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The generalized Langevin mode analysis (GLMA) is applied to chemical reactions in biomolecules in solution. The theory sees a chemical reaction in solution as a barrier-crossing process, similar to the Marcus theory. The barrier is defined as the crossing point of two free-energy surfaces that are attributed to the reactant and product of the reaction. It is assumed that both free-energy surfaces are quadratic or harmonic. The assumption is based on the Kim-Hirata theory of structural fluctuation of protein, which proves that the fluctuation around an equilibrium structure is quadratic with respect to the structure or atomic coordinates. The quadratic surface is a composite of many harmonic functions with different modes or frequencies. The height of the activation barrier will be dependent on the mode or frequency—the less the frequency, the lower the barrier. Hence, it is essential to decouple the fluctuational modes into a hierarchical order. GLMA is impeccable for this purpose. It is essential for a theoretical study of chemical reactions to choose a reaction coordinate along which the reaction proceeds. We suppose that the mode whose center of coordinate and/or the frequency changes most before and after the reaction is the one relevant to the chemical reaction and choose the coordinate as the reaction coordinate. The rate of reaction along the reaction coordinate is k rate = ν ⁡ exp − Δ F (†) / k B T , which is similar to the Marcus expression for the electron transfer reaction. In the equation, ΔF(†) is the activation barrier defined by Δ F (†) ≡ F (r) Q † − F (r) ( Q e q (r) ) , where F (r) ( Q e q (r) ) and F (r) Q † denote the free energies at equilibrium Q e q (r) and the crossing point Q†, respectively, both on the free energy surface of the reactant. [ABSTRACT FROM AUTHOR]

In 2012, Kim and Hirata derived two generalized Langevin equations (GLEs) for a biomolecule in water, one for the structural fluctuation of the biomolecule and the other for the density fluctuation of water, by projecting all the mechanical variables in phase space onto the two dynamic variables: the structural fluctuation defined by the displacement of atoms from their equilibrium positions, and the solvent density fluctuation. The equation has an expression similar to the classical Langevin equation (CLE) for a harmonic oscillator, possessing terms corresponding to the restoring force proportional to the structural fluctuation, as well as the frictional and random forces. However, there is a distinct difference between the two expressions that touches on the essential physics of the structural fluctuation, that is, the force constant, or Hessian, in the restoring force. In the CLE, this is given by the second derivative of the potential energy among atoms in a protein. So, the quadratic nature or the harmonicity is only valid at the minimum of the potential surface. On the contrary, the linearity of the restoring force in the GLE originates from the projection of the water's degrees of freedom onto the protein's degrees of freedom. Taking this into consideration, Kim and Hirata proposed an ansatz for the Hessian matrix. The ansatz is used to equate the Hessian matrix with the second derivative of the free-energy surface or the potential of the mean force of a protein in water, defined by the sum of the potential energy among atoms in a protein and the solvation free energy. Since the free energy can be calculated from the molecular mechanics and the RISM/3D-RISM theory, one can perform an analysis similar to the normal mode analysis (NMA) just by diagonalizing the Hessian matrix of the free energy. This method is referred to as the Generalized Langevin Mode Analysis (GLMA). This theory may be realized to explore a variety of biophysical processes, including protein folding, spectroscopy, and chemical reactions. The present article is devoted to reviewing the development of this theory, and to providing perspective in exploring life phenomena. [ABSTRACT FROM AUTHOR]

A new theoretical method, referred to as Generalized Langevin Mode Analysis (GLMA), is proposed to analyze the mode of structural fluctuations of a biomolecule in solution. The method combines the two theories in the statistical mechanics, or the Generalized Langevin theory and the RISM/3D‐RISM theory, to calculate the second derivative, or the Hessian matrix, of the free energy surface of a biomolecule in aqueous solution, which consists of the intramolecular interaction among atoms in the biomolecule and the solvation free energy. The method is applied to calculate the wave‐number spectrum of an alanine dipeptide in water for which the optical heterodyne‐detected Raman‐induced spectroscopy (RIKES) spectrum is available to compare with. The theoretical analysis reproduced the main features of the experimental spectrum with respect to the peak positions of the four bands around ~90 cm−1, ~240 cm−1, ~370 cm−1, and 400 cm−1, observed in the experimental spectrum, in spite that the physics involved in the two spectrum was not exactly the same: the experimental spectrum includes the contributions from the dipeptide and the water molecules interacting with the solute, while the theoretical one is just concerned with the solute molecule, influenced by solvation. Two major discrepancies between the theoretical and experimental spectra, one in the band intensity around ~100 cm−1, and the other in the peak positions around ~370 cm−1, are discussed in terms of the fluctuation mode of water molecules interacting with the dipeptide, which is not taken explicitly into account in the theoretical analysis. [ABSTRACT FROM AUTHOR]

The thermodynamics hypothesis, casually referred to as "Anfinsen's dogma," is described theoretically in terms of a concept of the structural fluctuation of protein or the first moment (average structure) and the second moment (variance and covariance) of the structural distribution. The new theoretical concept views the unfolding and refolding processes of protein as a shift of the structural distribution induced by a thermodynamic perturbation, with the variance-covariance matrix varying. Based on the theoretical concept, a method to characterize the mechanism of folding (or unfolding) is proposed. The transition state, if any, between two stable states is interpreted as a gap in the distribution, which is created due to an extensive reorganization of hydrogen bonds among back-bone atoms of protein and with water molecules in the course of conformational change. Further perspective to applying the theory to the computer-aided drug design, and to the material science, is briefly discussed. [ABSTRACT FROM AUTHOR]

