Extended Reference Interaction Site Model Research Articles

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.

Solvation Effect on the Conformations of Alanine Dipeptide: Integral Equation Approach

We present an implicit solvent model based on the extended reference interaction site model (XRISM) integral equation theory, which is a molecular theory of solvation. The solvation free energy is composed of additive potentials of mean force (PMF) of various functional groups. The XRISM theory is applied to determine the PMF of each group in water and NaBr electrolyte solutions. The method has been coupled to Brownian dynamics (BD) and is illustrated here on alanine dipeptide. The results of the method are compared with those obtained by explicit water simulations and other popular implicit solvent models for detailed discussion. The comparison of our model with other methods indicates that the intramolecular correlation and the solvation structure influence the stability of the PII and αR conformers. The results of NaBr electrolyte solutions show that the concentration of electrolyte also has a substantial effect on the favored conformations.

Solvation Dynamics in Polar Solvents Studied by Means of RISM/Mode-Coupling Theory

The extended reference interaction site model (RISM) theory coupled with the generalized Langevin/mode-coupling theory (MCT) is applied to the investigation of solvation dynamics in polar solvents. The RISM/ MCT framework used in this paper significantly upgrades the previous report by Nishiyama and co-workers [Nishiyama, K.; et al. J. Chem. Phys. 2003, 118, 2279.] for the calculation of the solvation response function, Ss(t). This function is experimentally observable from dynamic Stokes shift measurements, for example. Ss(t) obtained by RISM/MCT relaxes with an initial Gaussian decay followed by damped oscillation, which is in accordance with experimental results or molecular dynamics simulations published elsewhere. Ss(t) is then decoupled into the acoustic and optical modes of solvent, which indicate the translational and rotational motions of solvent, respectively. The majority (> 90%) of Ss(t) is explained by the optical mode, whereas the slower acoustic mode also plays an important role. Resultingly, RISM/MCT is shown to be an appropriate theoretical methodology to capture a molecular view of solvation dynamics, without assuming any empirical parameters.

Reference interaction site model study on the anomeric equilibrium of D-glucose in aqueous solution

The anomeric equilibrium of D-glucose in aqueous solution was studied by the extended reference interaction site model (XRISM) theory. In this study, all of the rotational degrees of freedom were considered upon the exocyclic hydroxyl and hydroxymethyl groups, namely 729 stereoisomers for each anomer. The free energy

Solvent effect on the nuclear magnetic shielding: ab initio study by the combined reference interaction site model and electronic structure theories

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.

Ab Initio Study on Molecular and Thermodynamic Properties of Water: A Theoretical Prediction of pKw over a Wide Range of Temperature and Density

The ionic product of water (pKw) has been calculated in a wide range of temperature (0−600 °C) and density (0.6−1.4 g/cm3) by means of ab initio electronic structure theory combined with the extended reference interaction site model in statistical mechanics for molecular liquids (RISM-SCF/MCSCF). We consider the autoionization process (H2O + H2O ⇌ H3O+ + OH-) by regarding H2O, H3O+, and OH- as “solute” molecules in an aqueous solution and evaluate molecular geometries, electronic structure, solvation structure, and free energy components of these species as functions of thermodynamical conditions. The results for pKw obtained from the theory have shown a monotonical decrease with increasing density at all the temperatures investigated, in good accord with the experimental observation. The behavior is determined essentially by the difference in solvation free energies, Δμ(H3O+) + Δμ(OH-) − 2Δμ(H2O), associated with the reaction. The Δμ(OH-) shows the density dependence, which is entirely different from tha...

Comparison of the potentials of mean force for alanine tetrapeptide between integral equation theory and simulation

The dielectrically consistent reference interaction site model (DRISM) integral equation theory is applied to determine the potential of mean force (PMF) for an alanine tetramer. A stochastic dynamics simulation of the alanine tetramer using this PMF is then compared with an explicit water molecular dynamics simulation. In addition, comparison is also done with simulations using other solvent models like the extended reference interaction site model (XRISM) theory, constant dielectric and linear distance-dependent dielectric models. The results show that the DRISM method offers a fairly accurate and computationally inexpensive alternative to explicit water simulations for studies on small peptides.

