Three-dimensional Reference Interaction Site Model Research Articles

Molecule–Surface Recognition between Heterocyclic Aromatic Compounds and Kaolinite in Toluene Investigated by Molecular Theory of Solvation and Thermodynamic and Kinetic Experiments

Molecular recognition interactions between kaolinite and a series of heterocyclic aromatic compounds (HAC) representative of the N- and S-containing moieties in petroleum asphaltene macromolecules are investigated using the three-dimensional reference interaction site model with the Kovalenko–Hirata closure approximation (3D-RISM-KH) theory of solvation and experimental techniques in toluene solvent. The statistical-mechanical 3D-RISM-KH molecular theory of solvation predicts the adsorption configuration and thermodynamics from the 3D site density distribution functions and total solvation free energy, respectively, for adsorption of HAC and toluene on kaolinite. Spectrophotometric measurements show that, among the HAC studied, only acridine and phenanthridine adsorb quantitatively on kaolinite. For these pyridinic HAC, the adsorption results fitted to the Langmuir isotherm in the monolayer domain suggest a uniform monolayer of HAC molecules. The 3D-RISM-KH studies predict that the aluminum hydroxide surf...

Efficient implementation of the three-dimensional reference interaction site model method in the fragment molecular orbital method.

The three-dimensional reference interaction site model (3D-RISM) method was efficiently implemented in the fragment molecular orbital (FMO) method. The method is referred to as the FMO/3D-RISM method, and allows us to treat electronic structure of the whole of a macromolecule, such as a protein, as well as the solvent distribution around a solute macromolecule. The formalism of the FMO/3D-RISM method, for the computationally available form and variational expressions, are proposed in detail. A major concern leading to the implementation of the method was decreasing the computational costs involved in calculating the electrostatic potential, because the electrostatic potential is calculated on numerous grid points in three-dimensional real space in the 3D-RISM method. In this article, we propose a procedure for decreasing the computational costs involved in calculating the electrostatic potential in the FMO method framework. The strategy involved in this procedure is to evaluate the electrostatic potential and the solvated Fock matrix in different manners, depending on the distance between the solute and the solvent. The electrostatic potential is evaluated directly in the vicinity of the solute molecule by integrating the molecular orbitals of monomer fragments of the solute molecule, whereas the electrostatic potential is described as the sum of multipole interactions when an analog of the fast multipole method is used. The efficiency of our method was demonstrated by applying it to a water trimer system and three biomolecular systems. The FMO/3D-RISM calculation can be performed within a reasonable computational time, retaining the accuracy of some physical properties.

Distinct configurations of cations and water in the selectivity filter of the KcsA potassium channel probed by 3D-RISM theory

The potassium channel is highly selective for K+ over other monovalent cations, and the narrow pore structure with 3Å in diameter named the selectivity filter (SF) is responsible for the selective permeation. Here we applied the statistical mechanics of liquids called three-dimensional reference interaction site model (3D-RISM) theory, and the binding configurations of the monovalent cations, Li+, Na+ and K+, with special attention on the contribution of water in the KcsA potassium channel were examined. All the three types of cations are bound in the open SF with high affinity, but with different binding coordinations: the in-cage configuration by eight carbonyl oxygens for K+, and the in-plane configuration by four carbonyl oxygens for Li+, whereas both configurations are allowed for Na+. In each case, water contributes an integral part of the ion coordination. In the case of Li+, a linear water-Li+-water complex is settled into two adjacent cages with the Li+ centered at the in-plane site. Positions of water around Na+ are more flexible, which may allow a transition between in-plane and in-cage configurations. K+ stably occupied in-cage configuration, and water occupies adjacent cages. The results provide the distinct configuration of ion and water in the SF, and serves clues for elementary process of selectivity.

Interfacial Structures, Surface Tensions, and Contact Angles of Diiodomethane on Fluorinated Polymers

The wetting behavior of diiodomethane on crystalline poly(tetrafluoroethylene) (PTFE), noncrystalline PTFE, and poly(vinylidene cyanide-alt-1H,1H,2H,2H-perfluorodecyl vinyl ether) surfaces are anal...

