquid dynamics, which splits the dynamics

into the translational and rotational degrees of freedom. A draw back of such a model isslow convergence of the spherical-harmonic expansion in describing the rotationalmotion. I have proposed an entirely different picture based on the interaction site modelof liquids to descirbe the liquid dynamics. According to the new model, the dynamics ofa molecule in liquid is veiwed as a correlated translational-diffusion of each atom in themolecule. For example, let us think the dynamics of a diatomic molecule in the liquid,
illustrated in Fig. 2.1. If the two atoms (or sites) in a molecule move in the same
direction, the entire molecular motion is a translational motion. On the other hand, if
the two atoms move in the opposite direction, the entire motion becomes a rotationalmotion. The actual motion is a combination of those two. The advantage of the model isto incorporate the RISM theory for the liquid structure, decribed in Chapter I, naturally
into the dynamics.

Fig. 2.1 Two pictures for the dynamics of a molecule in liquids

We choose the fluctuation of the number density ( δρα ) of atoms and its conjugatedmometum ( jα ) as the dynamic varaibles as,δρα (r,t) = ∑ δ ( r − riα (t)) − ραi(jα (r,t) = ∑ v αi δ r − riα (t)i)

The projection operator is defined from the dynamic variables as

P B(t) =C ⋅ ( C, B(t))(C,C)

where the vector C is defined byC(k,t) ≡ (δρ(k,t), j(k,t))

Following the recipe of the generalized Langevin theory, all other variables areprojected onto C(k,t) to give rise to the following equation for the atomic density andconjugated momentum.

∂ 2δρα (r,t) ρα kBT=∇ 2r Φ(r, r ')δρα (r ',t)dr '− ∫ K(t − τ ) * j(τ ) + m −1R(t)
∂t 2
mα ∫

(2.3)

Φ(r, r ') appeared in the first term in the right hand side is a functional inverse of thedensity correlation function ( χ (r, r ') ) which represents the structure of liquid in
equilibrium. The first term signifies a restoring force proportinal to the fluctuation (ordeviation) of density in the analogy with the harmonic oscillator, and the second
derivative of Φ(r, r ') plays a role of the “force constant.”- Site-site Smoluchowski-Vlasov (SSSV) Theory [F.Hirata, J. Chem.
Phys.,96, 4619 (1992) ] –Multiplying the both sides of Eq. (2.3) by the equilibrium density fluctuation( δρ(t = 0) ) at t=0, and taking the ensemble average, one gets the following equation
describing the time evolution of the site-site density correlation function in the Fourier
space,(2.4)

where F(k,t) is the Fourier transform of the space-time correlation function (van Hove
function) defined by

Gαγ (r,t) ≡1δρα (0, 0)δργ (r,t)ρ

Fαγ (k,t) = ∫ Gαγ (r,t)exp [ −ikir ]drand ω k2

is the collective frequency defined by

There is a reason why the quantity is called “collective frequency.” If one ignores thefriction term in Eq. (2.4), the equation is formally identical to that of a harmonic
oscillator. This indicates that the collective density fluctution in liquids becomes theGaussian process due to the central limiting theorem.

ω k2

corresponds to thefrequency of the collective density fluctuation.
If one assumes that the densty fluctuation is very slow compared to other varaibles,
Eq. (2.4) can be written in the diffusion limit as,∂F(k,t)= −D(k)k 2 ρχ −1 (k)F(k,t)
∂t

(2.5)

where D(k) corresponds to the diffusion coefficient of atoms. The equation is reffered toas the site-site Smoluchowski-Vlasov (SSSV) equation.
The equation is first applied to calculate the space-time correlation (van Hove)
function. Shown in Fig. 2.2 is the space-time correlation function (solid lines, dashedlines, and dotted lines) calculated by the SSSV theory, compared with the results from amolecular dynamics simulation (circle, +, *). It is seen that the results from SSSV
reproduce the simulaton (“experimental”) results fairly well.

Fig. 2.2

The space-time correlation function of water claculated from SSSV theory.
(solid lines, t=0.01 ps; dashed lines, t=0.1 ps; dotted lines, 1.0 ps)-Solvation dynamics (Dynamic Stokes shift) [F. Hirata, T. Munakata, F.
Raineri, H.L. Friedman, J. Mol. Liquids, 65/66, 15 (1999)]–
The theory of liquid dynamics, described above can be applied to the so called“solvation dynamics,” or the dynamic Stokes shift. A typical process of the dynamic
Stokes shift is initiated by a photo-excitation of a solute in polar solvent, due to socalled “pump light.” The solvent polarization becomes non-equilibrium with the newelectronic structure or charged state of the solute, instantaneously. Then, the solvent
structure as well as the solute-solvent interaction relaxes so as to recover theequilibrium to the new solute-state. The energy relaxation is probed by the time
evolution of the Stokes-shift concerning a spectrum of a light. The time evolution of thespectrum is described by the following equation.

S(t) =

ν (t) − ν (∞)ν (0) − ν (∞)

If the response of the solvent structure to the change in electronic or charged state ofsolute is linear, one can apply the linear response theory to the process, which gives riseto the following expression for the energy relaxation in terms of a time correlation
function.

S(t) =δε (t)δε (0))δε (0)δε (0)In the equation, δε (t) denotes the fluctuation of solvation energy, and

represents the ensemble average in an equilibrium state, before or after thephoto-excitation. We have derived the following equation to describe the timecorrelation function by expressing δε (t) in terms of the SSSV theory.
∞∫ dkk ∑ F (k,t)B (k)S(t) =∫ dkk ∑ F (k,t = 0)B (k)
∞

0

2

jj '

0

jj '

jj '

(2.5)

2

jj '

jj '

jj '

In Eq. (2.5), Fjj ' (k,t) is the space-time correlation function (some time called“intermediate scattering function”), j and j’ label atoms in slovent. B jj ' (k) denotes thepeturbation on the solvent, due to the photo-excitation of solute.
B jj ' (k) = ∑ ω λλ ' (k)Δφλ j (k)Δφλ ' j ' (k)λλ 'where ω λλ ' (k) the intra-molecular correlation function, defining the structure (orgeometry) of the solute molecule (see Chapter I). Δφλ j (k) is change in the“renormalized” interaction-energy ( Δφλ j (k) = φλFj (k) − φλI j (k) ) between solute andsovent before and after the photo-excitation, which is expressed by the following
equation using the solute-solvent direct corelation functions. (I and F denote theequilibrium states before and after the photo-excitation.)φλI ,jF (k) = −kBTcλI ,jF (k)As an example of applications of the theory, the energy relaxation function (S(t))

induced by a photo-ionization of a solute, from zero to +1, is shown in Fig. 2.3 for avariety of solvent.

Fig. 2.3

Energy relaxation function of a solute induced by a photo-excitation inpolar solvents

Although detailed explanation is skipped here, the figure demonstrates that thebehaivior of the energy relaxation strongly reflects the characteristics of solvent, such as“hydrogen-bonding” and/or “polarity.” It is of particular interest that methonol shows abehavior characterized by three relaxation times. The results reproduce the well-known
behavior observed by the experiments. Considering that the theory does not include any
phenomenological parameters for the relaxation times, the results are demonstrating
robustness of the theory.
- Analysis of collective excitations in “water” based on thesite-site interaction model [S. Chong and F. Hirata, J. Chem. Phys., 111,
3083, 3095 (1999) ]–In the previous section, I have presented a new picture to describe the dynamics ofa molecule in liquids, including water, based on the interaction-site model. Accordingto the picture, the dynamics of a molecule in solution is described by translationalmotions of atoms consisting the molecule, whcih are correlated each other. However, I
have not explained the relation of the new picture to the conventional one which
decouples the motion into translational and rotational motions. Here, I present a work
which touches this issue.
For that purpose, let’s go back to Eq. (2.4), describing the time evolution ofdensity correlation functions.

I have explained already that the equation is formally identical to that describing aharmonic osillator, if one ignores the third term in the left hand side, corresponding to
the friction term. That is, the equation implies that the restoring force exerted on
density fluctuation is proportional to the density fluctuation, and that the proportional
constant (or a “force constant”) is ω k2 . It is as if the same law as “Hook’s law” inthe harmonic oscillator is govering the density fluctuation. Then, with an analogy to
the normal mode analysis, “normal modes” of the density fluctuation of atoms,
corresponding to “eigen frequencies,” can be obtained by diagonalizing the matrix

ω k2 . The diagnalization corresponds to a transformation of the dynamic variablesfrom the density of atoms to their linear combination,

ρi (k) = ∑ xiα (k)ρα (k)αwhere ρi (k) denotes the i-th mode of the collective density fluctuation, ρα (k)denotes the density of atom α . In the case of water, α distinguishes an oxygen atom(O) and two hydrogen atoms (H1, H2). Thus obtained eigen values (frequency) andeigen functions (modes of atomic density fluctuation) of ω k2

for water are depictedagainst the wave number in Fig. 2.4. One of the three eigen frequencies exhibits thefollowing asymptotic behavior at the limit of k=0,

2
ω acou(k → 0) =k BT
k2
M χ ( k = 0)

(2.6)

where M denotes the mass of a molecule. The equation shows a relation between the
wave number ( k = 1 / λ ) and the frequency ( ω ). The proportional constant( kBT / M χ (k = 0) ) is the sound velocity. The mode satisfies the dispersion relationof the sound wave, c = λω , thereby it is assigned to an acoustic mode. It is also
understood that the mode is related to the translational motion, since Eq. (2.6) includes
the mass of a molecule, M. On the other hand, the other two modes are assigned tosome optical modes, since they have finite ω at the limit of k=0. Although detailed
explanation is skipped here, we found that the two optical modes correspond to thetwo rotational-vibrations of a water molecule, pitch and roll, as illustrated in Fig. 2.5.

Fig. 2.4 Collective modes of water

Fig. 2.5

Two rotational modes of a water molecule- Dynamics of an ion in water [S. Chong and F. Hirata, J. Chem. Phys., 111,
3654 (1999)]In the preceding section, I have explained how the two pictures of liquid dynamics,
translational motion of interaction-sites (or atoms) and translational and rotationalmotions of a whole molecule, can be transformed from one to the other. In thefollowing, the dynamics of an ion in water is analysed from a view point of theinteraction-site dynamics.
The dynamics of a small ion in water, such as alkali and halide ions, has attracted a
lot of attention from chemists due to its practical interest in, say, the electrochemistry.
The problem has also fascinated many theoretical physists including Nobel loureatessuch as M. Born and L. Onsager. Why it is so? It is because the dynamics of small ionsexhibits a non-Stokes-Einstein behavior. It is well regarded that the friction exerted on alarge ion from solvent follows the Stokes-Einstein law asς Stokes = 6πησ
where η and σ denote the viscosity of solvent and the mass of solute. The law saysthat the friction increases linearly with increasing the size of solute. However, thefriction on alkali-metal ions (Li+, Na+, K+, Rb+, Cs+) and halide ions （F−, Cl−, Br−, I−）
decreases with increasing ion size when the size is less, and then turns into increase, as
illustrated by a cartoon in Fig. 2.6.

Fig. 2.6 Illustration of the friction coefficient exerted on an ion in water

(a) Solventberg model(b) Dielectric friction modelFig. 2.7 Two models for the friction exerted in an ion

The latter behavior can be explained in terms of the Stokes-Einstein law, while thebehavior in the small ion-size is against the law. Two models have been proposed to
explain the anti-Stokes-Einstein behavior of the ion friction. (Fig. 2.7) One is (a)“solventberg model” and the other (b) “dielectric friction model.” The solventberg
model, that has been supported by many experimental chemists, regards the Stokes
radius as an effective radius of a solvated ion. If the strength of solvation is proportional
to the eletrostatic interaction between ion and solvent, the effective (or Stokes) radius ofa solvated ion will increase with decreasing the size of bare ion. That explains theanti-Stokes-Einstein behavior in small ion size. On the other hand, the dielectric friction
model, that was proposed and supported mainly by theorretical physicists including M.
Born, sees the origin of the anti-Stokes-Einstein behavior in the rotational relaxation ofsolvent molecules around an ion. Let’s imagine that an ion in polar solvent is inequilibrium. The ion would be in stable state by polarizing the surrounding solvent
isotropically. Suppose that the ion is displaced abruptly due to a perturbation, such as anelectrostatic field. The surrounding solvent may not follow the ion displacement
instantaneously, to make the polarization anisotropic (see the left hand side of Fig. 2.7(b)). The solvent polarization should relax (rotational or dielectirc relaxation) to recoverthe equilibrium with new position of the ion, and to restore the isotropic polarization.
Energy as well as momentum dissipation assoiciated with the relaxation is claimed to be
an origin of the friction.
We have analysed the friction exerted on an ion in water by means of the
GLE-RISM theory, described above. In the theory, the friction is considered as a
response of the collective excitation of solvent, described in the preceding section, tothe perturbation or ion-water interaction.