A new statistical mechanics formulation of characterizing the structural fluctuation of protein correlated with that of water is presented based on the generalized Langevin equation and the 3D-reference interaction site model (RISM)/RISM theory of molecular liquids. The displacement vector of atom positions, and their conjugated momentum, are chosen for the dynamic variables for protein, while the density fields of atoms and their momentum fields are chosen for water. Projection of other degrees of freedom onto those dynamic variables using the standard projection operator method produces essentially two equations, which describe the time evolution of fluctuation concerning the density field of solvent and the conformation of protein around an equilibrium state, which are coupled with each other. The equation concerning the protein dynamics is formally akin to that of the coupled Langevin oscillators, and is a generalization of the latter, to atomic level. The most intriguing feature of the new equation is that it contains the variance-covariance matrix as the 'Hessian' term describing the 'force' restoring an equilibrium conformation, which is the second moment of the fluctuation of atom positions. The 'Hessian' matrix is naturally identified as the second derivative of the free energy surface around the equilibrium. A method to evaluate the Hessian matrix based on the 3D-RISM/RISM theory is proposed. Proposed also is an application of the present formulation to the molecular recognition, in which the conformational fluctuation of protein around its native state becomes an important factor as exemplified by so called 'induced fitting.' [ABSTRACT FROM AUTHOR]

We present results of the theoretical description of ultrasonic phenomena in molecular liquids. In particular, we are interested in the development of a microscopical, i.e., statistical-mechanical, framework capable of explaining the long living puzzle of excess ultrasonic absorption in liquids. Typically, an ultrasonic wave in a liquid can be generated by applying a periodically alternating external pressure with an angular frequency that corresponds to the ultrasound. If the perturbation introduced by such a process is weak, its statistical-mechanical treatment can be done with the use of a linear response theory. We treat the liquid as a system of interacting sites, so that all the response/aftereffect functions as well as the energy dissipation and generalized (wave-vector and frequency-dependent) ultrasonic absorption coefficient are obtained in terms of familiar site-site static and time correlation functions such as static structure factors or intermediate scattering functions. To express the site-site intermediate scattering functions, we refer to the site-site memory equations in the mode-coupling approximation for first-order memory kernels, while equilibrium properties such as site-site static structure factors, and direct and total correlation functions are deduced from the integral equation theory of molecular liquids known as RISM, or one of its generalizations. All of the formalism is phrased in a general manner, hence the results obtained are expected to work for arbitrary types of molecular liquids including simple, ionic, polar, and nonpolar liquids. [ABSTRACT FROM AUTHOR]

The hydrophobic effects on partial molar volume (PMV) are investigated as a PMV change in the transfer of a benzenelike nonpolar solute from the nonpolar solvent to water, using an integral equation theory of liquids. The volume change is divided into two effects. One is the “packing” effect in the transfer from the nonpolar solvent to hypothetical “nonpolar water” without hydrogen bonding networks. The other is the “iceberg” effect in the transfer from nonpolar water to water. The results indicate that the packing effect is negative and a half compensated by the positive iceberg effect. The packing effect is explained by the difference in the solvent compressibility. Further investigation shows that the sign and magnitude of the volume change depend on the solute size and the solvent compressibility. The finding gives a significant implication that the exposure of a hydrophobic residue caused by protein denaturation can either increase or decrease the PMV of protein depending on the size of the residue and the fluctuation of its surroundings. [ABSTRACT FROM AUTHOR]

Statistical mechanical expressions for the partial molar volume (PMV) and the partial molar compressibility (PMC) of a solute molecule with internal degrees of freedom are derived. The equilibrium PMV is expressed simply by the conformational ensemble average of PMV. The equilibrium PMC consists of two terms: the conformational ensemble average of PMC and the mean square fluctuation of PMV along conformational axis. As an illustrative application of the theory, the equilibrium PMV and PMC of butane in aqueous solution are calculated from the relations, in which the thermodynamic quantities of each conformer appearing in the relations are obtained by the reference interaction site model theory. The conformational ensemble average of PMC is the predominant contribution to the equilibrium PMC in this particular example. Possibility of shedding light on the protein conformation in terms of PMV and PMC is discussed. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A combination of the reference interaction-site model theory and site-site Smoluchowski-Vlasov equation is applied to estimate the dynamic response function of the average-energy relaxation of the solute-solvent system, S[SUBS](t). We calculate S[SUBS](t) for 13 model solutes with different structure, from a simple ion to an octopole, in a polar solvent. The partial charges of the ions and multipoles are changed to investigate nonlinear character of S[SUBS](t). The "nonlinear character" we study here corresponds to the response of the solvent fluctuation after the sudden change of the solute charge-distribution. Our present results reveal that S[SUBS](t) depends on the molecular structure and charge distribution of the solute. S[SUBS](t) is decomposed into two parts: one corresponding to the optical mode of solvent, the other to the acoustic mode. We show that for multipoles the optical mode is responsible for the fast part of S[SUBS](t), while the acoustic mode plays an important role in the slower dynamics. The dual nature of S[SUBS](t) is essential for the nonlinearity of solvation dynamics. [ABSTRACT FROM AUTHOR]

