Molecular Ornstein Zernike Research Articles

A hybrid framework of first principles molecular orbital calculations and a three-dimensional integral equation theory for molecular liquids: multi-center molecular Ornstein-Zernike self-consistent field approach.

In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein-Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple SN2 reaction (Cl(-) + CH3Cl → ClCH3 + Cl(-)) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.

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.

Application of efficient algorithm for solving six-dimensional molecular Ornstein-Zernike equation

In this article, we propose an efficient algorithm for solving six-dimensional molecular Ornstein-Zernike (MOZ) equation. In this algorithm, the modified direct inversion in iterative subspace, which is known as the fast convergent method for solving the integral equation theory of liquids, is adopted. This method is found to be effective for the convergence of the MOZ equation with a simple initial guess. For the accurate averaging of the correlation functions over the molecular orientations, we use the Lebedev-Laikov quadrature. The appropriate number of grid points for the quadrature is decided by the analysis of the dielectric constant. We also analyze the excess chemical potential of aqueous ions and compare the results of the MOZ with those of the reference interaction site model.

The development of a revised version of multi-center molecular Ornstein–Zernike equation

Ornstein–Zernike (OZ)-type theory is a powerful tool to obtain 3-dimensional solvent distribution around solute molecule. Recently, we proposed multi-center molecular OZ method, which is suitable for parallel computing of 3D solvation structure. The distribution function in this method consists of two components, namely reference and residue parts. Several types of the function were examined as the reference part to investigate the numerical robustness of the method. As the benchmark, the method is applied to water, benzene in aqueous solution and single-walled carbon nanotube in chloroform solution. The results indicate that fully-parallelization is achieved by utilizing the newly proposed reference functions.

Fluid of hard spheres with dipolar-like patch interaction and effect of adding an isotropic adhesion

We compare two fluid models of spherical molecules with anisotropic, purely surface interactions. Both models admit an analytical solution of the molecular Ornstein–Zernike integral equation, within the Percus–Yevick approximation plus orientational linearization. In the first model, the molecular surface corresponds to a unique non-uniform patch, with a potential obtained by truncating a long-ranged dipolar interaction exactly at the contact distance between two hard sphere particles. In the second model, a further isotropic adhesion is added to the intermolecular potential. The study is focused on the local orientational ordering. Differences and similarities with respect to hard spheres with full long-ranged dipolar forces are analysed in detail. The effect of the competition between anisotropic patch interaction and isotropic adhesion is investigated through the pair correlation function as well as via two novel anisotropic order parameters.

Classical density functional theory of solvation in molecular solvents: Angular grid implementation

The solvation properties of a solute in a molecular solvent can be obtained by minimization of a position and orientation-dependent free-energy density functional, with the unknown excess term approximated by the angular-dependent direct correlation function of the pure solvent. We show how this function can be extracted from MD simulations of the pure solvent by computing the pair distribution function and solving subsequently the Molecular Ornstein–Zernike equation using angular grids. The corresponding functional can be minimized in the presence of an arbitrary solute on a three-dimensional cubic grid for positions and Gauss–Legendre angular grid for orientations to provide the solvation structure and free-energy. Applications are presented for solvation in acetonitrile.

Fast hybrid methods for the simulation of dielectric constants of liquids

The distance-dependent Kirkwood factors and dielectric constants of the SPC/E and TIP3P models of water, the H1 model of methanol, and the OPLS model of acetonitrile are investigated with the help of long molecular dynamics (MD) simulation runs and the hypernetted chain (HNC) approximation of the molecular Ornstein–Zernike (MOZ) theory. The MOZ theory predicts dielectric constants which show the same dependence on the liquid model as their simulated counterparts, are very accurate in the case of acetonitrile, but are too low by about 20% for the H-bonding liquids, because the HNC closure moderately accounts for the short-range orientational order of their molecules. In the case of too short simulation runs, some pitfalls concerning the accuracy of the dielectric properties and their errors are emphasized. For a given liquid model, if the distance-dependent Kirkwood factor of the MOZ theory has a long-range profile similar to the converged one of an accurate simulation, rapid and reliable hybrid methods based on the combination of the MOZ and simulation results can be proposed to estimate the dielectric constant. Test calculations on the above-mentioned models are carried out to assess the validity of the approach. Hybrid methods are shown to give dielectric constants of similar accuracy as those derived from long simulation runs of one million of steps or more, but with a CPU time demand at least 10 times shorter.