The ion-water interaction is decomposed

into two contributions, the short-range interaction and the electrostatic interaction, while
the response of the collective excitation is also decomosed into two contributions, theacoustic mode and the optical mode. Then, the friction coefficient is decomposed into
the three contributions (the detail is skipped) as,ς = ς NN + ς NZ + ς ZZ
where ς NN is the response of the acoustic mode of solvent to the short range interaction,that corresponds to the Stokes friction in the hydrodynamic model. ς ZZ is the responseof the optical mode to the electrostatic interaction, which corresponds to the dielectric
friction in its physical meaning. Finally, ς NZ is the cross term, namely the response of
the accoustic mode to the electrostatic interaction and that of the optical mode to theshort-range interaction. Depicted by circles in Fig. 2.8 is the friction coefficient ςagainst the ionic radii. In the same figure, each component of ς is plotted by triangles( ς NN ), squares ( ς ZZ ), and diamonds ( ς NZ ). The overall friction coefficient ( ς ) exhibits
an anti-Stokes-Einstein behavior in the small ion-size region, and follows the
Stokes-Einstein law in the larger ion-size region, in accord with the experimental
observation. Then, how about the component of ς ? ς ZZ decreases monotonically withincreasing the ion size both for cations and anions, indicating that the dielectric friction
reduces as the electrostatic interaction decreases. The behavior proves that an origin of
the anti-Stokes-Einstein behavior of ionic friction is the dielectric friction. On the other
hand, ς NN also shows anti-Stoke-Einstein behavior, except for Li+, in the small ion-size
region. This is due to reduction of the effective radii, represented by the direct
correlation function, with increasing (bare) ion size. This indicates that the solventberg
model also explains the anti-Stoke-Einstein behavior to some extent. However, themodel breaks down for the Li+. This may be because the effective ion radius is notproportinal to the electric field for such an extremely small ion.

Fig. 2.8 The friction exerted on small ions in water
We have also calculated the velocity auto-correlation functions ( z(t) = v(0)v(t) ) ofions in water, which is depicted in Fig. 2.9. This is the first results for the velocity
auto–correaltion function of ions in water, obtained entirely analytically by means of thestatistical mechanics. The most important feature seen in the figure is the oscillatory
behavior observed in the auto–correlation functions for small ions, Li+ and F-. Thosesmall ions are strongly coordinated by water molecules, and make a water-ion complex
with some lifetime. In another word, the water-ion complex as a unit makes diffusive
motion in water for some period. The ion can oscillate within the complex for someperiod characterized by the relaxation time. The oscillatory behavior seen in z(t) for thesmall ions reflects this physics.

Fig. 2.9 Velocity auto-correlation functions of ions in water

III. Development of the 3D-RISM/KH theory and its application tolife phenomena [N. Yoshida, T. Imai, S. Phongphanphanee, A. Kovalenko, F.
Hirata, J. Phys. Chem. B (Feature Article) 113, 873 (2009)]
In the beginning of this review, I have emphasized the life phenomena as a motivation
for studying water. When one views life phenomena in molecular level, it is a process
in which many molecules such as DNA and protein in cells express their functions
concertedly in order to maintain a life, and inherit it to next generation. If one looks
carefully a way how those molecules are working in our body, one may realize that two
physicochemical processes are commonly operating. One of those is theself-organization, and the other is the molecular recognition. A typical example of theself-organization is the protein folding. As been clarified by Anfinsen, an unfolded
protein refolds spontaneously into a three dimensional structure (or native
conformation), provided an amino-acid sequence as well as proper thermodynamic
conditions such as temperature, pressure and pH. The three dimensional stucture is anecessary condition for protein to function. The words “proper thermodynamic
conditions” in the above statement deserves for a special attention, because the words
are often forgotten by scientists in the field of biophysics. It is a big misunderstanding if
one ignores the statement concerning “thermodynamic condition” in “Anfinsen’sdogma,” because protein will never folds into its native structure without proper
thermodynamic conditions. In this regard, water plays a crucial role to the protein
folding, since the proper thermodynamic condition is almost synonym to the proper
solution condition.
The molecular recognition, the other physicochmeical process in life phenomena, is
a process in which a protein binds small molecules or ions in its active site. Therefore, it
is a process in which a protein should pass through whenever it expresses its function
such as an enzyme and an ion channel. In the following, the physics of molecular
recognition is explained taking an enzymatic reaction as an example.

Fig. 3.1 Illustration of enzymatic reaction
In Fig. 3.1, illustrated by a cartoon is a process of an enzymatic reaction. In the figure, ayellow-colored crescent and its eclipsed part illustrate a protein and its active site, while
red and green spheres represent, respectively, substrates before and after a chemical
reaction catalysed by the enzyme. Blue spheres mimic water molecules. In an enzymatic
reaction, enzyme should bind one or few numbers of substrate molecules at its active
site (or cavity) to make a Michaelis-Menten complex. This process is nothing but amolecular recognition. After that, electrons are exchanged between the substrate andenzyme or among the substrates, which produces new molecules. This process is achemical reaction. Finally, the produced molecules should get out of the active site to
become useful products for living system, which is just an inverse of the molecular
recognition, governed by the same physics law. The molecular recognition process (orinverse) is determined by affinity (or comfortableness) of a substrate with an active site.
Thermodynamic measure of affinity is the free energy change before and after thebinding, which consists of three contributions: (1) direct interaction energy between
protein and substrate, (2) the entropy change of protein and substrate, (3) change in thesolvation free energy of both protein and substrate before and after the binding. Amongthe three, the direct interaction works for promoting binding due to the electrostatic aswell as van der Waals interatcion. The entropy effect of solutes contributes in general topreventing from binding. It is because the degrees of freedom of both host and guest
molecules reduce. The change in the solvation free energy contributes in principle toeither direction, depending on detailed characetristics of atoms consisting protein
active-site as well as substrate molecules. For example, amino-acid resiudes at theactive-site include some charged residues, such as Asp or Lys, the free energy change
upon the binding is likely to be positive, because few water molecules arehydrogen-bonded to those charged residues before binding substrate, and those watermolecules should be removed (desolvation) in order for the substarte to be bound. The
free energy change associated with the desolvation is referred to as “desolvation
penalty.” If an active site consists only of neutral residues, such as Leu or Trp, thesituation may be different. In such a case, a substrate for such an active site is most
likely to be a hydrophobic molecule, and the free energy change associated with thebinding may become negative, due to a hydrophobic interaction. One may call the freeenergy change as negative desolvation penalty. Actual situation would be combinationof those two cases.
About 15 years ago, we tried to evaluate the solvation phenomena of protein using
the RISM (1D-RISM) theory, decribed in the preceeding two chapters, but the attempt
was in vain. It is becaue the solvent environment around protein is so inhomogeneousfor the theory to be applied. Most of globular proteins have a core regions consisting ofhydrophbic residues, where almost no water molecules exist. (Sometimes, there are few
water molecules which work as a building block of protein structure.) On the other hand,
there are many hydrophilic residues around the surface of protein, which works fordissolving the molecule in water. An active site of protein has an extremely
inhomogeneous environment in atomic level in terms of its geometrical shape and thecharge distribution, which regulates the binding affnity with substrates and ligands.
Furthermore, water molecules hydrated to protein exchange with those in bulk. The old
1D-RISM theory was not able to handle such inhomogenity. In order to overcome theproblem, we have developed a new theory called “3D-RISM/KH.”
It was explained in Chpater I that there are two models to describe theintermolecular interactions. One of those employs the explicit angular coordinate toexpress the orientational dependency of the interaction. The other is the interaction-site
model (ISM) which describes the intermolecular interaction by a sum of interatomic
interactions of the two molecules. The transformation from the former to the latter isperformed by applying the Chandler-Andersen transformation to the molecular
Ornstein-Zerinke (MOZ) equation. (See Chapter I) The Chandler-Andersentransformation corresponds to a physical process in which an interaction-site is fixed at
an atom of a molecule, and an average over the orientation is taken for the correlation
functions in MOZ. The transformation is applied to both solute and solvent molecules in
the case of 1D-RISM. Unfortunately, the inhomogeneous environment around the soluteis over-averaged due to some approximation included in the theory. Then, a question
came up to us. What happens if we apply the Chandler-Andesen transformation just forsolvent? That is to apply the orientational average around an interaction-site just forsovent, with fixing the coordinates of all atoms in solute at the three dimensional space.
The 3D-RISM theory was derived based on such an idea.
- 3D-RISM/KH Theory [A. Kovelenko and F. Hirata, Chem. Phys. Lett. 290, 237(1998); J. Chem. Phys., 110, 10095 (1999)]The theory is based on the molecular Ornstein-Zernike (MOZ) equation for the density
correlation function between solute and solvent in infinitely dilute solutions.
h uv (1, 2) = cuv (1, 2) + ∫ cuv (1, 2)ρ v (3)h vv (3, 2)d(3)(3.1)

In the equation, 1, 2, ... represent the coordinates of solute and solvent, describing both
position and orientation (see Chapter I), and the superscripts u and v denote solute andsolvent, respectively. If one apply the Chandler-Andersen tarnsformation

hαuv (r) =()

1
δ R 2 + lα2 − r h uv (1, 2)d(2)
∫
Ω

(3.2)

only to solvent coordinates, “2”, then, one gets the following equation (3D-RISM).

hαuv (r) =∑ ∑ ∫ χ ( r − r ' )c (r ')dr 'v '∈solvent η ∈v '

vv '
αη

v'u
α

(3.3)

vv ′
where χαηis defined by

vv '
χαη
( r ) ≡ ω αηv ' (r) + ρ v 'hαηvv ' (r)(3.4)

In Eq. (3.4), ω and h are intra- and inter-molecular correlation functions, respectively,in solvent. (see Chapter I)

The derivation of the equation is skipped here, and justphysics of the equation is explained in the following.
Let us consider the average density of solvent molecules at a position around asolute molecule. (Fig. 3.2) When the position is far from the solute molecule so as to be
regarded as the bulk, the density will be constant which is the same as in the puresolvent. On the other hand, when it is nearby solute, the density will be “perturbed”
significantly by the field due to the solute molecule, and be different from that in thebulk, depending on the strength of the perturbation. Physical meaning of the 3D-RISM
equation can be readily understood in terms of a non-linear response theory as follows.
Let us denote the average density of solvent atom γ at the bulk, the density nearby
solute, and the density response to the perturbation as ρ γ, ργ (r) , and Δργ (r) ,respectively. Then, statement above can be expressed as,

ργ ( r ) = ργ + Δργ ( r ) .
The density response to the perturbation can be expressed in terms of a non-linear
response theory asΔργ ( r ) = ∑ ∫ χ γα (r, r)ργ cα ( r ) dr ,αwhere the cα (r') is a non-linear perturbation due to the solute molecule, andχαγ ( r, r ') is a response function. (The reason why we call it “non-linear” will beclarified in a moment.) The equation can be viewed as the 3D-RISM equation by

identifying ca(r) as the direct correlation function and χαγ ( r, r ') as the correlation
function of density fluctuation in bulk solvent, that is,ρ 2 χαγ ( r, r ') = δρα(0) (r)δργ(0) (r ') ,where δρα(0) (r) is the density fluctuation of atom a in the pure liquid defined byδρα(0) (r) = ρα(0) (r) − ρα .
Several approximate equations have been devised for the direct correlation functions.
For examples, the hypernetted-chain approximation reads,

cαuv (r) = exp ⎡⎣ − β uαuv (r) + hαuv (r) − cαuv (r) ⎤⎦ − 1 − ⎡⎣ hαuv (r) − cαuv (r) ⎤⎦ .
In the expression, uαuv (r) is the direct interaction potential exerted on the solvent
molecules from the solute molecule, and hαuv (r) is the density fluctuation in solvent at
position r, normalized by the bulk density, namely,
hαuv (r) = Δρα (r) / ρ .

The three dimensional distribution function used in this study is defined from hαuv (r)bygαuv (r) = hαuv (r) + 1 .