The density-functional theory (DFT) for molecular fluids [J. Chem. Phys. 115, 6653 (2001)] is extended to the case of polymer liquids. A system consisting of the ideal chains is employed as a reference system for the DFT, where many-body effects are considered as an effective field that acts on each site of the ideal chains. We derived a relation between the site-site pair distribution functions and the site-density distribution functions under a mean field arising from a single polymer molecule. An integral equation for the site-site pair distribution functions is obtained by the DFT, where the external field is taken to be the mean field. We propose an approximate expression of the intramolecular correlation functions for isolated single-polymer chains to take account for the excluded volume effects inside a polymer chain. The intramolecular correlation function considering the excluded volume effects was in qualitative agreement with those obtained from a simulation for liquid consisting of freely jointed tangent-soft-core chains. The site-density integral equation under the mean field, using the intramolecular correlation function, reproduces the simulation results for site-site pair distribution functions of the system of freely jointed tangent-soft-core chains. [ABSTRACT FROM AUTHOR]

We develop a replica generalization of the reference interaction site model (replica RISM) integral equation theory to describe the structure and thermodynamics of quenched-annealed systems comprising polar molecular species. It provides a successful approach to realistic models of molecular liquids, and properly allows for the effect of a quenched disordered matrix on the sorbed liquid. The description can be extended to an electrolyte solution in a disordered material containing charged chemical functionalities that determine its adsorption character. The replica reference interaction site model (RISM) equations are complemented with the hypernetted chain (HNC) closure and its partial linearization (PLHNC), adequate to ionic and polar molecular liquids. In these approximations, the excess chemical potentials are derived in a closed analytical form. We extend the description to a quenched-annealed system with soft-core interaction potentials between all species, in which the liquid and matrix equilibrium distributions are characterized in general by two different temperatures. The replica RISM/PLHNC-HNC theory is applied to water sorbed in a quenched disordered microporous network of atoms associated into interconnected branched chains, with activating polar groups grafted to matrix chains. The results are in qualitative agreement with experiment for water confined in disordered materials. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Studies the keto-enol tautomerism of acetylacetone in solution with the reference interaction site model self-consistent-field method. Solvents used to represent protic polar, aprotic polar and polar solvents; Electronic correlation energy of solute molecule and solute vibrational energies; Differences in free energies.

Focuses on the electronic and liquid structures of water and its thermodynamic properties over a wide range of temperature and density based on the ab initio molecular orbital theory combined with the integral equation method of liquid. Decrease in the molecular dipole moments and electronic polarization energies with an increase in temperature and/or density.

Reports on a molecular theory for investigating the dynamics of ions in polar liquids. Interaction-site model for molecular liquids and on the generalized Langevian equation combined with the mode-coupling theory; Velocity autocorrelation function, diffusion and friction coefficients of ions in water.

Compares theoretical results for dynamical correlation functions characterizing collective excitations in liquid water with molecular dynamics simulation results performed on the same system. Validity and accuracy of the approximation scheme for memory functions; Dynamical correlation functions as faithful models.

Investigates collective excitations in liquid water using the recently developed theory for dynamics of molecular liquids. Interaction-site model for polyatomic fluids; Projector-operator formalism of Zwanzig and Mori; Approximation scheme for memory functions.

Studies the solvation dynamics of benzonitrile excited state in polar solvents. Evolution of solute electronic states associated with solvent relaxation; Electronic structure calculations; Effects of solvent relaxation on the charge polarization in solute.

Calculates the density matrix for an excess electron in a classical liquid like bath. Use of the values of solvent induced potential surfaces for the electron found from earlier calculations; Diagonalization of the resulting density matrix; Visualization of the transition of the electron to a state of self-trapping.

Develops a self-consistent description of an interface between a metal and a molecular liquid by combination of the density functional theory in the Kohn-Sham formulations for the electronic structure. Consideration of the body-effects of dense fluid on the metal-liquid interactions by averaging the pseudopotentials of liquid molecules.

Abstract A variety of models and hypothesis have been proposed to interpret the temperature dependence of the mean square displacement (MSD) of protein, that is obtained from the incoherent neutron scattering measurement, but a consensus seems yet to be achieved. The most controversial point is concerned with the physics behind the abrupt change of gradient of MSD plotted against temperature. The phenomenon is attributed to different physics by different authors, such as glass transition, alpha to beta transition, harmonic to anharmonic transition, coupling of protein and hydrated-water dynamics, and so forth. In the present paper, we propose a theory to analyse the elastic incoherent neutron scattering (EINS) data of aqueous solutions of protein, based on the generalized Langevin theory combined with the 3D-RISM/RISM equation [B. Kim and F. Hirata, J. Chem. Phys., 138, 054108 (2012)]. The theory gives closed equations for the elastic incoherent structure factor (EISF) and MSD as a function of temperature. Based on the theory, the abrupt change of the gradient of MSD in the temperature dependence is interpreted as an onset of " solvent - induced elasticity ," or "free energy elasticity," with increasing temperature. Highlights • A theory to analyse the incoherent neutron scattering data of protein is proposed. • The equation is derived based on the generalized Langevin theory and 3D-RISM. • The theory gives a closed equation for MSD as a function of temperature. • The inflection temperature of MSD is interpreted by solvent - induced elasticity. [ABSTRACT FROM AUTHOR]

Presents a molecular theory for ion friction coefficient based on the interaction-site molecular liquids model and mode-coupling theory. Account of the related ion friction studies; Formulation of molecular theory; Description of model potential parameters; Analysis of the solute and solvent viewpoints.