The solvation of ions in acetonitrile and acetone. II. Monte Carlo simulations using polarizable solvent models

Structural properties and energies of solvation are simulated for alkali and halide ions. The solvation structure is discussed in terms of various site–site distribution functions, of solvation numbers, and of orientational correlation functions of the solvent molecules around the ions. The solvent polarizability has notable effects which cannot be intuitively predicted. In particular, it is necessary to reproduce the experimental solvation numbers of small ions. The changes of solvation properties are investigated along the alkali and halide series. By comparing the solvation of ions in acetone to that in acetonitrile, it is shown that the spatial correlations among the solvent molecules around an ion result in a strong screening of the ion–solvent direct intermolecular potential and are essential to understand the changes in the solvation structures and energies between different solvents. The solvation properties derived from the simulations are compared to earlier predictions of the hypernetted chain (HNC) approximation of the molecular Ornstein–Zernike (MOZ) theory [J. Richardi, P. H. Fries, and H. Krienke, J. Chem. Phys. 108, 4079 (1998)]. The MOZ(HNC) formalism gives an overall qualitatively correct picture of the solvation and its various unexpected findings are corroborated. For the larger ions, its predictions become quantitative. The MOZ approach allows to calculate solvent–solvent and ion–solvent potentials of mean force, which shed light on the 3D labile molecular and ionic architectures in the solution. These potentials of mean force convey a unique information which is necessary to fully interpret the angle-averaged structural functions computed from the simulations. Finally, simulations of solutions at finite concentrations show that the solvent–solvent and ion–solvent spatial correlations at infinite dilution are marginally altered by the introduction of fair amounts of ions.

Theories of structural and dynamic properties of ions in discrete solvents. Application to magnetic resonance imaging

Abstract The molecular Ornstein­Zernike (MOZ) formalism used to compute the structure of a liquid solution is briefly presented. Its ability to describe the equilibrium properties of aprotic solvents and of their electrolyte solutions is demonstrated from selected examples. The potential of mean force and the relative motion of ions in water are studied by the powerful method of intermolecular nuclear magnetic relaxation dispersion (NMRD) in paramagnetic solutions. The interest of the ion­ion dynamics in medical magnetic resonance imaging (MRI) is shown by a typical NMRD study involving paramagnetic gadolinium Gd3+ complexes.

The solution of the Wertheim association theory for molecular liquids: Application to hydrogen fluoride

A general numerical method for solving the Wertheim association theory in the case of fully anisotropic polyatomic rigid molecules is proposed. In order to handle the nonspherical shapes of the molecules, the Wertheim association theory is combined with the rotational invariant approach of the molecular Ornstein–Zernike (MOZ) method. Therefore, this approach is called the WMOZ method. It is carried out in the association hypernetted chain (AHNC) approximation which is the only approximation and which consists of the neglect of the bridge functions. The method of solution is implemented by translating the set operations appearing in the Wertheim association theory into an algebraic formalism developed through a one-to-one correspondence between subsets and binary numbers. The Wertheim association theory is explicitly solved for hydrogen fluoride using two interaction site models. For these models, site–site distribution functions, internal excess energies, and dielectric constants obtained by the MOZ and WMOZ methods are compared to the exact molecular dynamics results. The WMOZ method strongly improves the structural description of the H bonding in comparison with the MOZ approximation. The quality of the dielectric and thermodynamic results obtained by the WMOZ approach is discussed in comparison with the simulation values. To our knowledge, this is the first solution of the Wertheim association theory for a liquid of particles of nonspherical shapes.

A generalized self-consistent mean-field theory for fluids of molecules with distributed polarizabilities: Comparisons with computer simulations

Abstract The generalized self-consistent mean field (GSCMF) approximation recently proposed provides a systematic approach for finding an effective pair potential for a fluid of molecules with atom, bond or other distributed polarizabilities. The GSCMF theory is combined with the molecular Ornstein-Zernike (MOZ) theory using the hypernetted chain (HNC) approximation to compute the liquid properties of polarizable interaction models of water, acetonitrile, and methanol. The average moments, the excess energies, the dielectric constants, and the site-site distribution functions are studied for models with a distributed polarizability or with an overall polarizability at the molecular centre. The MOZ(HNC)/GSCMF results are compared to the data of simulations using exact procedures to handle the molecular polarizabilities. Comparison of the results obtained by the MOZ/GSCMF theory and by simulations shows that the MOZ/GSCMF approach correctly predicts the relative changes of the liquid properties caused by a distribution of the polarizability. For the acetonitrile models, the MOZ/GSCMF and simulation results are in good agreement. In contrast for water and methanol, the MOZ/GSCMF theory gives strongly underestimated total excess energies and average dipoles and the liquid structure is less pronounced. However, this mainly occurs because the HNC approximation only provides a semi-quantitative description of H bonding liquids as recently observed for non polarizable models of water and methanol. The results suggest that the GSCMF approach is capable of providing accurate effective pair potentials for fluids of molecules with distributed polarizabilities.