It is not only the direct interaction uαuv (r) with solute that perturbs the density ofsolvent at a certain position, but also that from solvent molecules at the other positions,whose density is also perturbed by the existence of the same solute. Such “indirect”
perturbations are renormalized into the terms including ⎡⎣ hαuv (r) − cαuv (r) ⎤⎦ . Suchrenormalization makes the perturbation highly “non-linear.”Fig. 3.2 Density distribution of solvent around solute

-Water molecules confined in a protein cavity, and molecular
recognition [T. Imai, R. Hiraoka, A. Kovalenko, and F. Hirata J. Am. Chem. Soc.
(Communacation), 127, 15334 (2005)]
It is a common sense that water is essential for life. However, it is not wellunderstood in molecular level what role water plays. The biggest reason is because
almost nothing was understood about the state of water in cells, especially aroundprotein and DNA. For examples, in a (enzymatic) hydrolysis reaction, a water molecule
plays a role of substrate. In order for a water molecule to be invloved in the reaction, it
should be bound to an active site of protein with precise position and orientation. Untill
recently, the position of a water molecule in protein has been determined by the X-ray
crystalography. However, the method has serious difficulties. Firstly, water molecules
are moving around even in an active-site, and the electron density is largely smeared out.
Secondly, especilly in the case of a hydrolysis reaction, the water molecule as a
substrate disappears upon the reaction. Thirdly, the method cannot determineorientation of a water molecule anyway. We have found that the 3D-RISM/KH theory
can provide an alternative tool to resolve the problem.
We have calculated the spatial distribution ( g(r) ) of water molecules around ahen-eggwhite lysozyme using the 3D-RISM/KH theory. The results are shown in Fig.
3.3.

(a) g(r)>2(b) g(r)>4(c) g(r)>8

Fig. 3.3 Spatial distribution of water (oxygen) around lysozyme, calculated by
3D-RISM/KH.

The figure shows the distribution of oxygen atom, which corresponds almost exactly tothat observed by the X-ray crystalography. The three panels shown in the figure
correspond to the same data of the distribution, but depicted with the different thresholdvalues for g(r) : (a) g(r) > 2 , (b) g(r) > 4 , (c) g(r) > 8 . Since g(r) = 1 for bulk water
which is not perturbed by the protein, (a) represents water molecules which are weaklyinteracting with protein, while (b) exhibits those water molecules bound strongly to theprotein. In any case, it is obvious that the results are reproducing the inhomogeneous
distribution of water molecules around a protein quite faithfully.
However, the result shown in Fig. 3.3 is just a glimpse of the power which the
3D-RISM/KH theory posesses. The most important power of the theory is demonstrated
in Fig. 3.4, in which the distribution of water inside the active-site of lysozyme isdepicted. In Fig. 3.4(a), shown by the green and purple surfaces are, repsectively, thedistribution of oxygen and hydrogen atoms in the active site. Molecular model
representation corresponding to Fig. 3.4(a) is exhibited in Fig. 3.4(b), in which oxygenand hydrgen atoms are shown, respectively, by green and purple spheres. Fig. 3.4(c)shows corresponding X-ray results for water oxygen. The figures demonstrate that thetheory reproduces the experimental results faithfully. (Unfortunately, we cannot
compare the results for hydrogen atoms, since the X-ray cannot see hydrogen atoms.)

Fig. 3.4 Water molecules inside the active site of lysozyme, probed by 3D-RISM/KH.
The results are of great importance, because this is the first to give an answer to the
problem of molecular recognition by a statistical mechanics theory. Futhermore, theresults suggest a possibility of applying the theory to problems concerning themolecular recognition, including enzymatic reactions and drug screening. In fact, wehave applied the theory to molecular-recognition processes of a variety of small
molecules with protein, including ions and drug compounds, and derived useful
information concerning protein functions and their inhibition. Some of the applications
are described in the following.
- Selective ion binding by mutants of human lysozyme [N. Yoshida, S.
Phongphanphanee, Y. Maruyama, T. Imai, F. Hirata, J. Am. Chem. Soc.
(communication), 128 , 12042 (2006) ]–Small ions such as Na + and Ca 2+ play important roles in chemical reactions andsignal transductions in living systems. That can be understood immediately from thefact that lack of those ions causes some symptom to our body. Nontheless, it has not bewell understood how those ions are involved in protein functions. The biggest reason
why is because it is not so easy to determine experimentally the position in an active
site, where ions are bound. For examples, it is well regarded that Mg 2 + plays a role of“co-enzyme” in the restriction enzyme in E.coli, which cleaves DNA. However, itremains largely controversial where the ion is, and how many ions are concerned withthe reaction.
We have found that the 3D-RISM/KH theory is quite useful to identify the species
and position of ions bound to an active site of protein. Concerning the human lysozyme
we have studied, there has been an excellent experimental study reported by Kuroki and
Yutani. [R. Kuroki and K. Yutani, J. Biol. Chem. 273, 34310 (1998)] They have carriedout an X-ray crystalography for binding of cations ( Na + , K + ,Ca 2 + ) to the wild type andtwo mutants (Q86D, A92D) of human lysozyme, and led the following conclusions.
(1) The wild-type protein does not bind any cations studied.
(2) The Q86D mutant does not bind any cations as well.
(3) A92D mutant binds Na + , but not K + .
(4) The double mutant binds Ca 2 + .
We have carried out the 3D-RISM/KH calculation for the same system as Kuroki
and Yutani to obtain the spatial distribution ( g(r) ) of ion in the active site of humanlysozyme. The results are shown in Fig. 3.5.
In the figure, the surface colored red, yellow, and orange indicate g(r) of,respectively, water oxygen, Na + , and Ca 2 + , and white spheres represent position ofwater molecules, determined by X-Ray. In the figure, only water molecules are seen forthe wild type and the Q86D mutant, while the distribution (yellow) of Na + is observedin the A92D mutant, on top of water oxygen. And, a marked distribution (organge) of

Ca 2 + is seen in the(Q86D/A92D) mutant. Those results are in complete agreement withthose by Kuroki and Yutani, proving that the 3D-RISM/KH theory has capability ofprobing ions bound in the active-site of a protein.

wild typeFig. 3.5

	
 

Q86D

A92D

Q86D/A92D

The distribution of ions bound to human lysozyme-Aspirin bound to phospholipase A2 [Y. Kiyota, N. Yoshida, and F. Hirata,
J. Chem. Theor. Comp., 7, 3803 (2011)]In this section, I explain an application of the 3D-RISM/KH theory to a drug design.
The target protein is Phospholipase A2 (PLA2), which concerns the synthesis of
Arachidonic acid, a compound causing pain and/or fever. It is also known that theprotein binds acetylsalicylic acid (or Aspirin) to its active site. The protein is regarded
as a model protein for drug discovery.

Fig. 3.6 Distributin of Aspirin around Phospholipase A2

In the study, we have applied the 3D-RISM/KH theory to calculate the spatial
distribution ( g(r) ) of Aspirin around and inside the active site of PLA2. The result isshown in Fig. 3.6. The distributions colored blue, red, and yellow in the figure
correspond, respectively, to atoms in the three functional groups of Aspirin; -COOH,
phenyl group, and –COOCH3. (inserted picture) The picture in the right most figure is
the binding mode inferred from the electron denisty distribution due to the X-ray
crystalography. (green sphere is Mg 2 + ) It may be understood immediately from thefigure that the distribution of Aspirin inside the active site, calculated by 3D-RISM/KH,
corresoponds rougly to that inffered from X-ray.
We have made further analysis of the 3D-RISM/KH result to infer the binding mode
corresponding to the distribution. The result is shown in Fig. 3.7 in comparisonn withthat deduced from X-ray. The pictures colored blue and red corresponds to the binding
modes of Aspirin, respectively, from X-ray and 3D-RISM/KH. Since the both binding
modes are deduced from the analyses of the probability distribution, they are always
associated with some errors. Within the error bars, the agreement between the theory
and the experiment is fair.

	 Fig. 3.7 Binding mode of Aspirin at the active site of	 phospholipase A2

	
 
	
 
	
 
	
 

- Partial molar volume of protein [T. Imai, A. Kovalenko, F. Hirata, Chem.
Phys. Lett., 395 (1-3), 1 (2004); J. Phys. Chem. B, 109, 6658 (2005) ] Here, I talk about the partial molar volume of protein as an exmaple of applicationsof the 3D-RISM/KH theory to thermodynamics of protein. Many readers may not befamiliar with “partial molar volume.” However, the following thermodynamic
expression may convince the reader how important it is.

ΔV⎛ ∂ ln K ⎞⎜⎝⎟⎠ = −∂P T
RT
where K denotes the equilibrium constant of a chemical reacion, ΔV is the difference ofthe partial molar volume between reactant ( VR ) and product ( VP ); ΔV = VP − VR . The
equation describes the dependence of chemical equiribrium upon pressure. It is anexpression of Le’ Chaterier’s law, that is, the change of equilibrium due to pressure
takes place toward the direction in which the effect is minimized, or the volume reduces.
It means that we can predict the direction of change in chemical equilibrium due topresuure, if we are able to find the patial molar volume of the reactant and product.
There are three thermodynamic parameters which influence the structure of protein,temperature, pressure, and concentration of co-solvent. It is the partial molar volume
that determines the structural response of protein to pressure.
One may think that “partial molar volume” is a geometrical volume, but it is nottrue. The best example to understand why it is not is the partial molar volume of ions inaqueous solutions. For example, the partial molar volume for Li+ is reported as -11.2
cm3/mol due to experiments. “Is volume negative? What does it mean?” In fact, thegeometrical volume estimated from its ionic radius is V = ( 4 / 3) π R 3  1.0cm 3 / mol ,and it is positive.

Fig. 3.8 Partial molar volume of ion

However, the strong electrostatic-interaction between the ion and water molecules
contracts the solution, which makes the overall volume change of solution negative. The
situation is illustrated in Fig. 3.8. Like this example, the partial molar volume is athermodynamic quantity which reflects changes in the structure of solution due tosolute-solvent interactions.
There have been many experimental studies carried out for the partial molar volume
of biomolecules, protein and DNA. However. Virtually no theoretical study wasreported. A reason is because there was no statistical mechanics theory for molecularliquids. All biomolecules are desolved in water, thereby the statistical mechanics todescribe the structure and thermodynamics of water is a neccessary condition for such a
study. The problem has been solved by the development of RISM and 3D-RISM
theories.

Fig. 3.9 The partial molar volume of protein: cross, experimental results; black
dots, 3D-RISM/KH.
Let’s look at the application of 3D-RISM/KH to the partial molar volume of protein.
Shown in Fig. 3.9 is the partial molar volume of several proteins, experimentallystudied. It is obvious that the theoretical and experimental results show almost
quantitative agreement. One may think that the result may be readily obtained just by
calculating the geometrical volume of protein. However, it is not that simple. There atare least two reasons for that. Firstly, the geometrical volume does not take theprotein-water interaction into consideration. That was described above, taking Li+ ion
as an example. The second, the geometrical volume does not account for the watermolecules bound (recognised) at internal cavities of protein. If a water molecule isbound at a cavity of protein, then the volume is about 18 cm 3 / mol less compared tothe case in which no water molecule is bound. Therefore, unless one can estimate thenumber of water molecules bound to cavities in protein, the partial molar volume thus
calculated is erroneous. In this regard, the results shown in Fig. 3.9 provide athermodynamic proof for soundness of the 3D-RISM/KH theory to describe the
distribution of water molecules around/inside protein.

Publication list (2018)
Fumio Hirata
1.

F. HIRATA, K. ARAKAWA , "Ultrasonic Study of Solute-Solvent Interactions in Aqueous Solutionsof Tetraalkylammonium Salts," Bull. Chem. Soc. Japan, 45, 2715 (1972)

2.

F. HIRATA, K. ARAKAWA, "Molar Volume of Ions," Bull. Chem. Soc. Japan, 46, 3367 (1973)

3.

F. HIRATA, K. ARAKAWA, "The Computation of the Thermodynamic Properties of Aqueous
Electrolyte Solutions by Means of the Perturbation Theory of Fluid," Bull. Chem. Soc. Japan, 48,
2139 (1975)

4.

F. HIRATA, K. ARAKAWA, "Statistical Mechanical Calculation of the Radial Distribution Function
for a Water-like Fluid," Bull. Chem. Soc. Japan, 50, 1032 (1977)

5.

F. HIRATA, H. L. FRIEDMAN, H. HOLTZ, H. G. HERTZ, "NMR Relaxation Study of Li+-Ni2+
Interaction in Aqueous Solution," J. Chem. Phys., 73, 6031 (1980)

6.

F. HIRATA, P. J. ROSSKY, “On the Interpretation of Solute Induced Solvent Structure,” J. Chem.
Phys., 74, 6031 (1981)

7.

F. HIRATA, P. J. ROSSKY, "A Realization of 'V-structure' in Water," J. Chem. Phys., 74, 6867 (1981)

8.

F. HIRATA, P. J. ROSSKY, "An Extended RISM Equation for Molecular Polar Liquids," Chem. Phys.
Lett., 83, 329 (1981)

9.