Massively parallel implementation of 3D‐RISM calculation with volumetric 3D‐FFT

A new three-dimensional reference interaction site model (3D-RISM) program for massively parallel machines combined with the volumetric 3D fast Fourier transform (3D-FFT) was developed, and tested on the RIKEN K supercomputer. The ordinary parallel 3D-RISM program has a limitation on the number of parallelizations because of the limitations of the slab-type 3D-FFT. The volumetric 3D-FFT relieves this limitation drastically. We tested the 3D-RISM calculation on the large and fine calculation cell (2048(3) grid points) on 16,384 nodes, each having eight CPU cores. The new 3D-RISM program achieved excellent scalability to the parallelization, running on the RIKEN K supercomputer. As a benchmark application, we employed the program, combined with molecular dynamics simulation, to analyze the oligomerization process of chymotrypsin Inhibitor 2 mutant. The results demonstrate that the massive parallel 3D-RISM program is effective to analyze the hydration properties of the large biomolecular systems.

Theoretical Study of One-Electron Oxidized Mn(III)– and Ni(II)–Salen Complexes: Localized vs Delocalized Ground and Excited States in Solution

One-electron oxidized Mn(III)- and Ni(II)-salen complexes exhibit unique mixed-valence electronic structures and charge transfer (CT) absorption spectra. We theoretically investigated them to elucidate the reason why the Mn(III)-salen complex takes a localized electronic structure (class II mixed valence compound by Robin-Day classification) and the Ni(II)-analogue has a delocalized one (class III) in solution, where solvation effect was taken into consideration either by the three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) method or by the mean-field (MF) QM/MM-MD simulation. The geometries of these complexes were optimized by the 3D-RISM-SCF-U-DFT/M06. The vertical excitation energy and the oscillator strength of the first excited state were evaluated by the general multiconfiguration reference quasi-degenerate perturbation theory (GMC-QDPT), including the solvation effect based on either 3D-RISM-SCF- or MF-QM/MM-MD-optimized solvent distribution. The computational results well agree with the experimentally observed absorption spectra and the experimentally proposed electronic structures. The one-electron oxidized Mn(III)-salen complex with a symmetrical salen ligand belongs to the class II, as experimentally reported, in which the excitation from the phenolate anion to the phenoxyl radical moiety occurs. In contrast, the one-electron oxidized Ni(II)-salen complex belongs to the class III, in which the excitation occurs from the doubly occupied delocalized π1 orbital of the salen radical to the singly occupied delocalized π2 orbital; the π1 is a bonding combination of the HOMOs of two phenolate moieties and the π2 is an antibonding combination. Solvation effect is indispensable for correctly describing the mixed-valence character, the geometrical distortion, and the intervalence CT absorption spectra of these complexes. The number of d electrons and the d orbital energy level play crucial roles to provide the localization/delocalization character of these complexes.

A Cavity Corrected 3D-RISM Functional for Accurate Solvation Free Energies

We show that an Ng bridge function modified version of the three-dimensional reference interaction site model (3D-RISM-NgB) solvation free energy method can accurately predict the hydration free energy (HFE) of a set of 504 organic molecules. To achieve this, a single unique constant parameter was adjusted to the computed HFE of single atom Lennard-Jones solutes. It is shown that 3D-RISM is relatively accurate at predicting the electrostatic component of the HFE without correction but requires a modification of the nonpolar contribution that originates in the formation of the cavity created by the solute in water. We use a free energy functional with the Ng scaling of the direct correlation function [Ng, K. C. J. Chem. Phys.1974, 61, 2680]. This produces a rapid, reliable small molecule HFE calculation for applications in drug design.

Ion Counting from Explicit-Solvent Simulations and 3D-RISM

The ionic atmosphere around nucleic acids remains only partially understood at atomic-level detail. Ion counting (IC) experiments provide a quantitative measure of the ionic atmosphere around nucleic acids and, as such, are a natural route for testing quantitative theoretical approaches. In this article, we replicate IC experiments involving duplex DNA in NaCl(aq) using molecular dynamics (MD) simulation, the three-dimensional reference interaction site model (3D-RISM), and nonlinear Poisson-Boltzmann (NLPB) calculations and test against recent buffer-equilibration atomic emission spectroscopy measurements. Further, we outline the statistical mechanical basis for interpreting IC experiments and clarify the use of specific concentration scales. Near physiological concentrations, MD simulation and 3D-RISM estimates are close to experimental results, but at higher concentrations (>0.7 M), both methods underestimate the number of condensed cations and overestimate the number of excluded anions. The effect of DNA charge on ion and water atmosphere extends 20–25 Å from its surface, yielding layered density profiles. Overall, ion distributions from 3D-RISMs are relatively close to those from corresponding MD simulations, but with less Na+ binding in grooves and tighter binding to phosphates. NLPB calculations, on the other hand, systematically underestimate the number of condensed cations at almost all concentrations and yield nearly structureless ion distributions that are qualitatively distinct from those generated by both MD simulation and 3D-RISM. These results suggest that MD simulation and 3D-RISM may be further developed to provide quantitative insight into the characterization of the ion atmosphere around nucleic acids and their effect on structure and stability.