Examines the liquid structures of water at the electrode-solution interface. Use of the reference interaction site method; Types of surface geometry examined; Dependence of the water molecule orientation on the surface structure; Changes in the orientation of water molecules.

Presents a theoretical formulation for the solvent force constant and the asymmetry parameter which characterize the free energy profile governing the electrical potential fluctuations of the solvent molecules around solutes. Examination of the nonlinear effects in the solvent force constant and the validity of the linear approximation.

Develops robust and very efficient algorithms for solving the reference interaction site model equations for salt solutions in the bulk and near a solute atom of noble gases. Use of the theory of dielectric consistency developed for solutions at finite salt concentration in the formalism; Change in water structure in the bulk caused by addition of salts.

We have reformulated the reference interaction site model self-consistent-field (RISM-SCF) method to calculate the molecular properties of solute in solutions. The key feature is to introduce the Helmholtz free energy given as a sum of the solute electronic energy estimated by ab initio molecular orbital (MO) methods and the hypernetted-chain (HNC) excess chemical potential of solvation for the extended reference interaction site model (XRISM) method. The variational conditions for the multiconfigurational self-consistent-field (MCSCF) wave functions were derived. It was also shown that, in the case of the Hartree–Fock (HF) method, the present expression gives the same Fock matrix defined previously. Moreover the expression for first derivatives of the free energy with respect to the solute nuclear coordinates were obtained. Sample calculations for the chemical equilibrium of cis- and trans-isomers of 1,2-difluoroethylene are presented. With the use of analytical energy gradients for the MCSCF and HF methods, the solute molecular geometries were determined in an aqueous solution. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We consider the extended simple point charge (SPC/E) model water near uncharged and charged macroparticles. It is shown that the size of the macroparticle tested is sufficiently large and it acts in effect as a planar wall. The reference interaction site model (RISM) theory is employed, and a robust and very efficient algorithm has been developed for solving the basic equations. The algorithm is a hybrid of the Picard and Newton-Raphson methods. The Jacobian matrix is just part of the input data and need not be recalculated at all. Sufficiently accurate solutions are obtained in only 7 to 16 iterations. The reduced density profile of oxygen atoms near an uncharged macroparticle indicates significant dewetting and a clear contribution of the icelike structure. The surface potential calculated is positive but very small. When the macroparticle is charged, the number of water molecules in the close vicinity of the surface increases regardless of the sign of the charge. The interaction between uncharged macroparticles with sufficiently large sizes immersed in pure water is attractive and very strong at small separations. The interaction between negatively charged macroparticles is ‘‘more repulsive’’ than between positively charged macroparticles. On the whole, however, the asymmetry of the SPC/E water in responding to positively and negatively charged surfaces is not high. It has been shown that the results obtained from the RISM theory combined with the SPC/E water are in qualitative accord with those calculated by the reference hypernetted-chain (RHNC) theory for hard spheres with embedded dipoles and tetrahedral quadrupoles, in terms of reduced density profiles, surface potential, and macroparticle interactions. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In the previous study, Chem. Phys. Lett. 214, 391 (1993), we developed a new computational procedure for the solvation effect on the electronic structure of solute based upon the reference interaction site model (RISM) integral equation and the Hartree–Fock equation. The method enables us to calculate the solvent distribution and solute electronic wave functions simultaneously, which is free from such empirical parametrizations as appeared in the usual models based on the dielectric continuum picture. In the present article, we have applied the method to several carbonyl compounds in aqueous solution. The SPC model was used to describe the liquid water. The vertical n→π*, π→π*, and σ→π* transitions of formaldehyde are examined by the RISM-self-consistent field formalism coupled with the restricted Hartree–Fock approximation, and then the free energy calculation was performed for the excited state in order to estimate the contributions for the optical fluorescence spectra. The intramolecular energy turned out to give significant contribution to the bathochromic shift of fluorescence relative to the absorption in the liquid phase. Furthermore the importance of the structural effect of the functional group was discussed by the calculations of three more carbonyl compounds, acetaldehyde, acetone, and acrolein. [ABSTRACT FROM AUTHOR]

A site–site representation of the Smoluchowski–Vlasov equation is proposed based on the generalized Langevin equation, and on the site–site Ornstein–Zernike equation for the molecular liquid. The method is applied for calculating the space–time pair correlation function proposed by van Hove. The results are compared with a molecular dynamics simulation of water. The site–site Smoluchowski–Vlasov equation predicts most of the essential features of the van Hove function for water. [ABSTRACT FROM AUTHOR]

• An idea to analyze the spectrum of water molecules in an inhomogeneous environment around a biomolecule is proposed. • The idea is to solve an eigen-value problem of the collective frequency matrix of water. • The diagonalization of the matrix gives the mode and frequency of the density fluctuation of water around the biomolecule. • It is clarified how the mode and frequency of the density fluctuation are modulated by the field from the biomolecule. • The method provides a way to distinguish the mode of fluctuation with color. An idea to analyze the fluctuational mode or/and spectrum of water molecules in an inhomogeneous environment around a biomolecule such as protein and DNA is proposed based on the generalized Langevin equation (GLE) for water interacting with a biomolecule. The idea is to solve an eigen-value problem of the collective frequency matrix of water, which has a physical meaning similar to the Hessian matrix in the case of a connected harmonic-oscillator. The diagonalization of the matrix gives the mode and frequency of the density fluctuation of water around the biomolecule. The treatment is a natural extension of that made for water in a homogeneous environment by Chong and Hirata in 1999, in which the authors have found the four modes for density fluctuation; one for an acoustic mode, and the other three for optical modes. It is the point of the new approach how the mode and frequency of the density fluctuation are modulated by the field from the biomolecule. The method provides a way to distinguish the mode of fluctuation with color. A few possible applications of the theoretical approach to problems of the life science including medicine are also proposed. [ABSTRACT FROM AUTHOR]