F. HIRATA, B. M. PETTITT, P. J. ROSSKY, "Application of an Extended RISM Equation to Dipolar
and Quadrupolar Fluids," J. Chem. Phys., 77, 509 (1982)

10. P. J. ROSSKY, F. HIRATA, "The contribution of High Frequency Intermolecular Motions to the
Structure of Liquid Water," in Molecular based Study of Fluids, ACS advances in Chemistry Series,
American Chemical Society, Washington D. C., pp. 281-296 (1983)
11. F. HIRATA, P. J. ROSSKY, B. M. PETTITT, “The Interionic Potential of Mean Force in a Molecular
Polar Solvent from an Extended RISM Equation,” J. Chem. Phys., 78, 4133 (1983)
12. S. L. GALLION, R. M. LEVY, P. K. WEINER, F. HIRATA, “Implementation of a Macromolecular
Mechanics Program on a CYBER 205 Supercomputer,” Computers & Chemistry, 10, 165 (1986).
13. F. HIRATA, R. M. LEVY, “Ionic Association in Methanol and Related Solvents: An Extended RISM
Analysis,” J. Phys. Chem., 91, 4788 (1987)
14. F. HIRATA, R. M. LEVY, “A New RISM Integral Equation for Polymers Interacting with Solvent,” F.
HIRATA, R. M. LEVY, Chem. Phys. Lett., 136, 267 (1987)
15. F. HIRATA, R. M. LEVY, K. KIM, P. ZHANG, “Using Computer Simulations to Probe the Structure
and Dynamics of Biopolymers,” in Supercomputer Research in Chemistry and Chemical Engineering,
ACS Symposium Series, 353, (American Chemical Society, Washington D. C., 1987), pp. 82-105
16. D. BASSOLINO, F. HIRATA, D. B. KITCHEN, D. KOMINOS, A. PARDI, R. M. LEVY,“Determination of Protein Structures in Solution Using NMR Data and IMPACT,” International
Journal of Supercomputer Applications, 2, 41 (1988)

17. F. HIRATA, R. M. LEVY, “Viewing The Born Model for Ion Hydration through A Microscope,”
International Journal of Quantum Chemistry: Quantum Biologie Symposium, 15, 179 (1988)
18. F. HIRATA, R. M. LEVY, “Salt-Induced Conformational Change in DNA: Analysis Using thePolymer RISM Theory,” J. Phys. Chem., 93, 479 (1989)
19. D. B. KITCHEN, F. HIRATA, D. A. KOFKE, J. D. WESTBROOK, R. M. LEVY, “Conserving
Energy During Molecular Dynamics Simulations of Water, Proteins, and Proteins in Water,” J. Comp.
Chem., 11, 1169 (1990)
20. D. B. KITCHEN, F. HIRATA, R. M. LEVY, “Conserving Energy in Molecular Dynamics Simulationsof Proteins in Water,” Theoretical Chemistry & Molecular Biophysics, Eds., D. L. Beveridge & R.
Lavery, Adenine Press, 1990, pp. 77.
21. A. KITAO, F. HIRATA, N. GO, “The Effect of Solvent on the Conformation and the Collective
Motions of Protein: Normal Mode Analysis and Molecular Dynamics Simulations of Melittin in
Water and in Vacuum,” Chem. Phys., 158, 447 (1991)
22. F. HIRATA, “Interaction-site Representation of The Smoluchowski-Vlasov Equation: The
Space-Time Correaltion Functions in a Molecular Liquid,” J. Chem. Phys.,96, 4619 (1992)
23. M. IRISA, K. NAGAYAMA, F. HIRATA, “Extended Scaled Particle Theory for Dilute Solutions ofArbitrary Shaped Solute: An Application to Solvation Free Energies of Hydrocarbons,” Chem. Phys.
Letter, 207, 430 (1993)
24. S. HAYWARD, A. KITAO, F. HIRATA, N. GO, “Effect of Solvent on Collective Motions in BPTI,” J.
Mol. Biol., 234, 1207 (1993)
25. A. KITAO, F.HIRATA, N. GO, “The Effect of Solvent on the Conformation and the Collective
Motions of Protein: II. Structure of Hydration in Melittin,” J. Phys. Chem., 97, 10223 (1993)
26. A. KITAO, F.HIRATA, N. GO, “The Effect of Solvent on The Conformation and The Collective
Motions of Protein: III.Free Energy Analysis by The Extended RISM Theory,” J. Phys. Chem., 97,
10231 (1993)
27. S. TENNO, F. HIRATA, S. KATO, “A Hybrid Approach for the Solvent Effect on the Electronic
Structure of a Solute Based on the RISM and Hartree-Fock Equations,” Chem. Phys. Lett., 214, 391396 (1993)
28. F. O. RAINERI, H. RESAT, B. PERN, F. HIRATA, H. L. Friedman, “A Molecular Theory of
Solvation Dynamics,” J. Chem. Phys., 100. 1477 (1994)
29. S. TENNO, F. HIRATA, S. KATO, “Reference Interaction Site Model Self-Consistent Field Study for
Solvation Effect on Carbonyl Compounds in Aqueous Solution,” J. Chem. Phys., 100, 7443 (1994)
30. G. BASU, A. KITAO, F. HIRATA, N. GO, “A Collective Motion Description of the 310-/a-Helix
Transition: Implications for a Natural Reaction Coordinate,” J. Am. Chem. Soc., 116, 6307 (1994)
31. S. MIURA, F. HIRATA, “Temperature Dependence of the Stability of a Hydrated Electron: An
Integral Equation Study,” J. Phys. Chem., 98, 9649 (1994)
32. H. L. FRIEDMAN, F. RAINERI, F. HIRATA, B. PERN, “Surrogate Hamiltonian Description of

Solvation Dynamics Site-Number Density and Polarization Charge Density Formulation,” J. Stat.
Phys., 78, 239 (1995)
33. M. KAWATA, S. TENNO, S. KATO, F. HIRATA, “Irregular Order in Basicities of Methylamines in
Aqueous Solutions: A RISM-SCF Study,” J. Am. Chem. Soc., 117, 1638 (1995)
34. S.-H. CHONG, S. MIURA, G. BASU, F. HIRATA, “Molecular Theory for the Non- Equilibrium Free
Energy Profile in Electron Transfer Reaction,” J. Phys. Chem., 99, 10526 (1995)
35. M. KAWATA, S. TENNO, S. KATO, F. HIRATA, “The Solvation Effect on the Acidities of
Haloacetic Acids in Aqueous Solutions: A RISM-SCF Study,” Chem. Phys. Letter, 240, 199 (1995)
36. M. IRISA, T.TAKAHASHI, K. NAGAYAMA, F. HIRATA, “Solvation Free Energies of Non-polarand Polar Solutes Reproduced by the Combination of the Extended Scaled Particle Theory and the
Poisson-Boltzmann Equation,” Mol. Phys., 85, 1227 (1995)
37. F. HIRATA, T. MUNAKATA, F. RAINERI, H.L. FRIEDMAN, “An Interaction-Site Representationof the Dynamic Structure Factor of Liquid and Solvation Dynamics,” J. Mol. Liquids, 65/66, 15(1995)
38. S-H. CHONG, F. HIRATA, “Non-linear Effects in the Free Energy Profile of Electron Transfer
Reaction: an Integral Equation Approach,” J. Mol. Liquids, 65/66, 345 (1995)
39. M. IRISA, T. TAKAHASHI, F. HIRATA, T. YANAGIDA, “Solvation Free Energy of Protein
Reproduced by the Combination of the Extended Scaled Particle Theory and the Poisson-Boltzmann
Equation,” J. Mol. Liquids, 65/66, 381 (1995)
40. S.-H. Chong, F. Hirata, “The Free Energy Profiles for the Electron Transfer Reactions Calculated
from the Integral Equation Method of Liquids,” Molecular Simulation, 16, 3 (1996)
41. M. Kawata, S. Ten-no, S. Kato, F. Hirata, “Solvent Effect on Acidity: A Hybrid Approach Based on
the RISM and Hartree-Fock Equation,” J. Phys. Chem., 100, 1111 (1996)
42. M. Kawata, S. Ten-no, S. Kato, F. Hirata, “Theoretical Study of the Basicities of Methylamines in
Aqueous Solutions: A RISM-SCF Calculation of Solvation Theromodynamics,” Chem. Phys., 203, 53(1996)
43.

M. Kinoshita, F. Hirata, “Application of the Reference Interaction Site Model Theory to Analysis on
Surface-Induced Structure of Water,” J. Chem. Phys., 104, 8807 (1996)

44. R. Ueoka, Y. Matsumoto, K. Goto, T. Ito, S. Mori, Y.Matsumoto, A. Sakoguchi, Y. Ihara, F. Hirata,“A Remarkably Enhanced Diastereoselectivity for the Hydrolysis of Dipeptide Esters Responding to
pH and Temperature in Buffer Solutions,” Tetrahedron letters, 37, 3461 (1996)
45. H. Sato, F. Hirata, S. Kato, “Analytical Energy Gradient for the Reference Interaction Site Model
Multiconfigurational Self-Consistent-Field Method: Application to 1,2-Difluoroethylene in Aqueous
Solution,” J. Chem. Phys., 105, 1546 (1996)
46. S. Yoshida, F. Hirata, T. Munakata, “Shear-Induced Distortion of Intramolecular and IntermolecularCorrelations in Liquids: Time-Dependent Density-Functional Theory,” Phys. Rev. E. 52, 1763 (1996)
47. T. Munakata, S. Yoshida, F. Hirata, “Statistical Mechanics of Deformable Liquids: Thermal
Expansion and Isomerization of Diatomic Molecules,” Phys. Rev. E. 54, 3687 (1996)

48. S.-H. Chong, F. Hirata, “Nonlinear Electrical Potential Fluctuations of Solvent Around Solutes: An
Integral Equation Study,” J. Chem. Phys. 106, 5225 -- 523 (1997)
49. S.-H. Chong, F. Hirata, “Ion Hydration: Thermodynamic and Structural Analysis with an Integral
Equation Theory of Liquids,” J. Phys. Chem. B, 101 (106), 3209-3220 (1997)
50. M. Kinoshita, F. Hirata, “Analysis of Salt Effects on Solubility of Noble Gases in Water Using theReference Interaction Site Model Theory,” J. Chem. Phys., 106 (12), 5202-5215 (1997)
51. S. Maw, H. Sato, S. Tenno, F. Hirata, “Ab Initio Study of Water: Self-Consistent Determination ofElectronic Structure and Liquid State Properties,” Chem. Phys. Lett., 276 (1-2), 20-25 (1997)
52. M. Kinoshita, Y. Okamoto, F. Hirata, “Calculation of Hydration Free Energy for a Solute with Many
Atomic Sites Using the RISM Theory: A Robust and Efficient Algorithm,” J. Comp. Chem., 18 (10),1320-1326 (1997)
53. M. Kinoshita, Y. Okamoto, F. Hirata, “Solvation Structure and Stability of Peptides in Aqueous
Solutions Analyzed by the Reference Interaction Site Model Theory,” J. Chem. Phys., 107 (5),1586-1599 (1997)
54. S.-H. Chong, F. Hirata, “An Integral Equation Study for Non-Linear Electrical Potential Fluctuationsof Solvent Around Solute,” J. Electroanalytical Chem., 438 (1-2), 245 - 250 (1997)
55. S.-H. Chong, F. Hirata, “Interaction-Site-Model Description of Collective Excitations in ClassicalMolecular Fluids,” Phys. Rev. E, 57 (2), 1691 - 1701(1998)
56. H. Sato, F. Hirata, A.B. Myers, “Theoretical Study of the Solvent Effect on Triiodide Ion in
Solutions,” J. Phys. Chem., 102 (11), 2065-2070 (1998)
57. H. Sato, F. Hirata, “Theoretical Study for Autoionization of Liquid Water: Temperature Dependenceof the Ionic Product (pK(w)),” J. Phys. Chem., A102 (15), 2603-2608 (1998)
58. R. Akiyama, F. Hirata, Theoretical Study for Water Structure at Highly Ordered Surface: Effect ofSurface Structure, J. Chem. Phys., 108 (12), 4904-4911 (1998)
59. S.-H. Chong, F. Hirata, “Dynamics of Solvated Ion in Polar Liquids: An Interaction-Site- Model
Description,” J. Chem. Phys. 108 (17), 7339 - 7349 (1998)
60. T. Ishida, F. Hirata, H. Sato, S. Kato, “Molecular Theory of Solvent Effect on Keto-Enol Tautomers
of Formamide in Aprotic Solvents: RISM-SCF Approach,” J. Phys. Chem, B 102 (11), 2045-2050(1998)
61. M. Kinoshita, Y. Okamoto, F. Hirata, “First-principle Determination of Peptide Conformations in
Solvents: Combination of Monte Carlo Simulated Annealing and RISM Theory,” J. Am. Chem. Soc.,
120 (8), 1855-1863 (1998)
62. F. Hirata, T. Imai, M. Irisa, “Molecular Theories of Partial Molar Volume,” Rev. High Press. Sci. andTech., 8, 96-103 (1998)
63. A. Kovalenko, F. Hirata, “Three-Dimensional Density Profiles of Water in Contact with a Solute of
Arbitraly Shape: a RISM Approach,” Chem. Phys. Letter, 290 (1-3), 237-244 (1998)