Probing “ambivalent” snug-fit sites in the KcsA potassium channel using three-dimensional reference interaction site model (3D-RISM) theory

Abstract The potassium channel is highly selective for K+ over Na+, and the mechanism underlying this selectivity remains unclear. We show the three-dimensional distribution functions (3D-DFs) of small cations (Li+, Na+, and K+) and the free energy profile of ions inside the open selectivity filter (SF) of the KcsA channel. Our previous results [S. Phongphanphanee, N. Yoshida, S. Oiki, F. Hirata. Abstract Book of 5th International Symposium on Molecular Science of Fluctuations toward Biological Functions, P062 (2012)] indicate that the 3D-DF for K+ exhibits distinct peaks at the sites formed by the eight carbonyl oxygen atoms belonging to the surrounding peptide-backbone and residues (the cage site). Li+ has sharp distributions in the 3D-DF at the center of a quadruplex composed of four carbonyl oxygen atoms (the plane site). Na+ has a rather diffuse distribution throughout the SF region with peaks both in the plane and in cage sites. The results provide microscopic evidence of the phenomenological findings that Li+ and Na+ are not excluded from the SF region and that the binding affinity alone does not cause the ion selectivity of KcsA. In the present study, with an ion placed explicitly along the pore axis, the free energy profiles of the ions inside the SF were calculated; from these profiles we suggest a new mechanism for selective K+ permeation. According to the model, a K+ ion must overcome a free energy barrier that is approximately half that of Na+ to exit from either of the SF mouths due to the existence of an intermediate local minimum along the route for climbing the barriers.

Biomolecular Recognition Based on 3D Molecular Theory of Solvation

Protein-protein and protein-ligand recognition plays an essential role in many biomolecular processes. Understanding the mechanisms of protein-ligand binding is also crucial for designing new and optimizing existing therapeutic agents, and in different biotechnological applications. It is well known that solvation effects, including hydrophobicity and solvent mediated hydrogen bonding, are major factors implicated in biomolecular processes. Such processes often involve slow conformational changes and exchange of solvent and ligand molecules between bulk solution and biomolecular cavities.We develop new approaches for accurate account of molecular solvation effects in protein-ligand recognition and binding, which further extend the ligand mapping protocols based on the molecular theory of solvation, a.k.a. the three-dimensional reference interaction site model with the Kovalenko-Hirata closure (3D-RISM-KH). Based on statistical mechanics, this theory provides a natural link between different levels of coarse-graining details in a multiscale description of solvation structure and thermodynamics, from highly localized structural solvent and bound ligand molecules to effective desolvation potentials and self-assembling nanoarchitectures in solvents of different composition in a range of thermodynamic conditions.Implemented in the new 3D-RISM-Dock protocol, the theory provides a quantitative estimate of binding affinities, based on a detailed physical description of hydrogen bonding, hydrophobicity, and solvation entropic effects, with full account for molecular specificities, thermodynamic conditions, and concentration effects. The theory accurately predicts the solvation structure of biomolecules. This allows us to incorporate the 3D-RISM-KH description of structural solvation in a new docking protocol. The latter has been successfully applied to predict the binding modes of the periplasmic binding proteins in situations when structural solvation and desolvation effects are of importance. We also show that the 3D-RISM-KH theory provides valuable information on the role of the solvation entropic effects in the ligand binding and large scale conformation dynamics of proteins.