A theory to realize a multiscale dynamics of protein is proposed based on the generalized Langevin equation combined with the 3D-RISM theory. The idea of normal mode analysis (NMA) is adopted to decouple the dynamics into different modes having respective time scales. In order to decouple the modes, the variance–covariance matrix concerning the structural fluctuation of protein in solution is diagonalized, instead of the Hessian matrix of a harmonic oscillator in vacuum. An algorithm to estimate the friction coefficient exerted on each atom of protein due to solvent is also proposed. [ABSTRACT FROM AUTHOR]

Wederive, implement, and apply equilibrium solvation site analysisfor biomolecules. Our method utilizes 3D-RISM calculations to quicklyobtain equilibrium solvent distributions without either necessityof simulation or limits of solvent sampling. Our analysis of thesedistributions extracts highest likelihood poses of solvent as wellas localized entropies, enthalpies, and solvation free energies. Wedemonstrate our method on a structure of HIV-1 protease where excellentstructural and thermodynamic data are available for comparison. Ourresults, obtained within minutes, show systematic agreement with availableexperimental data. Further, our results are in good agreement withestablished simulation-based solvent analysis methods. This methodcan be used not only for visual analysis of active site solvationbut also for virtual screening methods and experimental refinement. [ABSTRACT FROM AUTHOR]

We have developed an algorithm for sampling the conformational space of large flexible molecules in solution, which combines the molecular dynamics (MD) method and the three-dimensional reference interaction site model (3D-RISM) theory. The solvent-induced force acting on solute atoms was evaluated as the gradient of the solvation free energy with respect to the solute-atom coordinates. To enhance the computation speed, we have applied a multiple timestep algorithm based on the RESPA (Reversible System Propagator Algorithm) to the combined MD/3D-RISM method. By virtue of the algorithm, one can choose a longer timestep for renewing the solvent-induced force compared with that of the conformational update. To illustrate the present MD/3D-RISM simulation, we applied the method to a model of acetylacetone in aqueous solution. The multiple timestep algorithm succeeded in enhancing the computation speed by 3.4 times for this model case. Acetylacetone possesses an intramolecular hydrogen-bonding capability between the hydroxyl group and the carbonyl oxygen atom, and the molecule is significantly stabilized due to this hydrogen bond, especially in gas phase. The intramolecular hydrogen bond was kept intact during almost entire course of the MD simulation in gas phase, while in the aqueous solutions the bond is disrupted in a significant number of conformations. This result qualitatively agrees with the behavior on a free energy barrier lying upon the process for rotating a torsional degree of freedom of the hydroxyl group, where it is significantly reduced in aqueous solution by a cancellation between the electrostatic interaction and the solvation free energy. © 2007 Wiley Periodicals, Inc. J Comput Chem 2008 [ABSTRACT FROM AUTHOR]

The three-dimensional reference interaction site model integral equation theory (3D-RISM) combined with the ab initio molecular orbital method (3D-RISM-SCF) is applied to a solvated macromolecular system. The solvation structure around a solute molecule is obtained from the 3D-RISM integral equation under the electrostatic potential of the solute molecule, calculated by the ab initio molecular orbital theory. The electrostatic potential should be calculated on each grid point in the three-dimensional real space. Therefore, the calculation of the electrostatic potential is the most time consuming part in this method. In this article, we propose a new procedure to save the computational cost for calculating the electrostatic potential and the solvated fock matrix. The strategy of this procedure is to evaluate the electrostatic potential and the solvated fock matrix in different ways, depending on the distance between solute and solvent. Inside the repulsive cores of solute atoms, it is possible to avoid the calculation of electrostatic potential and solvated Fock matrix by assuming the potential to be infinity. In the region sufficiently far from solute, they are evaluated classically by putting the effective point charge on each atom. In the intermediate region, the electrostatic potential is evaluated directly by integrating the molecular orbitals of the solute molecule. The electronic structure and the energy gradient of Methionine-Enkephalin and solvation structure are estimated by using this procedure in aqueous solution, and are compared with the results from other procedures. The results are compared also with those from the continuum model. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 453–462, 2006 [ABSTRACT FROM AUTHOR]

We briefly review developments of theories for phase transitions of molecular fluids and mixtures, from semi-phenomenological approaches providing equations of state with adjustable parameters to firstprinciples microscopic methods qualitatively correct for a variety of molecular models with realistic interaction potentials. We further present the generalization of the van der Waals-Maxwell description of fluid phase diagrams to account for chemical specificities of polar molecular fluids, such as hydrogen bonding. Our theory uses the reference interaction site model (RISM) integral equation approach complemented with the new closure we have proposed (KH approximation), successful over a wide range of density from gas to liquid. The RISM/KH theory is applied to the known three-site models of water, methanol, and hydrogen fluoride. It qualitatively reproduces their vapor-liquid phase diagrams and the structure in the gas as well as liquid phases, including hydrogen bonding. Furthermore, phase transitions of water and methanol sorbed in nanoporous carbon aerogel are described by means of the replica generalization of the RISM approach we have developed. The changes as compared to the bulk fluids are in agreement with simulations and experiment. The RISM/KH theory is promising for description of phase transitions in various associating fluids, in particular, electrolyte as well as non-electrolyte solutions and ionic liquids. [ABSTRACT FROM AUTHOR]