64. F. Hirata, “Chemical Processes in Solution Studied by an Integral Equation Theory of Molecular
Liquids,” Bull. Chem. Soc. Jpn., 71 (7), 1483-1499 (1998)
65. S.-H. Chong, F. Hirata, “Interaction-Site Representation for Collective Excitations in Diatomic
Dipolar Liquid,” J. Mol. Liquids, 77 (1-3), 105 - 120 (1998)
66. Y. Okamoto, and F. Hirata, “Calculation of Solvation Free Energy Using RISM Theory for Peptide in
Salt Solution,” M. Kinoshita, J. Comp. Chem. 19 (15), 1724 - 1735 (1998)
67. M. Kinoshita, Y. Okamoto, F. Hirata, “Singular Behavior of the Reference Interaction Site Model
Theory Observed for Peptide in Salt Solution,” Chem. Phys. Letters, 297 (5-6), 433 - 438 (1998)
68. S.-H. Chong and F. Hirata, “Effect of Molecular Symmetry on Electrical Potential Fluctuations ofSolvent Around Solute in Polar Liquid,” Chem. Phys. Lett. 293 (1-3), 119-126 (1998)
69. S.-H. Chong, F. Hirata, “Mode-Coupling Theory for Molecular Liquids Based on the Interaction-Site
Model,” Phys.Rev. E., 58 (5), 6188-6189 (1998)
70. S.-H. Chong, F. Hirata, “Time-Correlation Functions in Molecular Liquids Studied by theMode-Coupling Theory Based on the Interaction-Site Model,” Phys. Rev. E, 58 (6), 7296-7308 (1998)
71. T. Ishida, F. Hirata, S. Kato, “Thermodynamics Analysis of the Solvent Effect on Tautomerization ofAcetylacetone: An Ab initio Approach,” J. Phys. Chem., 110 (8), 3938 - 3945 (1999)
72. K. Naka, H. Sato, A. Morita, F. Hirata, S. Kato, “RISM-SCF Study for the Free Energy Profile ofMenshutkin Type Reaction NH3 + CH3Cl →NH3CH3+ + Cl- in Aqueous Solution,” Theor. Chem.
Acc., 102 (1-6), 165-169, (1999)
73. H. Sato, F. Hirata, “The Syn- / Anti- Conformational Equilibrium of Acetic Acid in Water Studied by
the RISM-SCF/MCSCF method,” THEOCHEM (Morokuma issue), 461: 113-120 (1999)
74. A. Kovalenko, S. Ten-no, F. Hirata, “Solution of Three-Dimensional Reference Interaction Site
Model and Hypernetted Chain Equations for Simple Point Charge Water by Modified Method of
Direct Inversion in Iterative Subspace,” J. Comp. Chem., 20 (19), 928 - 936 (1999)
75. M. Kinoshita, Y. Okamoto, F. Hirata, “Analysis on Conformational Stability of C-peptide of
Ribonuclease A in Water Using the Reference Interaction Site Model Theory and Monte Carlo
Simulated Annealing,” J. Chem. Phys., 110 (8), 4090 - 4100 (1999)
76.

H. Sato, F. Hirata, “Revisiting the Acid-Base Equilibrium in Aqueous Solutions of Hydrogen
Halides: Study by the Ab inition Electronic Structure Theory Combined with the Statistical
Mechanics of Molecular Liquids,” J. Am. Chem. Soc., 121 (14), 3460 - 3467 (1999)

77. A. Kovalenko, F. Hirata, “Self-Consistent Description of a Metal-Water Interface by the Kohn-Sham
Density Functional Theory and the Three-Dimensional Reference Interaction Site Model,” J. Chem.
Phys., 110 (20), 10095 - 10112 (1999)
78. A. Sethia, F. Hirata, Y. Singh, “Density Matrix for an Excess Electron in a Classical Fluid. Results fora One Dimensional System,” J. Chem. Phys., 110 (20), 10086 - 10094 (1999)
79. F. Hirata, S.-H. Chong, “Comment on ‘Dynamics of Solvated Ion in Polar Liquids: An
Interaction-Site-Model Description’ -Response,” J. Chem. Phys., 110 (3), 1835 - 1836 (1999)

80. S.-H. Chong, F. Hirata, “Dynamics of Ions in Liquid Water: An Interaction-Site-Model Description,”
J. Chem. Phys., 111 (8), 3654-3667 (1999)
81. S.-H. Chong, F. Hirata, “Interaction-Site-Model Descritption of Collective Excitations in Liquid
Water I: Theoretical Study,” J. Chem. Phys., 111 (7), 3083-3094 (1999)
82. S.-H. Chong, F. Hirata, “Interaction-Site-Model Descritption of Collective Excitations in Liquid
Water II: Comparison with Simulation Results,” J. Chem. Phys., 111 (7), 3095- 3104 (1999)
83. H. Sato, F. Hirata, “Ab Initio Study on Molecular and Thermodynamic Properties of Water: A
Theoretical Prediction of pKw over a Wide Range of Temperature and Density,” J. Phys. Chem. B,
103 (31), 6596-6604 (1999)
84. T. Ishida, F. Hirata, S. Kato, “Solvation Dynamics of Benzonitrile Excited State in Polar Solvents: A
Time-Dependent Reference Interaction Site Model Self-Consistent Field Approach,” J. Chem. Phys.,
110 (23), 11423 - 11432 (1999).
85. R. Akiyama, M. Kinoshita, F. Hirata, “Free Energy Profiles of Electron Transfer at Water-Electrode
Interface Studied by the Reference Interaction Site Model Theory,” Chem. Phys. Lett., 305 (3-4), 251- 257 (1999)
86. A. Mitsutake, M. Irisa, Y. Okamoto, F. Hirata, “Classification of Low-Energy Conformations of
Met-Enkephalin in the Gas Phase and in a Model Solvent Based on the Extended Scaled Particle
Theory,” Bull. Chem. Soc. Jpn., 72 (8), 1717-1729 (1999)
87. H. Sato, F. Hirata, “Ab Initio Study of Water (II): Liquid Structure, Electronic and Thermodynamic
Properties over a wide Range of Temperature and Density,” J. Chem. Phys., 111 (18), 8545-8555(1999)
88. A. Kovalenko, F. Hirata, “Potential of Mean Force between Two Molecular Ions in a Polar Molecular
Solvent: a Study by the Three-Dimensional Reference Interaction Site Model,” J. Phys. Chem. B, 103(37), 7942-7957 (1999)
89. A. Sethia, F. Hirata, Y. Tanimura, Y. Singh, “Polaron Density Matrix and Effective Mass at Finite
Temperature,” Phys. Rev.B, 60 (10), 7245-7251 (1999)
90. A. Sethia, S. Sanyal, F. Hirata, “Eigenstates from the Discretized Path Integral,” Chem. Phys. Lett.,
315 (3-4), 299-303 (1999)
91. Y. Harano, H. Sato, F. Hirata, “Solvent Effects on a Diels-Alder Reaction in Supercritical Water:
RISM-SCF Study,” J. Am. Chem. Soc., 122 (10), 2289-2293 (2000)
92. M. Kinoshita, Y. Okamoto, F. Hirata, “Peptide Conformations in Alcohol and Water: Analysis by the
Reference Interaction Site Model Theory,” J. Am. Chem. Soc., 122 (12), 2773-2779 (2000)
93. T. Imai, M. Kinoshita, F. Hirata, “Salt Effect on Stability and Solvation Structure of Peptide: An
Integral Equation Study,” Bull. Chem. Soc. Jpn., 73 (5), 1113-1122 (2000)
94. A. Kovalenko, F. Hirata, “Potentials of Mean Force of Simple Ions in Ambient Aqueous Solution. I.
Three-Dimensional Reference Interaction Site Model Approach,” J. Chem. Phys., 112 (23), 10391 10402 (2000)
95. A. Kovalenko, F. Hirata, “Potentials of Mean Force of Simple Ions in Ambient Aqueous Solution. II.

Solvation Structure from the Three-Dimensional Reference Interaction Site Model Approach, andComparison with Simulations,” J. Chem. Phys., 112 (23), 10403 - 10417 (2000)
96. A. Kovalenko, F. Hirata, “Hydration Free Energy of Hydrophobic Solutes Studied by a Reference
Interaction Site Model with a Repulsive Bridge Correction and a Thermodynamic Perturbation
Method,” J. Chem. Phys., 113 (7), 2793 - 2805 (2000)
97. Y. Harano, H. Sato, F. Hirata, “Theoretical Study on Diels-Alder Reaction in Ambient andSupercritical Water: Viewing Solvent Effect through the Frontier Orbitals,” Chem. Phys., 258 (2-3),
151 - 161 (2000)
98. H. Sato, A. Kovalenko, F. Hirata, “Self-Consistent Field, Ab Initio Molecular Orbital andThree-Dimensional Reference Interaction Site Model Study for Solvation Effect on Carbon
Monoxide in Aqueous Solution,” J. Chem. Phys., 112 (21), 9463 - 9468 (2000)
99. T. Imai, M. Kinoshita, F. Hirata, “Theoretical Study for Partial Molar Volume of Amino Acids in
Aqueous Solution: Implication of Ideal Fluctuation Volume,” J. Chem. Phys., 112 (21), 9469-9478(2000)
100. V. Shapovalov, T. N. Truong, A. Kovalenko, F. Hirata, “Liquid Structure at Metal Oxide-Water
Interface: Accuracy of a Three-Dimensional RISM Methodology,” Chem. Phys. Lett., 320 (1-2),
186-193 (2000)
101.H. Sato, N. Matsubayashi, M. Nakahara, F. Hirata, “Which Carbon Oxide is More Soluble? Ab Initio
Study on Carbon Monoxide and Dioxide in Aqueous Solution,” Chem. Phys. Lett., 323 (3-4), 257 262 (2000)
102. A. Sethia, F. Hirata, “Electron Self-Trapping in Two-Dimensional Fluid,” Chem. Phys. Lett. 326(3-4), 199 - 206 (2000)
103. T. Yamazaki, H. Sato, F. Hirata, “NMR Chemical Shifts in Solution: A RISM-SCF Approach,” Chem.
Phys. Lett., 325 (5-6), 668 - 674 (2000)
104. A. Kovalenko, F. Hirata, M. Kinoshita, Hydration Structure and Stability of Met-Enkephalin Studied
by a Three-Dimensional Reference Interaction Site Model with a Repulsive Bridge Correction andThermodynamic Perturbation Method, J. Chem. Phys., 113 (21), 9830 --9836 (2000)
105. K. Nishiyama, F. Hirata, T. Okada, “Importance of Acoustic Solvent Mode and Solute-Solvent
Radial Distribution Functions in Solvation Dynamics: Studied by RISM Theory,” J. Chin. Chem. Soc.,
47 (4A), 837 - 842 (2000)
106. K. Nishiyama, F. Hirata, T. Okada, “Relaxation of Average Energy and Rearrangement of Solvent
Shells in Various Polar Solvents in Connection with Solvation Dynamics: Studied by RISM Theory,”
Chem. Phys. Lett., 330 (1-2), 125 -- 131 (2000)
107. A. Mitsutake, M. Kinoshita, Y. Okamoto F. Hirata, “Multicanonical Algorithm Combined with the
RISM Theory for Simulating Peptide in Aqueous Solution,” Chem. Phys. Lett., 329 (3-4), 295 - 303(2000)
108. T. Nakabayashi, H. Sato, F. Hirata, N. Nishi, “Theoretical Study on the Structures and Energies ofAcetic Acid Dimers in Aqueous Solution,” J. Phys. Chem. A, 105 (1), 245 -- 250 (2001)
109. A. Sethia, S, Sanyal, F. Hirata, “Quantum Dynamics: Path Integral Approach to Time Correlation

