Pascal H. Fries

The solution of the hypernetted‐chain approximation for fluids of nonspherical particles. A general method with application to dipolar hard spheres

In this paper we describe a general method for the numerical solution of the full hypernetted‐chain (HNC) theory for fluids characterized by angle‐dependent pair potentials. This method is also applicable to the closely related reference hypernetted‐chain (RHNC) approximation. The only formal restriction is that the pair potential and correlation functions must be expandable in a basis set of rotational invariants. We present explicit numerical solutions of the RHNC theory for dense dipolar hard sphere fluids and detailed comparisons are made with previous theories and computer simulation results. It is found that the full RHNC theory generally improves upon the previous reference linearized and quadratic HNC approximations. The values given by the RHNC theory for the static dielectric constants are smaller than those given by these earlier approximations and are in much better agreement with computer simulations.

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 solve...

A Monte Carlo study of semi-dilute hard sphere mixtures

We present Monte Carlo results for the high density equation of state and the partial pair distribution functions of semi-dilute solutions of large hard spheres in a solvent of smaller spheres. The simulation data for diameter ratios of 2 : 1 and 3 : 1 agree reasonably well with the predictions of Percus-Yevick theory and its semi-empirical modifications, except for the solute-solute pair distribution function. A free volume analysis of the equation of state data points to the existence of a well defined, concentration dependent, amorphous close packed density which is significantly higher than for a pure hard sphere fluid.

Dielectric constants of liquid formamide, N-methylformamide and dimethylformamide via molecular Ornstein-Zernike theory

Abstract Kirkwood factors, yielding dielectric constants, are calculated from pair correlation functions, which are numerical solutions of the hypernetted-chain approximation of molecular Ornstein-Zernike (MOZ) theory. The combined influence of the molecular polarizability and the hydrogen bond strength is investigated. Using a reasonable diameter for the hydrogen size in the amide group, the MOZ Kirkwood factors and dielectric constants are in good agreement with the experimental values. This is explained by the statistical correlations between the orientations of two near molecules. This is consistent with hydrogen bonds, forming networks in formamide and chains in N-methylformamide.

The solution of the reference hypernetted-chain approximation for Stockmayer fluids

In this paper the reference hypernetted-chain (RHNC) theory is solved for fluids of Stockmayer (dipolar Lennard-Jones) particles and detailed comparisons are made with computer simulation results. It is shown that the RHNC approximation significantly improves upon integral equation theories previously solved for Stockmayer systems. In particular the static dielectric constants obtained are in much better agreement with the computer simulations.

The relative motion of ions in solution. I. Microdynamical models and intermolecular dipolar spin relaxation

This paper is the first in a series involving the theoretical and experimental study of the relative motion of ions in solution. In this paper we describe the general theoretical approach and make explicit calculations for model aqueous electrolytes. In all models the ions are considered to be charged hard spheres and in order to compare with real solutions effective hard sphere diameters must be estimated from crystal radii or space‐filling molecular models. Our object is to provide theoretical results for these model solutions which can be tested with nuclear magnetic resonance (NMR) experiments. Therefore, we have calculated the dimensionless spectral density j2(ωτ) by solving the Smoluchowski equation including a force term dependent upon the ion–ion potential of mean force. Experimentally, j2(ωτ) can be determined from NMR measurements of the interparticle dipole–dipole relaxation rate of the nuclear spins I located on a diamagnetic ion and interacting with the electronic spins S of a paramagnetic ...

The solution of the reference hypernetted-chain approximation for fluids of hard spheres with dipoles and quadrupoles

The reference hypernetted-chain (RHNC) theory is solved for fluids of hard spheres with dipoles and axially symmetric quadrupoles. The results are evaluated by comparing with earlier Monte Carlo calculations, and it is shown that the RHNC approximation significantly improves upon previous theories for this model.

The solution of the Percus–Yevick approximation for fluids with angle‐dependent pair interactions. A general method with results for dipolar hard spheres

A general method is presented which allows the Percus–Yevick (PY) and reference Percus–Yevick (RPY) integral equation theories to be solved for fluids of particles interacting with anisotropic pair potentials. The numerical solution is based upon a fast quasianalytic method of expanding the closure relationships in a basis set of rotational invariants. The RPY equations are solved explicitly for dense dipolar hard sphere fluids and the results obtained are compared with Monte Carlo data and with other integral equation approximations.

The relative motion of ions in solution. II. An NMR relaxation study of attractive ions in water at low ionic strength

In this paper we describe a nuclear magnetic resonance study of the relative motion of the attractive ion pairs (CH3)4N+/⋅ON(SO3)−22 and (CH3)4N+/ in dilute D2O solutions of varying ionic strength. Our major purpose is to test previous theoretical calculations for different model electrolytes. We have measured the interparticle dipole–dipole spin‐lattice relaxation rate at 400 MHz of the (CH3)4N+ protons due to their interaction with the electronic spins of the paramagnetic nitroxide ions. At 400 MHz this relaxation rate is proportional to the reduced spectral density j2(ωpτ) which depends upon the relative ion distribution and motion, and can be directly compared with theoretical results. The present experiments verify the large charge and ionic strength effects predicted by the theory and allow us to distinguish between molecular and continuum solvent models. For the molecular solvent picture good agreement is obtained between the experimental and theoretical results. This is true for both ion pairs an...

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 exper...