Molecular Ornstein–Zernike approach to the solvent effects on solute electronic structures in solution

A new approach to ab initio electronic structure calculations of solute molecules in solution is presented. Combined with the molecular Ornstein–Zernike (MOZ) integral equation theory for polyatomic liquids, solute electronic wave function and solvent distribution around a solute are determined in a self-consistent manner. The hypernetted chain approximation is employed for solving the MOZ equation. In order to describe the short-range solute–solvent interactions, the effective potential operating solute electron is placed on a solute molecule, which is determined by a least-squares fitting to ab initio exchange repulsion/charge transfer energies. The present method, referred to as the MOZ self-consistent-field (SCF) method, is applied to a solute H2O molecule in water solvent. The solvent shift for the vertical excitation to the nπ* state of H2CO in aqueous solution is also examined. The results obtained by the MOZ-SCF calculations are compared with those by the reference interaction site model-SCF theory and the polarizable continuum model.

Can the molecular Ornstein-Zernike theory be used to study water under supercritical conditions?

The molecular Ornstein-Zernike (MOZ) theory and Monte Carlo simulations are used to calculate the fluid properties of water for the well-known SPC/E model and a recently published polarizable model at four thermodynamic states. At ambient conditions the MOZ theory significantly underestimates the internal energies, the dielectric constants and the heights of the distribution function peaks. The agreement between simulation and theory considerably improves at supercritical states. The MOZ approach correctly describes the partially connected H bond network at high temperatures, whereas it fails to reproduce the tetrahedral network at ambient conditions. The self-consistent mean-field (SCMF) treatment is successfully applied to take the effects of the molecular polarizability into account. We conclude that the MOZ/SCMF method is a fast and well suited tool to study water under supercritical conditions.

On the connection between the reference interaction site model integral equation theory and the partial wave expansion of the molecular Ornstein–Zernike equation

We develop an integral equation theory based on the partial wave expansion of the molecular Ornstein–Zernike (OZ) equation. The theory provides a rigorous and transparent framework for multiple site treatments of molecular fluids. We examine free-energy functional and closure expressions with pilot calculations of homonuclear diatomic Lennard-Jones liquids.

Influence of the intermolecular electrostatic potential on properties of polar polarizable aprotic solvents

The liquid properties of models of acetonitrile, acetone and chloroform are calculated within the framework of the hypernetted chain approximation of the molecular Ornstein—Zernike theory. The shape of a molecule is described by a set of Lennard-Jones sites. Its electrostatic properties are modelled either by the first multipole moments up to the octopole or by partial charges, and by a point polarizability tensor. The multipole moments and the partial charges are computed by ab initio molecular orbital methods. In the liquid phase, the polarizability is taken into account by calculating an effective induced point dipole moment using a self-consistent mean-field approximation. While the Lennard-Jones part of the internal excess energy is nearly independent of the description of the electrostatic interaction and of the polarizability, the electrostatic part and the dielectric constant change notably. The models with the partial charges lead to dielectric constants which are in good agreement with the experimental data, provided that the molecular polarizability is correctly taken into account. The internal excess energies are also correctly predicted except for acetone. How the approximation of the intermolecular electrostatic interaction modifies the liquid structure is studied by investigating the dominant bimolecular configurations. These configurations allow one to understand better why the Kirkwood factor changes with the electrostatic description. The Ornstein—Zernike formalism is a practical tool for studying with light numerical effort how the liquid properties depend on the intermolecular interaction. It can help in the development of new accurate potentials for liquid simulation.

Comparison of different water models from ambient to supercritical conditions: A Monte Carlo simulation and molecular Ornstein–Zernike study

Structural, thermodynamic, and dielectric properties of three polarizable and two nonpolarizable water models are compared with experimental data at four different thermodynamic states from ambient to supercritical conditions. Pair-correlation functions and thermodynamic data are obtained from Monte Carlo simulations, performed both on the (N,V,T) and (N,p,T) ensembles. The dielectric constants are determined with the molecular Ornstein–Zernike theory. It is found that the polarizable models can reproduce the experimental structure considerably better than the nonpolarizable ones at the high-temperature states. In particular, the elongation of the hydrogen bonds with increasing temperature, which is observed by neutron diffraction measurements, in only seen in the simulations with the polarizable potential models. On the other hand, the polarizable models fail to describe the correct temperature dependence of the thermodynamic properties. Although at ambient conditions they overestimate both the density and the dielectric constant of the system, around the critical temperature they result in 10%–50% lower densities than the experimental values. The obtained magnitude of the internal energies as well as the dielectric constants are also considerably smaller than their experimental values at these thermodynamic state points. The results of this study point out the need of new polarizable water models which, besides the reasonable reproduction of the experimental pair-correlation functions, are also able to describe the dependence of the thermodynamic properties on the temperature and pressure.