In the Comment on our paper [J. Chem. Phys. 123, 167103 (2005), preceding paper], Graziano argues based on the scaled particle theory that the partial molar volume change in the transfer of a hydrophobic solute from “hypothetical nonpolar water” to water can be explained simply by the difference in the effective size of solvent molecules. Opposing to the argument, we clarify using the reference interaction site model theory that the attractive interactions represented by the hydrogen bonding play an essential role for the volume change, and that the explanation given by Graziano replaces the real physics by a fake model based on an “effective” molecular diameter. We also make a general argument against the use of hard-sphere models when one considers the properties of hydration. [ABSTRACT FROM AUTHOR]

Presents the study on the revisiting of the acid-base equilibrium in aqueous solutions of hydrogen halides. Determination of the free energy changes linked with the chemical equilibrium; Ab initio electronic structure theory combined with the statistical mechanics of molecular liquids; Solvation energies of the anions.

Replies to the comments by Ranjit Biswas and Biman Bagchi on the paper 'Dynamics of Solvated Ion in Polar Liquids: An interaction-Site-Model Description,' by the authors, published in the volume 108, year 1998, of the 'Journal of Chemical Physics' periodical. Lack of basis for the comments and assertion that the article contains errors.

The extended RISM (XRISM) theory with a new closure relation is proposed. The new equation incorporates the chain sum of the dipole-dipole interactions into XRISM as the bridge diagrams (Dipole Bridge: DB) in its closure relation. The new theory reproduces the dielectric constant of polar liquids without using phenomenological parameters, but with a parameter which reflects the effect of short-range correlation onto the dipole-dipole interaction between the two molecules. The parameter is essentially universal in dipolar liquids including water. The computational algorithm to solve the XRISM-DB equation is identical to that of XRISM, so that all the programs developed for XRISM can be transferred to the new equation by adding few lines which define the screening constant concerning the dipole-dipole interaction. • The XRISM theory fails to reproduce the dielectric constant of polar liquids. • The problem is caused by not including the bridge diagrams representing the dipole-dipole interactions. • The new theory overcomes the defect by incorporating the dipole-dipole interactions as the bridge diagrams. • The new XRISM theory gives a priscription to calculate the dielectric constant from the first principle. [ABSTRACT FROM AUTHOR]