Statistical Thermodynamics for Binding of an RNA Aptamer and a Partial Peptide of a Prion Protein

It has been reported that a novel RNA aptamer with 12 residues (R12) binds to a partial peptide of a prion protein (P16) [1]. This binding is expected to prevent prion diseases, but its driving force remains rather unclear. Here we calculate the free-energy change upon the binding of R12 and P16 using molecular mechanics, the three-dimensional (3D) reference interaction site model (RISM) theory [2], and the hybrid method in which the angle-dependent integral equation theory [3] applied to a multipolar water model [4] is combined with the morphometric approach [5]. The 3D-RISM theory and the hybrid method are employed for calculating the hydration energy and the hydration entropy, respectively. We show that the large decrease in the intermolecular energy upon the binding is almost cancelled out by a correspondingly large increase in the hydration energy. The binding is driven by a large gain in the translational, configurational entropy of water originating primarily from the reduction in water crowding in the system. Our physical picture of the binding can be described as follows: The binding, which is driven by the water-entropy effect, accompanies a loss of R12-water and P16-water electrostatic attractive and van der Waals interactions. But the loss is compensated by a gain in R12-P16 electrostatic attractive and van der Waals interactions.[1] T. Mashima, et al., Nucleic Acids Res. 41, 1355 (2013).[2] T. Imai, et al., J. Chem. Phys. 126, 225102 (2007).[3] M. Kinoshita, J. Chem. Phys. 128, 0245071 (2008).[4] P. G. Kusalik and G. N. Patey, Mol. Phys. 65, 1105 (1988).[5] R. Roth, Y. Harano, and M. Kinoshita, Phys. Rev. Lett. 97, 078101 (2006).

Multiple time step molecular dynamics in the optimized isokinetic ensemble steered with the molecular theory of solvation: Accelerating with advanced extrapolation of effective solvation forces

We develop efficient handling of solvation forces in the multiscale method of multiple time step molecular dynamics (MTS-MD) of a biomolecule steered by the solvation free energy (effective solvation forces) obtained from the 3D-RISM-KH molecular theory of solvation (three-dimensional reference interaction site model complemented with the Kovalenko-Hirata closure approximation). To reduce the computational expenses, we calculate the effective solvation forces acting on the biomolecule by using advanced solvation force extrapolation (ASFE) at inner time steps while converging the 3D-RISM-KH integral equations only at large outer time steps. The idea of ASFE consists in developing a discrete non-Eckart rotational transformation of atomic coordinates that minimizes the distances between the atomic positions of the biomolecule at different time moments. The effective solvation forces for the biomolecule in a current conformation at an inner time step are then extrapolated in the transformed subspace of those at outer time steps by using a modified least square fit approach applied to a relatively small number of the best force-coordinate pairs. The latter are selected from an extended set collecting the effective solvation forces obtained from 3D-RISM-KH at outer time steps over a broad time interval. The MTS-MD integration with effective solvation forces obtained by converging 3D-RISM-KH at outer time steps and applying ASFE at inner time steps is stabilized by employing the optimized isokinetic Nosé-Hoover chain (OIN) ensemble. Compared to the previous extrapolation schemes used in combination with the Langevin thermostat, the ASFE approach substantially improves the accuracy of evaluation of effective solvation forces and in combination with the OIN thermostat enables a dramatic increase of outer time steps. We demonstrate on a fully flexible model of alanine dipeptide in aqueous solution that the MTS-MD/OIN/ASFE/3D-RISM-KH multiscale method of molecular dynamics steered by effective solvation forces allows huge outer time steps up to tens of picoseconds without affecting the equilibrium and conformational properties, and thus provides a 100- to 500-fold effective speedup in comparison to conventional MD with explicit solvent. With the statistical-mechanical 3D-RISM-KH account for effective solvation forces, the method provides efficient sampling of biomolecular processes with slow and/or rare solvation events such as conformational transitions of hydrated alanine dipeptide with the mean life times ranging from 30 ps up to 10 ns for "flip-flop" conformations, and is particularly beneficial for biomolecular systems with exchange and localization of solvent and ions, ligand binding, and molecular recognition.

Three-Dimensional RISM Integral Equation Theory for Polarizable Solute Models.