A molecular Ornstein–Zernike study of popular models for water and methanol

Some effective models of water (TIP3P, SPC, SPC/E, TIP4P) and methanol (OPLS, H1) are studied with the help of the molecular Ornstein–Zernike (MOZ) theory using the hypernetted chain (HNC) approximation. The quality of the results obtained within the HNC approximation is discussed by comparison with values from molecular dynamics (MD) simulations. The MOZ-HNC theory yields internal excess energies and dielectric constants which are about 20% smaller than the simulation results found in the literature. The relative trends of the properties observed by simulation for the different interaction models are correctly predicted. In order to calculate the rotational invariant coefficients which define the liquid structure, new MD simulations were carried out. The rotational invariant coefficients derived from the simulation and from the MOZ theory strongly differ. In particular, the center–center distribution functions show that the theory is not able to reproduce the tetrahedral structure of water. In this solvent a comparison of the O–H distribution function indicates that the MOZ theory underestimates the H bonding. The use of a spherically symmetric bridge function in the reference HNC approximation does not lead to an improvement of the MOZ results. The observed defects of the MOZ-HNC approach contrast with the good agreement found for aprotic solvents and are presumably due to the association by H bonds in water and methanol.

Liquid acetone and chloroform: a comparison between Monte Carlo simulation, molecular Ornstein-Zernike theory, and site-site Ornstein-Zernike theory

Site-site distribution functions, internal energies, compressibilities, and dielectric constants of liquid acetone and chloroform are computed and compared. The hypernetted chain approximation is used for the molecular Ornstein-Zernike (MOZ) and site-site Ornstein-Zernike (SSOZ) theories. Both solvent molecules are described as sets of interaction sites, which are the centres of Lennard-Jones potentials and which carry partial electric charges. How the approximations inherent in both OZ theories affect the calculated liquid properties is discussed. In contrast to SSOZ theory, MOZ theory yields a correct description of the liquid structure as defined by the site-site distribution functions of simulations. The MOZ results for the dielectric constants are in good agreement with simulation, but both OZ theories slightly underestimate the internal excess energies. In contrast to the SSOZ formalism and to the simulations, the molecular pair distribution of MOZ theory can be computed readily for all two-molecule configurations, allowing a detailed study of the complex relief of this distribution. A search was performed for configurations that are highly probable in the liquid. They can be assigned to a small number of peaks of the molecular distribution function. These peaks have major contributions to the Kirkwood factors, which measure the orientational order in the liquid, and to the electrostatic part of the excess energies. The partitioning of the whole two-molecule configuration space makes it possible to study the details of the site-site distribution functions. For instance, a sharp peak in the oxygen-oxygen distribution in acetone results from many superimposed contributions of acetone-acetone arrangements of low and medium statistical weights, and not from the highly probable arrangements.

The solvation of ions in acetonitrile and acetone: A molecular Ornstein–Zernike study

The solvation of alkali and halide ions in acetonitrile and acetone has been investigated via the molecular Ornstein–Zernike theory using the hypernetted chain approximation. Theoretical Gibbs solvation energies and solvation numbers are compared with experiments and numerical simulations. The calculated single-ion solvation energies are used to check the hypotheses serving to split-up the measured solvation energies of salts into their single-ion components. The solvation structure around the ions is discussed in detail and shown to be strongly influenced by the solvent–solvent spatial correlations. The calculated interionic potentials of mean force are presented and used to compute ion-ion association constants which are compared with experiment. The influence of the Lennard-Jones parameters of the ions upon the calculated properties is emphasized.

An accurate theoretical description of fluids composed of fully anisotropic molecules: Application to C2v symmetry

We use two molecular integral equation approximations to compute the thermodynamic properties and microscopic structure of two liquids composed of planar molecules with C2v symmetry, namely SO2 and H2S. These approximations couple the exact molecular Ornstein–Zernike equation with the hypernetted chain (HNC) and reference-hypernetted chain (RHNC) closures. The theoretical results obtained for various thermodynamic states agree remarkably well with molecular dynamics calculations. In particular, the atom-atom distribution functions are very well reproduced. We find that the RHNC approximation with a hard-sphere fluid reference system offers notable improvement over HNC in the pressure calculation. We include also a self-consistent mean field calculation to incorporate the effect of polarizability on the dielectric constant of liquid SO2. Final results for this quantity are in excellent agreement with experimental values. In contrast, the model used for the electrostatic interactions in H2S leads to anomalously high permanent dipole moments, compared to experiment, and consequently to dielectric constants that are completely off the experimental data.