Functions in Finite Temperature,” J. Chem. Phys., 114 (11), 5097 -- 5098 (2001)
110. A. Sethia, S. Miura, F. Hirata, “Density Matrix and Eigenstates for an Excess Electron in Water,” J.
Mol. Liquids, 90 (1-3), 225 - 231 (2001)
111. M. Kinoshita, Y. Okamoto, F. Hirata, “Solvent Effects on Conformational Stability of Peptides:
RISM Analyses,” J. Mol. Liquids, 90 (1-3), 195 - 204 (2001)
112. A. Kovalenko, F. Hirata, “Self-Consistent, Kohn-Sham DFT and Three-Dimensional RISM
Description of a Metal-Molecular Liquid Interface,” J. Mol. Liquids, 90 (1-3), 215 - 224 (2001)
113. K. Nishiyama, F. Hirata, T. Okada, “Average Energy Relaxation and Rearrangement of
Solute-Solvent Radial Distribution Function in Solvation Dynamics: A Connection between
Spectroscopic Results and RISM Theory,” J. Mol. Liquids, 90 (1-3), 251 - 260 (2001)
114. Y. Harano, T. Imai, A. Kovalenko, M. Kinoshita, F. Hirata, “Theoretical Study for Partial Molar
Volume of Amino Acids and Polypeptides by the Three-Dimensional Reference Interaction Site
Model,” J. Chem. Phys., 114 (21), 9506-9511 (2001)
115. K. Nishiyama, F. Hirata, T. Okada, “Nonlinear Response of Solvent Molecules Induced by
Instantaneous Change of Solute Electronic Structure: Studied by RISM Theory,” J. Mol. Struct., 565:
31-34 (2001)
116. A. Kovalenko, F. Hirata, “A Replica Reference Interaction Site Model Theory for a Polar Molecular
Liquid Sorbed in a Disordered Microporous Material with Polar Chemical Groups,” J. Chem. Phys.,
115 (18), 8620 -- 8633(2001)
117. H. Sato, F. Hirata, “Realization of Three-Dimensinal Solvation-Structure from the Site-Site Radial
Distribution Functions in Liquids,” Bull. Chem. Soc. Jpn., 74 (10), 1831 -- 1839 (2001)
118. T. Imai, Y. Harano, A. Kovalenko, F. Hirata, “Theoretical Study for Volume Changes Associatedwith the Helix-Ciol Transition of Peptides,” Biopolymers, 59 (7), 512--519 (2001)
119. T. Sumi T. Imai, F. Hirata, “Integral Equations for Molecular Fluids Based on Interaction Site
Model: Density-Functional Formulation,” J. Chem. Phys., 115 (14), 6653 -- 6662(2001)
120. T. Yamazaki, H. Sato, F. Hirata, “Solvent Effect on the Nuclear Magnetic Shielding: Ab Initio Studyby the Combined Reference Interaction Site Model and Electronic Structure Theories,” J. Chem.
Phys., 115 (19), 8949-8957 (2001)
121. T. Yamaguchi, F. Hirata, “Site-Site Mode-Coupling Theory for the Shear Viscosity of Molecular
Liquids,” J. Chem. Phys., 115 (20), 9340 --9345(2001)
122. A. Kovalenko, F. Hirata, “First-Principles Realization of a Van Der Waals-Maxwell Theory for
Water,” Chem. Phys. Lett., 349, 496 (5-6) -- 502 (2001)
123. A. Kovalenko, F. Hirata, “Description of a Polar Molecular Liquid in a Disordered Microporous
Material with activating chemical groups by a replica RISM theory,” Cond. Mat. Phys., 4, 643 -- 678(2001)
124. K. Nishiyama, F. Hirata, T. Okada, “Solute-Shape Dependence in Solvation Dynamics: Investigatedby RISM Theory,” J. Mol. Liquids, 96-7: 391 - 395 (2002)

125. M. Kinoshita, T. Imai, A. Kovalenko, F. Hirata, “Improvement of the Reference Interaction Site
Model Theory for Calculating the Partial Molar Volume of Amino Acids and Polypeptides,” Chem.
Phys. Lett., 348 (3-4), 337 -- 342 (2001)
126. T. Yamaguchi, F. Hirata, “Translational Diffusion and Reorientational Relaxation of Water Analyzed
by Site-Site Generalized Langevin theory,” J. Chem. Phys., 116 (6), 2502 -- 2507 (2002)
127. H. Sato, F. Hirata, “Equilibrium and Nonequilibrium Solvation Structure of Hexaamineruthenium(II,III) in Aqueous Solution: Ab Initio RISM-SCF Study,” J. Phys. Chem. A, 106 (10), 2300 -- 2304
(2002)
128. K. Yoshida, A. Kovalenko, T. Yamaguchi, F. Hirata, “Structure of Tert-Butyl Alcohol-Water
Mixtures Studied by the RISM Theory,” J. Phys. Chem. B., 106 (19), 5042 (2002)
129. T. Imai, H. Nomura, M. Kinoshita, F. Hirata, “Partial Molar Volumes and Compressibilities of
Alkali-Halide Ions in Aqueous Solution: Hydration Shell Analysis with an Integral Equation Theoryof Molecular Liquids,” J. Phys. Chem. B, 106 (29), 7308-- 7314 (2002)
130. T. Yamaguchi, F. Hirata, “Interaction-Site Model Description of the Reorientational Relaxation of
Molecular Liquids: Incorporation of the Interaxial Coupling into the Site-Site Generalized Langevin /Mode-Coupling Theory,” J. Chem. Phys., 117 (5), 2216-- 2224 (2002)
131. H. sato, F. Hirata, M. Nakahara, Enthalpy and Entropy Decomposition of Free-Energy Changes forSide-Chain Conformations of Asparatic Acid and Asparagine in Acidic, Neutral, and Basic Aqueous
Solutions, T. Kimura, N. Matsubayashi, J. Phys. Chem., B, 106 (47), 12336--12343 (2002)
132. T. Sumi, F. Hirata, “A Density-Functional Theory for Polymer Liquids Based on Interaction Site
Model,” J. Chem. Phys., 118 (5), 2431 -- 2442 (2003).
133. K. Nishiyama, F. Hirata, T. Okada, “Solute-Structure Dependence of Solvation Dynamics Studied by
Reference Interaction-Site Model Theory,” J. Chem. Phys. 118 (5), 2279-- 2285 (2003)
134. T. Yamaguchi, S.-H. Chong, F. Hirata, “Dielectric Relaxation Spectrum of Water Studied by the
Site-Site Generalized Langevin / Modified Mode-Coupling Theory,” Mol. Phys., 101 (8), 1211 - 1220
(2003)
135. T. Yamaguchi, S.-H. Chong, F. Hirata, “Theoretical Study of the Molecular Motion of Liquid Water
under High Pressure,” J. Chem. Phys., 119 (2), 1021-- 1034(2003)
136. T. Imai, F. Hirata, “Partial Molar Volume and Compressibility of a Molecule with Internal Degrees
of Freedom,” J. Chem. Phys., 119 (11), 5623-- 5631 (2003)
137. H. Sato, Y. Kobori, S. Tero-Kubota, F. Hirata, “Theoretical Study on Electronic and Solvent
Reorganization Associated with a Charging Process of Organic Compounds: I. Molecular and Atomic
Level Description of Solvent Reorganization,” J. Chem. Phys., 119 (5) 2753-- 2760 (2003)
138. I. Omelyan, A. Kovalenko, F. Hirata, “Compressibility of Tert-Butyl Alcohol - Water Mixtures: theRISM Theory,” J. Theo. Comp. Chem., 2 (2), 193-- 203 (2003)
139. A. Sethia, E. R. Bittner F. Hirata, “Interplay between the Repulsive and Attractive Interaction and
the Spacial Dimesionality of an Excess Electron in a Simple Fluid,” J. Theor. Comp. Chem., 2 (2),129--138 (2003)

140. A. Tanimura, A. Kovalenko, F. Hirata, “Molecular Theory of an Electrochemical Double Layer in a
Nanoporous Carbon Supercapacitor,” Chem. Phys. Lett., 378 (5-6), 638--646 (2003)
141. T. Yamazaki, H. Sato, F. Hirata, “A Quantum Solute-Solvent Interaction Using Spectral
Representation Technique Applied to the Electronic Structure Theory in Solution,” J. Chem. Phys.,
119 (13), 6663--6670 (2003)
142. A. Kovalenko, F. Hirata, “Molecular Description of Electrolyte Solution in a Carbon Aerogel
Electrode,” Cond. Matt. Phys., 6, 583 -- 609 (2003)
143. T. Yamaguchi, S.-H. Chong, F. Hirata, “Mode-Coupling Analysis of the Translational and Rotational
Diffusion of Polar Liquids; Acetonitrile and Water,” J. Mol. Liquids, 112 (3): 117-124 (2004)
144. Y. Kobori, T. Yago, K. Akiyama, S. Tero-Kubota, H. Sato, F. Hirata, J. R. Norris, Jr.,
“Superexchange Electron Tunneling Mediated by Solvent Molecules: Pulsed Electron Paramagnetic
Resonance Study on Electronic Coupling in Solvent-Separated Radical Ion Pairs,” J. Phys. Chem. B,
108 (29), 10226 -- 10240 (2004)
145. Y. Kobori, T. Yago, K. Akiyama, S. Tero-Kubota, H. Sato, F. Hirata, J. R. Norris, Distortion ofElectronic Structure in Solvated Molecules: Tautomeric Equilibrium of 2-Pyridone and2-Hydroxypridine in Water Studied by the RISM-SCF Method, H. Sato, F. Hirata, S. Sakaki, J. Phys.
Chem., A 108 (11), 2097--2102 (2004 )146. H. Sato, Y. Kobori, S. Tero-Kubota, F. Hirata, “Theoretical Study on Electronic and Solvent
Reorganization Associated with a Charging Process of Organic Compounds: 2. A New
Decomposition Procedure into Electrostatic and Nonelectrostatic Responses,” J. Phys. Chem. B, 108(31), 11709 -- 11715 (2004)
147. T. Imai, A. Kovalenko, F. Hirata, “Solvation Thermodynamics of Protein Studied by the 3D-RISM
Theory,” Chem. Phys. Lett., 395 (1-3), 1--6 (2004)
148. A. Mitsutake, M. Kinoshita, Y. Okamoto, F. Hirata, “Combination of the Replica-Exchange Monte
Carlo Method and the Reference Interaction Site Model Theory for Simulating a Peptide Molecule in
Aqueous Solution,” J. Phys. Chem. B, 108 (49), 19002--19012(2004)

149. K. Nishiyama, T. Yamaguchi, F. Hirata, T. Okada, “Solute Dependence of Polar Solvation Dynamics
Studied by RISM/Mode-Coupling Theory,” J. Solution Chem., 33 (6-7), 631-639 (2004)
150. I. Omelyan, A. Kovalenko, F. Hirata, “Microscopic Description of a Liquid-Vapor Interface by an
Inhomogeneous Integral Equation Theory,” Chem. Phys. Lett., 397 (4-7), 368--373 (2004)
151. K. Nishiyama, T. Yamaguchi, F. Hirata, T. Okada, “Polar Solvention Dynamics: A Combination of
the Reference Interaction-Site Model and Model-Coupling Theories,” Pure and Applied Chem., 76(1) (2004)
152. T. Imai, F. Hirata, “Hydrophobic Effects on Partial Molar Volume,” J. Chem. Phys., 122 (9), Art. No.
094509(2005)
153. A.E. Kobryn, T. Yamaguchi, F. Hirata, “Pressure Dependence of Diffusion Coefficient andOrientational Relaxation Time for Acetonitrile and Methanol in Water: RISM/Mode-Coupling Study,”
J. Mol. Liquids, 119 (1-3), 7-13 (2005)

154. K. Nishiyama, T. Yamaguchi, F. Hirata, T. Okada, “Solvation Dynamics in Water Investigated by
RISM/Mode-Coupling Theory,” J. Mol. Liquid, 119 (1-3), 63-66 (2005)
155.

T. Imai, A. Kovalenko, F. Hirata, “Partial Molar Volume of Proteins Studied by theThree-Dimensional Reference Interaction Site Model Theory,” J. Phys. Chem. B, 109 (14), 6658 -6665(2005)

156. A.E. Kobryn, T. Yamaguchi, F. Hirata, “Site-Site Memory Equation Approach in Study of Density /Pressure Dependence of Translational Diffusion Coefficient and Rotational Relaxation Time of Polar
Molecular Solutions: Acetonitrile in Water, Methanol in Water, and Methanol in Acetonitrile,” J.
Chem. Phys., 122 (18), 184511 -- 184524 (2005)
157. A. Kovalenko, F. Hirata, “A Molecular Theory of Liquid Interfaces,” Phys. Chem. Chem. Phys., 7(8), 1785 -- 1793 (2005)
158. T. Imai, T. Takahiro, A. Kovalenko, F. Hirata, M. Kato, Y. Taniguchi, “Theoretical Study of Volume
Changes Associated with the Helix-Coil Transition of an Alanine-Rich Peptide in Aqueous Solution,”
Biopolymers, 79 (2), 97-105(2005)
159. T. Imai, R. Hiraoka, A. Kovalenko, F. Hirata, “Water Molecules in a Protein Cavity Detected by aStatistical-Mechanical Theory,” J. Am. Chem. Soc., 127 (44), 15334-15335 (2005)
160.