Modeling solute polarizability is a key ingredient for improving the description of solvation phenomena. In recent years, polarizable molecular mechanics force fields have emerged that circumvent the limitations of classical fixed charge force fields by the ability to adapt their electrostatic potential distribution to a polarizing environment. Solvation phenomena are characterized by the solute's excess chemical potential, which can be computed by expensive fully atomistic free energy simulations. The alternative is to employ an implicit solvent model, which poses a challenge to the formulation of the solute-solvent interaction term within a polarizable framework. Here, we adapt the three-dimensional reference interaction site model (3D RISM) integral equation theory as a solvent model, which analytically yields the chemical potential, to the polarizable AMOEBA force field using an embedding cluster (EC-RISM) strategy. The methodology is analogous to our earlier approach to the coupling of a quantum-chemical solute description with a classical 3D RISM solvent. We describe the conceptual physical and algorithmic basis as well as the performance for several benchmark cases as a proof of principle. The results consistently show reasonable agreement between AMOEBA and quantum-chemical free energies in solution in general and allow for separate assessment of energetic and solvation-related contributions. We find that, depending on the parametrization, AMOEBA reproduces the chemical potential in better agreement with reference quantum-chemical calculations than the intramolecular energies, which suggests possible routes toward systematic improvement of polarizable force fields.

Extended molecular Ornstein-Zernike integral equation for fully anisotropic solute molecules: Formulation in a rectangular coordinate system

An extended molecular Ornstein-Zernike (XMOZ) integral equation is formulated to calculate the spatial distribution of solvent around a solute of arbitrary shape and solid surfaces. The conventional MOZ theory employs spherical harmonic expansion technique to treat the molecular orientation of components of solution. Although the MOZ formalism is fully exact analytically, the truncation of the spherical harmonic expansion requires at a finite order for numerical calculation and causes the significant error for complex molecules. The XMOZ integral equation is the natural extension of the conventional MOZ theory to a rectangular coordinate system, which is free from the truncation of spherical harmonic expansion with respect to solute orientation. In order to show its applicability, we applied the XMOZ theory to several systems using the hypernetted-chain (HNC) and Kovalenko-Hirata approximations. The quality of results obtained within our theory is discussed by comparison with values from the conventional MOZ theory, molecular dynamics simulation, and three-dimensional reference interaction site model theory. The spatial distributions of water around the complex of non-charged sphere and dumbbell were calculated. Using this system, the approximation level of the XMOZ and other methods are discussed. To assess our theory, we also computed the excess chemical potentials for three realistic molecules (water, methane, and alanine dipeptide). We obtained the qualitatively reasonable results by using the XMOZ/HNC theory. The XMOZ theory covers a wide variety of applications in solution chemistry as a useful tool to calculate solvation thermodynamics.

Three-Dimensional Reference Interaction Site Model Self-Consistent Field Study of the Electronic Structure of [Cr(H2O)6]3+ in Aqueous Solution

The three-dimensional reference interaction-site model self-consistent-field (3D-RISM-SCF) method was applied to the electronic structure of hexahydrated chromium trication [Cr(H2O)6](3+) in aqueous solution. The 3D distribution around [Cr(H2O)6](3+) showed 12 maximum density points arising from hydrogen bonds, as well as eight local maximum points at the hollow sites, in the second hydration shell. The 3D distribution function also indicated 20 local maximum sites in the third hydration shell. The low-lying excited states of vertical transitions were computed using time-dependent density functional theory (TD-DFT), including the electric field from the solvent. The electronic configurations and excitation energies calculated using DFT and 3D-RISM-SCF were very similar, although the orbital energies involved in the transition were rather different. The two lowest excited states (1(4)T and 2(4)T) were roughly assigned to the d-d transitions, and the third and fourth excited states (3(4)T and 4(4)T) were assigned to ligand-to-metal charge-transfer transitions. The computed excited energies were in good agreement with the experimental values.

Role of Interfacial Structure of Water in Polymer Surface Wetting

We present a theoretical approach to investigate the structures and contact angles of water in contact with different polymer surfaces. In the theoretical approach, the three-dimensional reference interaction site model integral equation and the three-dimensional density functional method are combined through the bridge function. First, the three-dimensional distribution functions of water over the crystalline polyethylene surface and the amorphous polyethylene, polypropylene and polystyrene surfaces are calculated. According to the isosurface representations of the distributions, the wetting processes of these four polymer surfaces are simply analyzed. Then, the three-dimensional distributions of free energy are calculated by the density functional equation to obtain the interfacial tensions. Finally, the contact angles are estimated. It is shown that the predicted contact angles are in good agreement with the literature data, indicating that above structure and energy descriptions are quantitatively reasonable.

