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We present the site-site direct correlation function c(r) for a fluid of hard diatomic symmetric molecules obtained from Monte Carlo simulation data via the RISM integral equation. This c(r) ensures that the site-site correlation function given by the RISM equation is exact, and thus provides a basis for critically examining the usual closure for the RISM equation. As an example of an improved closure we present the analytic solution of the RISM integral equation with a Yukawa closure for c(r).

The solution of the Ornstein-Zernike equation for a direct correlation function c(x) with damped oscillations and a hard core condition imposed upon the total correlation function h(x) has been proposed by Cummings as a means of treating a simple model potential for liquid metals in the mean spherical approximation [1]. Here some numerical results are given for this model and their significance is discussed. The solution of the Ornstein-Zernike equation is also extended; the hard core condition is generalized to a soft core condition, and Yukawa terms are added to the oscillatory c(x). Ways in which these extensions can be incorporated into more accurate liquid metal models, as well as into more accurate approximations for these models, are discussed. Finally, it is shown that our solution of the Ornstein-Zernike equation, after a change in the core condition, yields the structure of a spin glass model considered by Høye and Stell in the MSA-like approximation they propose [22].

Neutron diffraction measurements have been made on methyl alcohol at room temperature for an incident wavelength of 0·94 Å. Cross sections have been obtained for CD3OD, CD3OH, and mixtures of these compounds. These data are subtracted to obtain the separated structure factors for intermolecular H0H0, the hydroxyl components, and the non-hydroxyl components. The Fourier transformations of the structure factors show components of both intra- and intermolecular distribution functions. Width parameters obtained from model fits are too large for thermal vibrations and are interpreted as geometrical broadening due to the stretching of bonds, variations in bond angles, and rotation of the methyl group. Differences in the real space distribution function between hydrogen and deuterium are noted.

We consider a closure to the site-site Ornstein-Zernike (SSOZ) equation that is solvable analytically in closed form and represents a considerable improvement over both the zero pole approximation and reference interaction site approximation for the hard dumbell fluid. The central idea is to add a Yukawa term to the functional form for the site-site direct correlation function outside the core region, the parameters of which are adjusted by thermodynamic and/or structural criteria. Numerical results using the simplest possible assignment scheme are reported.

We introduce models for the association of spherically symmetric atoms into diatomic molecules. In the Percus-Yevick approximation, we solve analytically for the equilibrium properties of a one-parameter family of such models corresponding to A + B ⇌ AB association. We focus in detail on the behaviour of the association constant, comparing alternative definitions of that quantity. We find that our results are insensitive to the details of the repulsive core of the AB potential as long as it is several times larger than kBT (kB = Boltzmann's constant, T = temperature). As a result, we conclude that a limiting-case model in which the repulsive core of the AB potential is a hard core is of particular interest and utility. The mathematics of the Percus-Yevick approximation simplifies considerably in this limiting-case analysis.

Three approximations for the orientational correlation function of molecular fluids - the single super chain/linearized hypernetted chain (SSC/LHNC), single super chain f-expansion (SSCF) and Percus-Yevick (PY) approximation - are evaluated in the dense liquid state for a fluid inter-acting with short ranged anisotropic interactions. These interactions are prototypical of the forces that determine the non-spherical shape of symmetric linear molecules. We find that SSC/LHNC is very poor, failing to predict many of the structural features present in the Monte Carlo (MC) simulation results. The PY and SSCF approximations produce much better results; however, neither approximation is completely satisfactory.

We present Monte Carlo simulation results for the dielectric constant of the polar hard dumb-bell fluid. The Ewald sum technique is used to take account of the long range nature of the electrostatic interactions. The results for the dielectric constant are found to be sensitive to the choice of the dielectric constant of the continuum which surrounds the simulation sample. We include comparisons with experimental results on chloromethane and the predictions of an analytically solvable approximation for the polar hard dumb-bell fluid.

A detailed study is made of the atom-atom (i.e. site-site) correlation functions - especially the direct correlation function - for the interaction site model (ISM) of Andersen and Chandler. The work is based on the observation of Høye and Stell that the site-site Ornstein-Zernike-like equation of Chandler and Andersen can be regarded as a rewritten version of the usual Ornstein-Zernike equation for particle-particle correlations, where the particles are identified with the atoms that constitute the ISM molecules. Our new results include (i) new compressibility theorems in terms of the site-site direct correlation functions, and (ii) for ISM diatomics (both polar and non-polar) full asymptotic (i.e. large-r) characterization of the site-site direct correlation function based on the assumption that the corresponding particle-particle direct correlation function behaves asymptotically like the particle-particle potential times -1/kBT (kB = Boltzmann's constant and T = absolute temperature). Further asymptotic results are also given for a wider class of ISMs, in particular for triatomics. All our asymptotic results (except those for two classes of homonuclear symmetric n-atomics) are in fundamental disagreement with assumptions of the reference interaction site approximation (RISA) and the more general interaction site approximation (ISA), both originally proposed by Chandler and Andersen, as well as with all subsequently proposed approximations of which we are aware. (iii) A characterization is given of a family of ISMs containing point charges that is solvable in a class of linear approximations, including the ISA, as well as an approximation that is asymptotically faithful to the results noted in the preceding item. The family of ISMs considered includes models that have heretofore lacked analytic solution. (iv) The relation between the exact analytic solution of the Chandler-Andersen RISA and its approximate solution according to the widely-used Lowden-Chandler ansatz is examined on the basis of the particle-particle picture. It is pointed out how the relatively good liquid density agreement and the relatively poor low density agreement between the two solutions can be easily understood within this framework.