I. Omelyan, F. Hirata, A. Kovalenko, “Criticality of a Liquid-Vapor Interface from an
Inhomogeneous Integral Equation Theory,” Phys. Chem. Chem. Phys., 7 (24), 4132 - 4137 (2005)

161. T. Imai, F. Hirata, Reply to “Comment on ‘Hydrophobic Effects on Partial Molar Volume’, [ J.
Chem. Phys., 123, 167103 (2005)] J. Chem. Phys., 123 (16), Art. No. 167104 (2005)
162. R. Ishizuka, F. Hirata, “Conformational Equilibria in Liquids Consisting of Small Chain Molecules,”Chem. Phys. Lett., 420 (1-3), 135-139 (2006)
163. N. Yoshida, F. Hirata, “A New Method to Determine Electrostatic Potential Around a
Macromolecule in Solution from Molecular Wave Functions,” J. Comput. Chem., 27 (4), 453-462(2006)
164. N. Yoshida, R. Ishizuka, H. Sato, F. Hirata, “Ab Initio Theoretical Study of Temperature and Density
Dependence of Molecular and Thermodynamic Properties of Water in the Entire Fluid Region:
Autoionization Processes,” J. Phys. Chem. B, 110 (16), 8451—8458 (2006)
165. A.E. Kobryn, T. Yamaguchi, F. Hirata, “Study of Anomalous Mobility of Polar Molecular Solutions
by Means of the Site-Site Memory Equation Formalism,” J. Mol. Liquids, 125 (1), 14—21(2006)
166. T. Imai, H. Isogai, T. Seto, A. Kovalenko, F. Hirata, “Theoretical Study of Volume Changes
Accompanying Xenon-Lysozyme Binding: Implications for Molecular Mechanism of Pressure
Reversal of Anesthesia,” J. Phys. Chem. B, 110 (24), 12149—12154 (2006)
167. T. Imai, Y. Harano, M. Kinoshita, A. Kovalenko, F. Hirata, “A Theoretical Analysis on Hydration
Thermodynamics of Proteins,” J. Chem. Phys. 125 (2), 024911 (2006)
168. J.Y. Lee, N. Yoshida, F. Hirata, “Conformational Equilibrium of 1,2-Dichloroethane in Water:
Comparison of PCM and RISM-SCF Methods,” J. Phys. Chem. B (32), 110, 16018 – 16025 (2006)

169. N. Yoshida, S. Phongphanphanee, Y. Maruyama, T. Imai, F. Hirata, “Selective Ion-Binding byProtein Probed with the 3D-RISM Theory,” J. Am. Chem. Soc., 128 (37), 12042 -12043 (2006) .
170. A.E. Kobryn, F. Hirata, “Statistical-Mechanical Theory of Ultrasonic Absorption in Molecular
Liquids,” J. Chem. Phys., 126 (4), Art. No. 044504 (2007)
171. T. Imai, R. Hiraoka, A. Kovalenko, F. Hirata, “Locating Missing Water Molecules in Protein
Cavities by the Three- Dimensional Reference Interaction Site Model Theory of Molecular
Solvation,” Proteins-Structure Function and Bioinformatics, 66 (4), 804 - 813 (2007)172. Y. Ikuta, Y. Maruyama, M. Matsugami, F. Hirata, “Probing Cations Recognized by a Crown
Ether with the 3D-RISM Theory,” Chem. Phys. Lett., 433 (4-6), 403 – 408 (2007)
173. A. Tanimura, A. Kovalenko, F. Hirata, “Structure of Electrolyte Solutions Sorbed in Carbon
Nanospaces, Studied by the Replica RISM Theory,” Langmuir, 23 (3), 1507 – 1517 (2007)
174. T. Yamazaki, T. Imai, F. Hirata, A. Kovalenko, “Theoretical Study of the Cosolvent Effect on the
Pratial Molar Volume Change of Staphylococcal Nuclease Associated with Pressure Denaturation,” J.
Phys. Chem. B, 111 (5), 1206 – 1212 (2007)
175. N. Yoshida, S. Phonphanphanee, F. Hirata, “Selective Ion-Binding by Protein Probed with theStatistical Mechanical Integral Equation Theory,” J. Phys. Chem. B, 111 (17), 4588-4595 (2007)
176. Y. Ikuta, Y. Maruyama, F. Hirata, S. Tomoda, “Theoretical Study of Solvent Effect on Diastereo
Selectivity in Protonation of Methyl 3-Fluorobutanoate Anion by Ethanol: Application of the
3D-RISM Theory,” J. Mol. Struct.-Theochem, 811 (1-3), 183-190 (2007)
177. Takashi Imai, Shusaku Ohyama, Andriy Kovalenko, and Fumio Hirata, “Theoretical study of thepartial molar volume change associated with pressure-induced structural transition of ubiquitin,”Protein Science. 16, 1927 – 1933 (2007)
178. T. Imai, H. Harano, M. Kinoshita, and A. Kovalenko, “A theoretical analysis on changes inthermodynamic quantities upon protein folding: Essential role of hydration,” J. Chem. Phys., 126,
225102 – 225102 (2007).
179. Takashi Imai, Ryusuke Hiraoka, Tomoyoshi Seto, Andriy Kovalenko, and Fumio Hirata,“Three-Dimensional Distribution Function Theory for the Prediction of Protein-Ligand Binding Sites
and Affinities: Application to the Binding of Noble Gases to Hen Egg-White Lysozyme in Aqueous
Solution,” J. Phys. Chem. B, 111, 11585 (2007).
180. Tatsuhiko Miyata and Fumio Hirata, “Combination of Molecular Dynamics Method and 3d-RISM
Theory for Conformational Sampling of Large Flexible Molecules in Solution,” J. Compt. Chem., 29,
871-882 (2008).
181. S. Phonphanphanee, N. Yoshida, and F. Hirata, “A statistical mechanics study on equilibrium water
distribution in aquaporin,” Chem. Phys. Lett., 449, 196-201 (2007).
182. R. Ishizuka, S.-H. Chong, and F. Hirata, “An intergral equation theory for inhomogeneous molecular
fluids: The reference interaction site model approach,” J. Chem. Phys., 128, 34504—34513 (2008).
183. S. Phongphanphanee, N. Yoshida, and F. Hirata, “On the proton exclusion of aquaporins: A
statistical mechanics study,” J. Am. Chem. Soc. (Communications), 130, 1540 – 1541 (2008).

184. N. Yoshida, T. Ishida, and F. Hirata, “Theoretical study of temperature and solvent dependence ofthe free energy surface of the intramolecular electron transfer based on the RISM-SCF theory;
Application to 1,3-dinitrobenzene radical anion in acetonitrile and methanol,” J. Phys. Chem., (Hynes
issue), 112, 433-440 (2008).
185. B. Kim, S-H. Chong, R. Ishizuka, and F. Hirata, “An attempt toward the generalized Langevindynamics simulation,” Cond. Matter Phys., 11, 179-190 (2008).
186. Y. Ikuta, S. Karita, Y. Kitago, N. Watanabe, and F. Hirata, “Detecting Reaction Intermediate in
Enzymatic Reaction of Cel44A, GH family 44 endoglucanase with 3D-RISM Theory,” Chem. Phys.
Lett., 465, 279 – 284 (2008). doi:10.1016/j.cplett.2008.09.075
187.Yoshiteru Yonetani, Yutaka Maruyama, Fumio Hirata, and Hidetoshi Kono, “Comparison of DNA
hydration patterns obtained using two distinct computational methods, molecular dynamics
simulation and three-dimensional reference interaction site model theory,” J. Chem. Phys., 128,
185102-1 – 185102-9 (2008).
188.Katusra Nishiyama, Tsuyoshi Yamaguchi, and Fumio Hirata, “Solvation Dynamics in Polar Solvents
Studied by Means of RISM/Mode-Coupling Theory, J. Phys. Chem. B, 113, 2800 – 2804 (2009).
189.Norio Yoshida, Takashi Imai, Saree Phongphanphanee, Andriy Kovalenko, and Fumio Hirata,“Molecular Recognition in Biomolecules Studied by Statistical-Mechanical Integral-Equation Theoryof Liquids,” J. Phys. Chem.B, (Feature Article) 113, 873-886 (2009).
190.Yasuomi Kiyota, Ryusuke Hiraoka, Norio Yoshida, Yutaka Maruyama, Takashi Imai, and Fumio
Hirata, “Theoretical Study of CO escaping pathway in Myoglobin with the 3D-RISM Theory,” J. Am.
Chem. Soc. (Communication), 131, 3852-3853 (2009).
191.Saree Phongphonphanee, Norio Yoshida, and Fumio Hirata, “The potential of mean force of waterand ions in aquaporin channels investigated by the 3D-RISM method,” J. Molecular Liquids, 147,
107-111 (2009).
192.Takashi Imai, Andriy Kovalenko, Fumio Hirata, and Akinori Kidera, “Molecular Thermodynamics of
Trifluoroethanol-Induced Helix Formation: Analysis of the Solvation Structure and Free Energy by
the 3D-RISM Theory,” Interdiscip. Sci. Comput. Life Sic., 1, 156-160 (2009).
193.Takashi Imai, Koji Oda, Andriy Kovalenko, Fumio Hirata, and Akinori Kidera, “Ligand Mapping on
Protein Surfaces by the 3D-RISM Theory; Toward Computational Fragment-Based Drug Design,” J.
Am.Chem. Soc., 131, 12430 – 12440 (2009).
194.Yui, Toshifumi; Shiiba, Hirohide; Tsutsumi, Yuya; Hayashi, Sachio; Miyata, Tatsuhiko; Hirata, Fumio,“Systematic Docking Study of Carbohydrate Binding Module Protein of Cel7A with Cellulose Iα
Crystal Model,” J. Phys. Chem.B., 114, 49-58 (2009).
195.Ryosuke Ishizuka and Fumio Hirata, “The dynamics of solvent around a solute: generalized Langevintheory,” Phys. Rev. E., 81, 011202 (2010).
196.Yutaka Maruyama, Norio Yoshida, and Fumio Hirata, “Revisiting the Salt-induced Conformational
Change of DNA with 3D-RISM Theory,” J. Phys. Chem. B, 114, 6464-6471 (2010).
197.Saree Phongphonphanee, Norio Yoshida, and Fumio Hirata, “Molecular Selectivity in Aquaporin
Channels Studied by the 3D-RISM Theory,” J. Phys. Chem. B, 114, 7967 (2010).

198.Saree Phongphonphanee, Thanyada Rungromongkol, Norio Yoshida, Supot Hannongbua, and Fumio
Hirata, “Proton Transport through the Influenza A M2 Channel: 3D-RISM Study,” J. Am. Chem.
Soc.,132, 9782 – 9788 (2010).
199.Tatsuhiko Miyata, Yasuhiro Ikuta, and Fumio Hirata, “Free energy calculation using molecular
dynamics simulation combined with three dimensional reference interaction site model (3D-RISM)
theory. I. Free energy perturbation and thermodynamic integration along coupling parameter,” J.
Chem. Phys. (査読あり), 133, (2010) 044114 - 044129. (doi: 10.1063/1.3462276)
200.Hidetsugu Tanaka, Norio Yoshida, Yasuhiro Ikuta, Yasuomi Kiyota, and Fumio Hirata, “RISM-SCF
study of the solvation effect on a nucleophilic aromatic substitution between 4-fluoronitrobenzen andazide anion,” International Journal of liquid State Sciences, 2(1), 15 – 24 (2010)
201.Norio Yoshida, Yasuomi Kiyota, and Fumio Hirata, “The electronic-structure theory of alarge-molecular system in solution: Application to the intercalation of proflavine with solvated
DNA,” J. Mole. Liq., 159, 83 -92 (2011).
202.Yasuomi Kiyota, Norio Yoshida, and Fumio Hirata, “Affinity of Small Ligands to Myoglobin Studied
by the 3D-RISM Theory,” J. Mole. Liq., 159, 93 - 98 (2011).
203.Yutaka Maruyama, Taku Matsushita, Ryuichi Ueoka, and Fumio Hirata, “Solvent and Salt Effects on
Structural Stability of Human Telomere,” J. Phys. Chem.B, 115, 2408 – 2416 (2011).
204.Tatsuhiko Miyata, Yasuhiro Ikuta, and Fumio Hirata, “Free energy calculation using molecular
dynamics simulation combined with three dimensional reference interaction site model (3D-RISM)
theory. II. Thermodynamic integration along reaction coordinates,” J. Chem. Phys., 134,44127-44144 (2011).
205.Imai, Takashi; Miyashita, Naoyuki; Sugita, Yuji; Kovalenko, Andriy; Hirata, Fumio; Kidera, Akinori,“Functionality Mapping on Internal Surfaces of Multidrug Transporter AcrB Based on Molecular
Theory of Solvation: Implications for Drug Efflux Pathway,” J. Phys. Chem.B, 115, 8288 – 8295
(2011).
206.Danniel J. Sindhikara, Norio Yoshida, Mikio Kataoka, Fumio Hirata, “Solvent Penetration in
Photoactive Yellow Protein R52Q mutant: A Theoretical Study,” J. Mol. Liq. 164, 120 – 122 (2011).
207.Y. Kiyota, N. Yoshida, and F. Hirata, “A New Approach for Investigating the Molecular
Recognition of Protein: Toward Structural-Based Drug Design Based on the 3D-RISM Theory,” J.
Chem. Theor. Comp., 7, 3803-3815 (2011).
208.Sindhikara, Daniel; Yoshida, Norio; Hirata, Fumio*: “Placevent: An Algorithm for Predicting of
Explicit Solvent Atom Distribution - Application to HIV-1 Protease and F-ATP Synthase,” J. Comp.
Chem., 33, 1536 – 1543 (2012).
209.Hong, Jooyeon; Yoshida, Norio; Chong, Song-Ho; Lee, Chewook; Ham, Sihyun; Hirata, Fumio*:“Elucidating the Molecular Origin of Hydrolysis Energy of Pyrophosphate in Water,” J. Chem.
Theory Comput., 8, 2239-2246 (2012).
210.Maruyama, Yutaka; Hirata, Fumio*: “Modified Anderson Method for Acceleating 3D-RISM
Calculations Using Graphics Processor Unit,” J. Chem. Theory Comput., 8, 3015 - 3021 (2012). DOI:
10.1021/ct300355r