XSOL, a Combined Integral Equation (XRISM) and Quantum Mechanical Solvation Model: Free Energies of Hydration and Applications to Solvent Effects on Organic Equilibria

A combined XRISM integral equation and quantum mechanical solvation model (XSOL) is presented and tested for the computation of free energies of hydration of organic compounds. The method features the extended reference interaction site model (XRISM) for the description of solute−solvent interactions and a quantum mechanical representation of the solute molecule. A coupled self-consistent-field procedure is used to achieve the convergence of the solvent structural reorganization and the electronic polarization of the solute molecule in solution. The present XSOL model is tested through computation of free energies of hydration of a series of organic compounds and the medium dependence of a number of organic equilibria in solution. The method complements continuum self-consistent reaction field (SCRF) methods and explicit Monte Carlo and molecular dynamics simulations, and it is much more efficient than QM/MM simulation approaches for estimating solvent effects on organic processes in aqueous solution.

A dielectric theory of spin-lattice relaxation for nuclei with electric quadrupole moments

The spin-lattice relaxation time for nuclei possessing electric quadrupole moments is determined mainly by the electric quadrupolar interactions between the nucleus and its environment. Here we give a microscopic formulation of the nuclear quadrupolar relaxation problem for a nucleus of a monatomic solute dissolved in molecular fluids. Our formulation is based on classical statistical mechanics and the interaction site model representation of the intermolecular potential. We assume that the fluctuating field gradient felt by the nucleus is caused mainly by the charge distribution of the surrounding solvent molecules, modulated by the Sternheimer (anti)shielding factor of the nucleus. In the extreme narrowing condition, the problem reduces to the determination of a time integral of the field gradient time correlation function G(t) on the nucleus position. By separation of G(t) into a static contribution G(t=0) and a normalized time correlation function, we seek microscopic expressions for both G(t=0) and its correlation time τQ. Within certain approximations we express τQ in terms of the wavevector-dependent polarization charge correlation time τμ(k), and G(t=0) in terms of the pure solvent charge structure factor Sμ(k) and an analytical function of the solute cavity radius a. Taking as input τμ(k) from molecular dynamics simulations of the pure solvent and Sμ(k) from the extended reference interaction-site model (XRISM) calculation, we apply the theory to the spin lattice relaxation rate of seven quadrupolar nuclei in acetonitrile solution. The solutes considered cover a wide range of size, charge, and nuclear spin quantum number. With reasonable choices of the solute cavity radii, the theory successfully reproduces the experimentally measured 1/T1 for these solutes. Using molecular dynamics simulation, we also investigate the effects on 1/T1 of neglecting the solute mobility. Our simulated data suggest that the solute mobility can reasonably be neglected for spin relaxation of heavy quadrupolar nuclei such as Kr and Xe. Finally, the dielectric continuum limit of our theory is discussed and compared with the related theory developed by Hynes and Wolynes.

Structural investigations of fluid carbon tetrafluoride by statistical mechanical calculations and Monte Carlo simulation

AbstractStatistical mechanical calculations with the extended reference interaction site model (XRISM) and Monte Carlo simulations are performed on fluid CF4. The parameters of a five‐center (12‐6) Lennard Jones potential with added point charges are deduced. The results are compared with total atom pair correlation functions recently determined by neutron diffraction experiments at three supercritical densities. Apart from the good agreement between experimental and theoretical results, we found that depending on the method used, different potentials are able to describe the investigated system. The atom pair correlation functions and angular distribution functions indicate a completely disordered arrangement of the molecules in fluid CF4 with no significant short‐range orientational order except for very close distances. The comparison of the results with former Reverse Monte Carlo (RMC) simulations allows the conclusion that the RMC method is an effective tool, equivalent to the well established Monte Carlo and XRISM methods, in determining the microscopic structure of fluid CF4, but without the exact knowledge of intermolecular potentials.