Generalised canonical–isokinetic ensemble: speeding up multiscale molecular dynamics and coupling with 3D molecular theory of solvation

We have proposed a new canonical–isokinetic ensemble for efficient sampling of conformational space in molecular dynamics (MD) simulations which leads to the optimised isokinetic Nosé–Hoover (OIN) chain algorithm for atomic and molecular systems. We applied OIN to multiple time step (MTS) MD simulations of the rigid and flexible models of water to demonstrate its advantage over the standard canonical, isokinetic and canonical–isokinetic ensembles. With the stabilising effect of OIN thermostatting in MTS-MD, gigantic outer time steps up to picoseconds can be employed to accurately calculate equilibrium and conformational properties. Furthermore, we developed the atomic version of OIN for MTS-MD of a biomolecule in a solvent potential of mean force obtained at sequential MD steps by using the molecular theory of solvation, aka three-dimensional reference interaction site model with the Kovalenko–Hirata closure (3D-RISM-KH). The solvation forces are obtained analytically by converging the 3D-RISM-KH integral equations once per several OIN outer time steps, and are calculated in between by using solvation force-coordinate extrapolation (SFCE) in the subspace of previous successive solutions to 3D-RISM-KH. For illustration, we applied the multiscale OIN/SFCE/3D-RISM-KH algorithm to a fully flexible model of alanine dipeptide in aqueous solution. Although the computational rate of solvent sampling in OIN/SFCE/3D-RISM-KH is already 20 times faster than standard MD with explicit solvent, further substantial acceleration of sampling stems from making solute evolution steps in a statistically averaged potential of mean force obtained from 3D-RISM-KH. The latter efficiently samples the phase space for essential events with rare statistics such as exchange and localisation of solvent and ligand molecules in confined spaces, pockets and at binding sites of the solute macromolecule, as distinct from MD with explicit solvent which requires enormous computational time and number of steps in such cases.

Structure-Solubility Correlation Model for Carbon Dioxide in Ionic Liquids

In this work, the density distributions of carbon dioxide around different ionic liquids are calculated using the three-dimensional reference interaction site model integral equation. According to the density distributions, the corresponding excess adsorptions are calculated to estimate the solubilities of carbon dioxide in these ionic liquids. Some predicted results are in good agreement with available experimental data, showing that the structure descriptions are accurate and the direct correlation of solubility with structure is reasonable at low temperature and pressure. As a result, the present theoretical model provides a simple and efficient tool to evaluate dissolving capacity of ionic liquids and their mixtures.

Development of the isotropic site-site potential for exchange repulsion energy and combination with the isotropic site-site potential for electrostatic part

We extended the previously reported isotropic site-site potential for the exchange part [D. Yokogawa, Chem. Phys. Lett. 515, 179 (2011)] and combined it with isotropic site-site potential for the electrostatic part. To treat complex systems, such as excited-state molecules and metal complexes, multi-configuration self-consistent field method was employed. The method was applied to the calculation of intermolecular interactions between H(2)O and aromatic compounds, namely, p-nitoroaniline, imidazolium cation, and cyclopentadienyl anion. The potential thus obtained was combined with the extended reference interaction site model and the three-dimensional reference interaction site model for the calculation of the solvation structure. The present method gave reasonable intermolecular interactions and solvation structures at ground and excited states.

Evaluation Procedure of Electrostatic Potential in 3D-RISM-SCF Method and Its Application to Hydrolyses of Cis- and Transplatin Complexes

In the three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) method, a switching function was introduced to evaluate the electrostatic potential (ESP) around the solute to smoothly connect the ESP directly calculated with the solute electronic wave function and that approximately calculated with solute point charges. Hydrolyses of cis- and transplatins, cis- and trans-PtCl(2)(NH(3))(2), were investigated with this method. Solute geometries were optimized at the DFT level with the M06-2X functional, and free energy changes were calculated at the CCSD(T) level. In the first hydrolysis, the calculated activation free energy is 20.8 kcal/mol for cisplatin and 20.3 kcal/mol for transplatin, which agrees with the experimental and recently reported theoretical results. A Cl anion, which is formed by the first hydrolysis, somehow favorably exists in the first solvation shell as a counteranion. The second hydrolysis occurs with a similar activation free energy (20.9 kcal/mol) for cisplatin but a somewhat larger energy (23.2 kcal/mol) for transplatin to afford cis- and trans-diaqua complexes. The Cl counteranion in the first solvation shell little influences the activation free energy but somewhat decreases the endothermicity in both cis- and transplatins. The present 3D-RISM-SCF method clearly displays the microscopic solvation structure and its changes in the hydrolysis, which are discussed in detail.