211.Bongsoo Kim and Fumio Hirata, “Structural fluctuation of protein in water around its native state: A
new statistical mechanics formulation,” J. Chem. Phys., 138, 054108-1 ~ 054108-11 (2012).
212.Katsura Nishiyama, Yasuhiro Watanabe, Norio Yoshida, and Fumio Hirata, “Solvent Effects on
Electronic Structures of Coumarin 153: Parallel Studies by Means of Spectroscopy and RISM-SCF
Calculations,” J. Phys. Soc. Jpn. 81, SA016 (2012).
213.Katsura Nishiyama, Yasuhiro Watanabe, Norio Yoshida, and Fumio Hirata, “Solvent dependence of
Stokes shift for organic solute-solvent sysytems: A comparative study by spectroscopy and reference
interaction-site model-self-consistent-field theory,” J. Chem., Phys., 139, 094503-1~11 (2013). (doi:
10.1063/1.4819268)
214.Daniel Sindhikara and Fumio Hirata, “Analysis of Biomolecular Solvation Sites by 3D-RISM
Theory,” J. Phys. Chem.B, 117, 6718~6723 (2013). (DOI: dx.doi.org/10.1021/jp4046116)
215.N. Yoshida, H. Tanaka, F. Hirata, “Theoretical Study of Salt Effects on Diels-Alder Reaction of
Cyclopentadiene With Methyl Vinyl Ketone Using RISM-SCF Theory," J. Phys. Chem. B, 2013, 117(45), pp 14115–14121
DOI: 10.1021/jp4091552
216.Saree Phongphanphanee, Norio Yoshida, *Shigetoshi Oiki, and *Fumio Hirata, “The ‘ambivalent’snug-fit sites in the KcsA potassium channel probed by 3D-RISM theory,” Pure Appl. Chem., 86,
97-104 (2014) DOI 10.1515/pac-2014-5018 Pure Appl. Chem. 2014; aop
217.Masaru Matsugami, Norio Yoshida, and Fumio Hirata, “Theoretical Characterization of the ‘Ridge’in the Supercritical Region in the Fluid Phase Diagram of Water,” J. Chem. Phys., 140, 104511-1 104511-6 (2014)1414
218.Yutaka Maruyama, Norio Yoshida, Hiroto Tadano, Daisuke Takahashi, Mitsuhisa Sato, and Fumio
Hirata, “Massively Parallel Implementation of 3D-RISM Calculation with Volumetric 3D-FFT,” J.
Comp. Chem., 35, 1339-1410 (2014).
DOI: 10.1002/jcc.23619
219.Saree Phongphanphanee, Norio Yoshida, Shigetoshi Oiki, and Fumio Hirata, “Distinct Configurationsof Cations and Water in the Selective Filter of the KcsA Potasium Channel Probed by the 3D-RISM
Theory,” J. Mol. Liquid., 200, 52-58 (2014).: DOI: 10.1016/j.molliq.2014.03.050
220.Akihiro Maeno, Daniel Sindhikara, Fumio Hirata, Renee Otten, Frederick Dahlquist, Shigeyuki
Yokoyama, Kazuyuki Akasaka, Frans A. A. Mulder, and Ryo Kitahara, "Cavity as a source ofconformational flctuation and high-energy state: High-pressure NMR study of a cavity-enlarged
mutant of T4 lysozyme, published in Biophysical Joumal, vol. 108, No. 1.
221.Ajay S. Tanwar, Daniel J. Sindhikara, Fumio Hirata, and Ruchi Anand, “Determination of theFormylglycinamide Ribonucleotide Amidotransferase Ammonia Prathway by Combining 3D-RISM
Theory with Experiment,” ACS Chem. Biol., 10, 698-704 (2015) (DOI: 10.1021/cb501015r)
222.Fumio Hirata and Kazuyuki Akasaka, “Structural fluctuation of proteins induced by thermodynamic
perturbation,” J. Chem. Phys., 142, 044110 - (2015). (dx.doi.org/10.1063/1.4906071)
223.Jiraphorn Phanich, Thanyada Rungrotmongkol, Daniel Sindhikara, Saree Phongphanphanee, Norio
Yoshida, Fumio Hirata, Nawee Kungwan, and Spot Hannongbua, “A 3D-RISM/RISM Study of theOseltamivir Binding Efficiency with the Wild-type and Resistance-Associated Mutant Forms of theViral Influenza B Neuraminidase,” Protein Science, 25, 147 – 158 (2016)

224.Fumio Hirata, Bogsoo Kim, “Multi-scale dynamics simulation of protein based on the generalized
Langevin equation combined with 3D-RISM theory,” J. Mol. Liquids, 217 23-38 (2016).
225.Myroslav Holovko, Andriy Kovalenko, and Fumio Hirata, “Partial molar volume of nonionicsurfactants in aqueous solution studied by the KB/3D-RISM-KH theory,” J. Mol. Liquids, 217, 103 –
111 (2016)
226.Masatake Sugita and Fumio Hirata, “Predicting the binding free energy of the inclusion process of
2-hydroxypropyl-b-cyclodextrin and small molecules by means of the MM/3D-RISM method,” J.
Phys.:Condens. Matter, 28, 384002-384013 (2016)
227.Fumio Hirata, “A molecular theory of the structural dynamics of protein induced by a perturbation,” J.
Chem. Phys., 145, 234106 (2016); doi: 10.1063/1.4971799
228.F. Hirata, M. Sugita, M. Yoshida, and K. Akasaka, J. Chem. Phys. (Persepctive), 148, 020901 (2018).
229.Takeshi Hasegawa, Masatake Sugita Takeshi Kikuchi, and Fumio Hirata, “A Systematic Analysis of
the Binding Affinity bewteen the Pim-1 Kinase and Its Inhibitors Based on the MM/3D-RISM/KH
Method,” J. Chem. Inf. Model, 57, 2789-2798 (2017) DOI: 10.1021/acs.jcim.7b00158
230.Fumio Hirata, Masatake Sugita, Masasuke Yoshida, and K. Akasaka, “Perspective: Structuralfluctuation of protein and Anfinsen’s thermodynamic hypothesis,” J. Chem. Phys., 148,
020901-020909 (2018).
231.Yuji Hayashino, Masatake Sugita, Hidetoshi Arima, Tetsumi Irie, Takeshi Kikuchi, and Fumio Hirata,“Predicting the Binding Mode of 2-Hydroxypropyl-β-Cyclodextrin (HPβCD) to Cholesterol by
Means of the MD Simulation and the 3D-RISM/KH Theory,” J. Phys. Chem. B, 122, 5716 –
5725(2018).
232.Fumio Hirata, “On the interpretation of the temperature dependence of the mean sqaure ofdisplacement (MSD) of protein, obtained from the incoherent neutron scattering,” J. Mol. Liq.,
published online (DOI: https://doi.org/10.1016/j.molliq.2018.01.096).
233.Itaru Onishi, Shunya Sunaba, Norio Yoshida, Fumio Hirata, and Masayuki Irisa, “Role of Mg2+ ionsin DNA hydrosis by EcoRV, studied by the 3D-Reference Interaction Site Model and Molecular
Dynamics,” JPCB, published online (DOI: 10.1021/acs.jpcb.7b12555).
-------------------------------------------------------------------------------------Other publications:[Reviews (in English)]
1. Hirata, F. (1998) Chemical Processes in Solution Studied by an Integral Equation Theory of Molecular
Liquids. Bull. Chem. Soc. Jpn. (Account). 71 (7), 1483-1499 (review)
2. Yoshida, N. Imai, T., Phongphanphanee, S., Kovalenko, A., Hirata, F. (2009). Molecular Recognitionin Biomolecules Studied by Statistical-Mechanical Integral-Equation Theory of Liquids. J. Phys.
Chem.B, (Feature Article) 113, 873-886 (2009). (review)
3. A. Kovalenko and F. Hirata, "Towards a Molecular Theory for the Van Der Waals-Maxwell
Description of Fluid Phase Transition," J. Theor. Comp. Chem., 1, 381--406 (2002).
4. Yutaka Maruyama, Norio Yoshida, and Fumio Hirata, “Electrolytes in Biomolecular Systems Studied

with the 3D-RISM/RISM Theory,” Interdiscip. Sci. Comput. Life Sci., 3, 1- 18 (2011).
5. S. Phongphanphanee, Norio Yoshida, and Fumio Hirata, “Molecular Recognition Explored by aStatistical-Mechanics Theory of Liquids,” Current Pharmaceutical Design, 17, 1740 – 1757 (2011).

[Book or book chapter (in English)]
1. Fumio Hirata, Norio Yoshida, and Bongsoo Kim, “Theory of Molecular Recognition and Structural
Fluctuation of Biomolecules,” in “Molecular Science of Fluctuations Toward Biological Functions,”
eds., M. Terazima, M. Kataoka, R. Ueoka, and Y. Okamoto, Springer, 2016.
2. Fumio Hirata, “Water Turns the ‘Non-biological’ Fluctuation of Protein into ‘Biological’ One,” in K.
Akasaka & H. Matsuki eds., “High Pressure Bioscience – Basic Concepts, Applications andFrontiers,” Springer, 2015.
3. Norio Yoshida, Yasuomi Kiyota, Saree Phongphanphanee, Takashi Imai and Fumio Hirata,
Statistical-mechanics theory of molecular recognition: water and other molecules recognized byprotein, in Bihan and Fukuyama(Ed.):"Water, the forgotten biological molecule." (Pan Stanford
Publishing, Singapore, 2010)
4. N. Yoshida, Y. Kiyota, Y. Ikuta, T. Imai, and F. Hirata, “Model-Free “Solvent Modeling” in Chemistry
and Biochemistry Based on the Statistical Mechanics of Liquids,” in “Modeling Solvent
Environment,” Ed. M. Feig, Wiley-VCH, 2009.
5. T. Imai, N. Yoshida, A. Kovalenko, and F. Hirata, “A Statistical Mechanics Theory of Molecular
Recognition,” in “Water and Biomolecules,” Eds, K. Kuwajima, Y. Goto, F. Hirata, M. Kataoka, and
M, Terazima, Springer, 2009.
6. A. Kovalenko and F. Hirata, Chapter 5 in “Interfacial Nanochemistry,” ed. H. Watarai, N. Teramae,
and T. Sawada, Kluwer Academic/Plenum Publishers, 2005.
7. Hirata F. (2003) Molecular Theory of Solvation. (Dordrecht: Kluwer Academic Publisher) (book,
editor & author)
8. Yoshida, N., Kiyota, Y., Ikuta, Y. , Imai, T., Hirata, F. (2010) Model Free “Solvent Modeling” inChemistry and Biochemistry Based on the Statistical Mechanics of Liquids. (Modeling Solvent
Environments,” ed. M. Feig, Wiley-VCH, Weinheim.) (book chapter)
9. F. HIRATA, H. SATO, S. TEN-NO, and S. KATO, "RISM-SCF Study of Solvent Effect on Electronic
Structure and Chemical Reaction in Solution: Temperature Dependence of pKw," ACS symposium
series "Combined Quantum Mechanical and Moleular Mechanical Methods," ed. J. Gao and M. A.
Thompson, 1998.
10. F. Hirata, H. Sato, S. Tenno, and S. Kato, "The RISM-SCF/MCSCF Approach for Chemical Processes
in Solutions," in "Computational Biochemistry and Biophysics," O. M. Becker, A. D. Mackerell, B.
Roux, and M. Watanabe, Eds., Maecel Dekker, Inc., 2001.
11. F. Hirata and H. Sato, "Ab Initio Theoretical Study of Water: Extension to Extreme Conditions," in"Biological Sysytems Under Extreme Condtions: Sturcture and Functions," Y. Taniguchi, H. E. Stanly,and H. Ludwig, Eds., Springer, 2001.