Three pulse stimulated photon echo experiments as a probe of polar solvation dynamics: Utility of harmonic bath models

The three pulse photon echo peak shift technique was used to study solvation dynamics in acetonitrile (297 K), methanol (297 and 323 K), and ethylene glycol (297 and 397 K) utilizing the tricarbocyanine laser dye, IR144, as a probe. The spectral density, ρ(ω), governing the solute-solvent interaction was obtained for each solvent and temperature through numerical fitting of the three pulse photon echo peak shift relaxation using finite temporal-duration optical fields. An ultrafast three pulse photon echo peak shift relaxation, ascribed to the inertial component, was nearly identical for ethylene glycol at 297 and 397 K; this indicates the spectral density is essentially temperature independent from 10 to 250 cm−1 over this temperature range. Conversely, the low-frequency spectral density (0–10 cm−1) obtained from three pulse photon echo peak shift relaxation of ethylene glycol at 297 and 397 K showed a strong temperature dependence which cannot be predicted using harmonic bath models. We calculated spectral densities for ethylene glycol, acetonitrile, and methanol using the simple dielectric continuum model and the dynamical mean spherical approximation, using where possible, the relative permittivity constants calculated from experimental far-infrared absorption data and dielectric dispersion data. Additionally, we calculated spectral densities in terms of the extended reference interaction site model for methanol and acetonitrile. These calculated spectral densities describe our experimental methanol and acetonitrile photon echo better than all other solvation model spectral densities. Our results give insight into the domain of applicability of the harmonic model of liquid dynamics.

Solvent-induced interactions between hydrophobic and hydrophilic polyatomic sheets in water and hypothetical nonpolar water

Hydrophobic and hydrophilic interactions are two major intermolecular forces between hydrophobic nonpolar and hydrophilic polar sites of macromolecules or materials surfaces in solvents. To further understand these two interactions at the microscopic level, an idealized polyatomic model is devised, which includes hydrophobic, hydrophilic, and partially hydrophilic polyatomic planar square molecular sheets. The hydrophobic molecular sheet is composed of the Lennard-Jones particles while the hydrophilic molecular sheet consists of positive and negative charge sites. In the framework of the extended reference interaction site model integral equation theory the solvent-induced interactions (or the potential of mean forces) between two parallel molecular sheets in water and in the hypothetical nonpolar water are investigated in a systematic fashion. Such a highly idealized model allows us to isolate and to explore the important effects of molecular size, relative intermolecular position (e.g., in- or out-of-registry configuration), and hydrophilic site distribution on the hydrophobic and hydrophilic interactions in both water and the hypothetical nonpolar water. Significant insight into these effects at the molecular level is obtained. For the hydrophobic planar molecules in water we find solvent separated hydrophobic interaction becomes less favored as sheet size increases. Moreover, the contact hydrophobic interaction between two molecular sheets in the out-of-registry configuration is always most favorable. For the latter case we find it is the van der Waals attraction, rather than the hydrophobic attraction, that dominates the total interaction. We also find that in both water and the hypothetical nonpolar water the solvent-induced interaction between two hydrophobic sheets behaves similarly. One possible explanation is that the hydrophobic hydration originating from the hydrogen bonding network in water plays an insignificant role in the solvent-induced interaction, at least in the infinitely dilute aqueous solution. For hydrophilic planar molecular sheets in water, we find water-induced hydrophilic interaction is much more substantial compared with the hydrophobic one. In many cases, the hydrophilic interaction is found directly against the intermolecular force between two parallel molecular sheets in vacuum. Finally, for the partially hydrophilic planar molecules in water, a newly discovered feature is that a disperse hydrophilic site distribution gives rise to stronger solvent-induced interaction compared with the clustered hydrophilic site distribution.

Neutron scattering of molecular liquids over a broad range of densities

High-pressure neutron diffraction measurements on fluid hydrogen chloride, carbon dioxide, ammonia, sulphur hexafluoride and methane at different supercritical states are reported. Some aspects of the experiment and the data evaluation are mentioned.The measurements were performed to assess the usefulness of some pair potentials reported in the literature for statistical mechanical calculations, based on the extended reference interaction site model (RISM) in combination with the HNC closure. The density-dependent measurements proved to be useful for tests of the individual potentials.

Analytical energy gradient for the reference interaction site model multiconfigurational self-consistent-field method: Application to 1,2-difluoroethylene in aqueous solution

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.

High-pressure neutron diffraction on fluid methane.