We study the hydration structure and free energy of several conformations of Met-enkephalin in ambient water by employing the one-dimensional (1D) as well as three-dimensional (3D) reference interaction site model (RISM) integral equation theories, complemented by the hypernetted chain (HNC) closure with the repulsive bridge correction (RBC). The RBC contribution to the excess chemical potential of solvation is calculated by means of the thermodynamic perturbation theory (TPT), which crucially reduces computational burden and thus is especially important for a hybrid algorithm of the RISM with molecular simulation. The 3D-RISM/HNC+RBC-TPT approach provides improved prediction of the solvation thermodynamics and gives a detailed description of the solvation structure of a biomolecule. The results obtained are discussed and compared to those following from the 1D-RISM/HNC theory. The latter yields physically reasonable results for the conformational stability of biomolecules in solution, which is further improved by adding the 1D-RBC. The modified, 1D-RISM/HNC+RBC-TPT integral equation theory combined with the simulated annealing or generalized-ensemble Monte Carlo simulation methods is capable of reliable prediction of conformations of biomolecules in solution with due account for the solvent effect at the microscopic level. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We modify the site-site as well as three-dimensional (3D) versions of the reference interaction site model (RISM) integral equations with the hypernetted chain (HNC) closures by adding a repulsive bridge correction (RBC). The RBC treats the overestimation of water ordering around a hydrophobic solute in the RISM/HNC approximation, and thus refines the entropic component in the hydration free energy. We build up the bridge functions on r[sup -12] repulsive core potentials, and propose RBC expressions for both the site-site and 3D-RISM approaches. To provide fast calculation, we obtain the excess chemical potential of hydration by using the thermodynamic perturbation theory (TPT). The site-site RISM/HNC+RBC as well as 3D-RISM/HNC+RBC approaches are applied to calculate the structure and thermodynamics of hydration of rare gases and alkanes in ambient water. For both approaches, the RBC drastically improves the agreement of the hydration chemical potential with simulation data and provides its correct dependence on the solute size. For solutes of a nonspherical form, the 3D treatment yields the hydration structure in detail and better fits simulation results, whereas the site-site approach is essentially faster. The TPT approximation gives the hydration thermodynamics in good qualitative agreement with the exact results of the thermodynamic integration, and substantially reduces computational burden. The RBC-TPT approximation can improve the predictive capability of the hybrid algorithm of a generalized-ensemble Monte Carlo simulation combined with the site-site RISM theory, used to describe protein folding with due account for the water effect at the microscopic level. The RBC can be optimized for better fit to reference simulation data, and can be generalized for solute molecules with charged groups. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We applied the three-dimensional reference interaction site model (3D-RISM) integral equation theory with the 3D hypernetted chain (3D-HNC) closure or its partial linearization (3D-PLHNC) to obtain the potentials of mean force (PMFs) and the solvation structure of sodium chloride in ambient water. The bulk solvent correlations are treated by the dielectrically consistent site-site RISM/HNC theory (DRISM/HNC) to provide a proper description of the dielectric properties of solution and to include the case of a finite salt concentration. The PMF is calculated as a difference in the solvation free energy of an ion pair and of individual ions. We obtained and analyzed in detail the PMFs and solvation structure for ion pairs of NaCl at infinite dilution and a concentration of 1 M. The results are in reasonably good agreement with molecular dynamics simulations for the same model of the solution species. Positions and orientations of water molecules in the first solvation shell around the ion pair are deduced. The short-range hydration structure of the ion pairs at infinite dilution and at moderate concentration is very similar. Ionic ordering and clustering is found in 1 M solution. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We adapt the three-dimensional reference interaction site model (3D-RISM) to calculate the potentials of mean force for ion-molecular solution as a difference between the chemical potential of solvation of a cluster of solutes and of individual ones. The method yields the solvation structure around the cluster of solutes in detail. The solvation chemical potential is obtained for the three-dimensional hypernetted chain (3D-HNC) closure as well as for its partial linearization (3D-PLHNC approximation). The solvation chemical potential is obtained in a closed analytical form for both the 3D-HNC and 3D-PLHNC closures. The 3D-RISM integral equations are solved by using the supercell technique. A straightforward supercell treatment of ionic solute in polar molecular solvent leads to a big error in the potential of mean force as well as the solvation chemical potential, which for simple ions in water amounts to about 35 kcal/mol. We elaborated corrections to the 3D-RISM integral equations, alleviating the artifact of the supercell periodicity with an accuracy of 0.05 kcal/mol or better and restoring the long-range asymptotics of the solute-solvent correlation functions. The dielectrically consistent site-site RISM/HNC theory (DRISM/HNC) is employed for the solvent correlations to provide a proper description of the dielectric properties of solution. This allowed us to extend the description to solution at a finite salt concentration. We converge both the 3D-RISM and site-site DRISM integral equations by using the method of modified direct inversion in the iterative subspace. Owing to the proper initial guess of the correlation functions, iteration begins at once for a given temperature and full molecular charge, avoiding a gradual decrease of the temperature and increase of the site charges, which greatly reduces the computation time. We calculate and discuss the potentials of mean force for sodium chloride in ambient water at infinite dilution as well as at a f... [ABSTRACT FROM AUTHOR]

The density fluctuation of water in the supercritical region was investigated theoretically using the reference interaction site model theory combined with the Kovalenko-Hirata closure relation, the so-called RISM-KH theory. The density fluctuation was evaluated by the numerical differentiation of density with respect to pressure at constant temperature. The density fluctuations plotted against density show finite maxima along a line slightly off from the critical isochore, in accordance with experimental results. The microscopic structures of water on both regions that were separated by the line were investigated by analyzing the site-site radial distribution functions. The analysis clearly indicates that the structure is determined by the two effects featuring liquid states: the packing or volume exclusion effect and the screening of the Coulomb interaction or the hydrogen bond, both becoming more important at higher densities. An interplay of the two effects creates maxima of the density fluctuation in the supercritical region of water. [ABSTRACT FROM AUTHOR]

We propose the thermodynamic integration along a spatial reaction coordinate using the molecular dynamics simulation combined with the three-dimensional reference interaction site model theory. This method provides a free energy calculation in solution along the reaction coordinate defined by the Cartesian coordinates of the solute atoms. The proposed method is based on the blue moon algorithm which can, in principle, handle any reaction coordinate as far as it is defined by the solute atom positions. In this article, we apply the present method to the complex formation process of the crown ether 18-Crown-6 (18C6) with the potassium ion in an aqueous solution. The separation between the geometric centers of these two molecules is taken to be the reaction coordinate for this system. The potential of mean force (PMF) becomes the maximum at the separation between the molecular centers being ∼4 Å, which can be identified as the free energy barrier in the process of the molecular recognition. In a separation further than the free energy barrier, the PMF is slightly reduced to exhibit a plateau. In the region closer than the free energy barrier, approach of the potassium ion to the center of 18C6 also decreases the PMF. When the potassium ion is accommodated at the center of 18C6, the free energy is lower by -5.7 ± 0.7 kcal/mol than that at the above mentioned plateau or converged state. By comparing the results with those from the free energy calculation along the coupling parameters obtained in our previous paper [T. Miyata, Y. Ikuta, and F. Hirata, J. Chem. Phys. 133, 044114 (2010)], it is found that the effective interaction in water between 18C6 and the potassium ion vanishes beyond the molecular-center-separation of 10 Å. Furthermore, the conformation of 18C6 is found to be significantly changed depending upon the 18C6-K+ distance. A proper conformational sampling and an accurate solvent treatment are crucial for realizing the accurate PMF, and we believe that the proposed method is useful to evaluate the PMF in a solution. A discussion upon the PMF in terms of the three-dimensional distribution function for the solvent is also presented. [ABSTRACT FROM AUTHOR]