High pressure neutron diffraction measurements of the structure factor of fluid methane (C${\mathrm{D}}_{4}$) at $T=370$ K and three supercritical densities are presented, and the intra- and intermolecular structures are determined. The variation of the density has only a weak effect on the intermolecular distribution functions. Statistical mechanical calculations according to the extended reference interaction site model formalism were performed, and an intermolecular potential of a (12-6) Lennard-Jones type with partial charges on the atoms was deduced that reproduces the experimental total atom correlation functions at all investigated thermodynamic states. Additionally, the corresponding structure factor of statistically orientated methane molecules was calculated. As the agreement between experiment and theory is very good, it is concluded that no orientational correlation exists in fluid methane. Reverse Monte Carlo calculations (RMC) were performed with the recently developed optimization algorithm great deluge [G. Dueck, J. Comput. Phys. 104, 86 (1993)]. This is a non-Boltzmann sampling method specially used for minimizing the difference between the experimental and the simulated intermolecular distribution function. The results, obtained by RMC, confirm the statistical mechanical calculations and show that the distribution of the molecules in fluid methane is randomly distributed and no orientational correlation between the molecule axes exists.

A hybrid approach for the solvent effect on the electronic structure of a solute based on the RISM and Hartree-Fock equations

A new approach is proposed to evaluate the solvent effect upon the electronic structure of a solute molecule in the liquid phase. The Hartree-Fock and the extended reference interaction site model integral equations are solved in a self-consistent manner to simultaneously optimize the electronic structure of the solute, and the solvent distribution around it. The method is applied to a formaldehyde molecule in water. The result shows a clear indication of enhanced polarization of the solute molecule due to the solvent. The blue-shift induced by the solvent, which is observed in the absorption spectrum corresponding to the vertical 1A 1→ 1A 2 transition, is reproduced.

Acetonitrile pair formation in aqueous solution

Extended reference interaction site model (RISM) theoretical calculations and molecular dynamics simulation have been carried out for dilute aqueous solution of acetonitrile. Potential of mean force between two solute molecules was calculated. Two solute molecules tend to associate with each other by an attractive interaction between two negatively charged nitrogen atoms. It is found that ‘‘bifurcated hydrogen bonds’’ between a hydrogen atom on a water molecule and nitrogen atoms on acetonitrile molecules play an important role in the solute–solute interaction.

Solvation thermodynamics of polar molecules in aqueous solution by the XRISM method

The aqueous solvation free energies and the average solute-solvent interaction energies of a diverse set of organic molecules were calculated by the XRISM (extended reference interaction-site model) method for two related potential-energy functions based upon the optimized potentials for liquid simulation (OPLS) parameter set. The results are compared with available data obtained from experimental and other theoretical methods. The XRISM method with the given potential-energy function parameter sets produces reasonable free-energy values for a number of molecules but not for all of the molecules studied. For some molecules, the results were also quite sensitive to the potential-energy function parameters used

A site–site theory for finite concentration saline solutions

A liquid state theory based on site–site integral equations is constructed to have the asymptotics given by angular expansion theory. This results in a theory which shows dielectric consistency, e.g., the dielectric constant as viewed from the solvent is the same as that viewed by the ions. Such consistency is lacking in other extended reference interaction site model (XRISM)-based theories and leads to unrealistic structural predictions. The Kirkwood–Buff route to thermodynamics is used and allows a physical partitioning of the terms responsible for the solvation process. Sample results for a 1–1 salt are given.

Statistical mechanics of small chain molecular liquids. II. Structure and thermodynamic properties of modeled n-butane liquid

The theory of molecular liquids based on the extended reference interaction site model (RISM) equation is used to describe the intermolecular structure of a small hydrocarbon chain liquid like n-butane. The model treats the methyl and methylene groups as single interaction centers with pair interactions modeled by a Lennard-Jones (12:6) function and located at the position of the carbon nuclei in the molecule. The theory assumes that the equilibrium internal states distribution of nonpolar flexible molecules are determined primarily by the short range, hard repulsive portions of the intermolecular potential (see preceding paper). The molecular structure factor has been calculated from the theory, and the results are in good agreement with recent x-ray scattering experiments. From this structural information a perturbative scheme to obtain the thermodynamic properties is employed. The theoretical predictions compare favorably with recent simulation results, giving quantitative agreement with the equation state and the intermolecular energy. The effective energy difference between trans and gauche states is obtained from Van’t Hoff plots, giving a value of 0.486 kcal/mol. Also, the effective difference of molar volumes between conformers is calculated from ln K vs P plot, obtaining a value of −3.1 cm3/mol, the same order of magnitude than the experimental value observed on liquid 1,2-dichloroethane.