This article proposes a free energy calculation method based on the molecular dynamics simulation combined with the three dimensional reference interaction site model theory. This study employs the free energy perturbation (FEP) and the thermodynamic integration (TDI) along the coupling parameters to control the interaction potential. To illustrate the method, we applied it to a complex formation process in aqueous solutions between a crown ether molecule 18-Crown-6 (18C6) and a potassium ion as one of the simplest model systems. Two coupling parameters were introduced to switch the Lennard-Jones potential and the Coulomb potential separately. We tested two coupling procedures: one is a “sequential-coupling” to couple the Lennard-Jones interaction followed by the Coulomb coupling, and the other is a “mixed-coupling” to couple both the Lennard-Jones and the Coulomb interactions together as much as possible. The sequential-coupling both for FEP and TDI turned out to be accurate and easily handled since it was numerically well-behaved. Furthermore, it was found that the sequential-coupling had relatively small statistical errors. TDI along the mixed-coupling integral path was to be carried out carefully, paying attention to a numerical behavior of the integrand. The present model system exhibited a nonmonotonic behavior in the integrands for TDI along the mixed-coupling integral path and also showed a relatively large statistical error. A coincidence within a statistical error was obtained among the results of the free energy differences evaluated by FEP, TDI with the sequential-coupling, and TDI with the mixed-coupling. The last one is most attractive in terms of the computer power and is accurate enough if one uses a proper set of windows, taking the numerical behavior of the integrands into account. TDI along the sequential-coupling integral path would be the most convenient among the methods we tested, since it seemed to be well-balanced between the computational load and the accuracy. The numerical results reported in this article qualitatively agree with the experimental data for the potassium ion recognition by the 18C6 in aqueous solution. [ABSTRACT FROM AUTHOR]

Because proteins and DNA interact with each other and with various small molecules in the presence of water molecules, we cannot ignore their hydration when discussing their structural and energetic properties. Although high-resolution crystal structure analyses have given us a view of tightly bound water molecules on their surface, the structural data are still insufficient to capture the detailed configurations of water molecules around the surface of these biomolecules. Thanks to the invention of various computational algorithms, computer simulations can now provide an atomic view of hydration. Here, we describe the apparent patterns of DNA hydration calculated by using two different computational methods: Molecular dynamics (MD) simulation and three-dimensional reference interaction site model (3D-RISM) theory. Both methods are promising for obtaining hydration properties, but until now there have been no thorough comparisons of the calculated three-dimensional distributions of hydrating water. This rigorous comparison showed that MD and 3D-RISM provide essentially similar hydration patterns when there is sufficient sampling time for MD and a sufficient number of conformations to describe molecular flexibility for 3D-RISM. This suggests that these two computational methods can be used to complement one another when evaluating the reliability of the calculated hydration patterns. [ABSTRACT FROM AUTHOR]

We present results of the theoretical study and numerical calculation of the dynamics of molecular liquids based on the combination of the memory equation formalism and the reference interaction site model (RISM). Memory equations for the site-site intermediate scattering functions are studied in the mode-coupling approximation for the first-order memory kernels, while equilibrium properties such as site-site static structure factors are deduced from RISM. The results include the temperature-density (pressure) dependence of translational diffusion coefficients D and orientational relaxation times τ for acetonitrile in water, methanol in water, and methanol in acetonitrile—all in the limit of infinite dilution. Calculations are performed over the range of temperatures and densities employing the extended simple point charge model for water and optimized site-site potentials for acetonitrile and methanol. The theory is able to reproduce qualitatively all main features of temperature and density dependences of D and τ observed in real and computer experiments. In particular, anomalous behavior, i.e, the increase in mobility with density, is observed for D and τ of methanol in water, while acetonitrile in water and methanol in acetonitrile do not show deviations from the ordinary behavior. The variety exhibited by the different solute-solvent systems in the density dependence of the mobility is interpreted in terms of the two competing origins of friction, which interplay with each other as density increases: the collisional and dielectric frictions which, respectively, increase and decrease with increasing density. [ABSTRACT FROM AUTHOR]

A method for calculating the nuclear magnetic shielding constant of atoms in solution is proposed based on the ab initio electronic structure theory combined with the extended reference interaction site model in statistical mechanics for molecular liquids. The method is applied to a water molecule solvated in water, acetone, chloroform, and carbon tetrachloride. The results for solvation effect demonstrate capability to predict the experimental results. The theory provides a tool to investigate the solvent effect on the nuclear magnetic shielding and its temperature dependence from a molecular viewpoint. The theory takes account for the effect of the electrostatic interaction on the electronic structure of solute, but disregards the electron overlap. The effect of intermolecular overlap of the electron on the nuclear magnetic shieldings is examined using a molecular cluster model. [ABSTRACT FROM AUTHOR]

We have developed a three-dimensional (3D) extension of the reference interaction site model-self-consistent field (RISM-SCF) method to treat the electronic structure of a solvated molecule. The site-site treatment of the solute-solvent correlations involving the approximation of radial averaging constitutes a bottleneck of the RISM-SCF method, and thus lacks a 3D picture of the solvation structure for complex solutes. To resolve this problem, we devised out a 3D generalization of the RISM integral equations which yields the 3D correlation functions of interaction sites of solvent molecules around a solute of arbitrary shape. In the present article, we propose a SCF combination of the ab initio molecular orbital (MO) methods and 3D-RISM approach. A benchmark result for carbon monoxide in ambient water is also presented. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]