A closed form analytic theory for the structure of the hard dumbell fluid is introduced and evaluated. It is found to be comparable in accuracy to the reference interaction site approximation (RISA) of Chandler and Andersen.

A statistical mechanical model of chemically reactive fluids in an inert solvent exhibiting liquid-gas criticality is studied using analytically solvable integral equation approximations. The model consists of a mixture of three molecular species (A, B and C), two of which (the solutes A and B) can undergo reaction and one of which (the solvent C) is inert. Particular interest centres on the results for the chemical equilibrium obtained near the mixture critical point of the solution.

The self-diffusion of simple liquids is studied in the presence of strong shear-free flow fields. At the state point of the system the shape of the velocity autocorrelation function is markedly different in the extension or contraction directions of elongation flow. Despite this pronounced directional dependence of the autocorrelation functions, the diagonal elements of the diffusion tensor are more uniform than in the case of planar Couette flow.

We describe a non-equilibrium molecular dynamics algorithm for thermal conductivity/diffusion in binary simple fluid mixtures. The external field drives both a heat current and a diffusive current permitting calculation of the linear response coefficients LQQ and L1Q which are required for the calculation of the thermal conductivity and the thermal diffusion (Soret effect). The algorithm is momentum-preserving and has the interesting property it does not satisfy the adiabatic incompressibility of phase space. However, it does generate the correct response.

The statistical mechanical study of chemically reactive fluids via the analytic solution of integral equation approximations for such fluids (Cummings, P. T., and Stell, G., 1984, Molec. Phys., 51, 253; 1985, Ibid., 55, 33) is extended to a consideration of solvent effects. This is achieved by studying mixtures of molecular species some of which can undergo reaction (the solute(s)) and one of which is inert (the solvent). The results obtained near infinite dilution of the reacting solute in the inert solvent are similar in magnitude to those observed in experiments on the dissociation equilibrium of dinitrogen tetroxide.

The recently published (Gude, M. T., and Teja, A. S., 1994, Molec. Phys., 81, 599) expression for (∂P/∂x2)∞ρ, T is demonstrated to be valid only at the solvent critical point, and the more general microscopic connection is shown between the isothermal-isochoric finite pressure change (∂P/∂x2)∞ρ, T and the rearrangement of the solvent structure around an infinitely dilute solute. Finally, there is discussion of some properties of this derivative and some theoretical implications in the interpretation of solvation at near critical conditions.

We use the Percus-Yevick approximation to study indirect correlation functions in the sticky hard-sphere model introduced by Baxter. The model has a critical point below which there is a liquid gas transition. We illustrate the changes in the structure of the correlation function as the density increases on the critical isotherm and on supercritical and subcritical isotherms. We also examine the local effects on this structure of introducing a large isolated sticky particle. For the gas part of the subcritical isotherm, such a particle can act as a condensation nucleus. We examine the dependence of the structure changes on the radius of the large particle.

A proof of the theoretical equivalence between the E. Helfand, 1960, Phys. Rev., 119, 1 and the D. McQuarrie, 1976, Statistical Mechanics (Harper & Row), Chap. 21 equations for the calculation of thermal conductivity via the Einsteintype relations is presented here. Some theoretical implications of that equivalence are also discussed, such as the unification of the thermal conductivity expressions into one similar to that given for linear transport coefficients by F. C. Andrews, 1967, J. Chem. Phys., 47, 3161.

We calculate the thermal conductivity of supercritical and liquid carbon dioxide using a recently developed nonequilibrium molecular dynamics (NEMD) algorithm for molecular fluids. We evaluate the translational, rotational, potential energy and force contributions to the heat flux separately. We find that at high density both the rotational contribution for a nonspherical molecule and the contribution from the total force acting on the molecule are important for predicting the thermal conductivity accurately. The NEMD results for the thermal conductivity agree well with experimental data. At a near critical state point, we observed a phase separation induced by the fictitious external field. The contribution to the thermal conductivity from the Lennard-Jones potential energy becomes important at this state point.

We report Gibbs ensemble simulations of the coexistence region of the hard core two-Yukawa fluid with Yukawa parameters chosen to mimic the Lennard-Jones fluid. The phase envelope of the Lennard-Jones fluid is found to be well approximated by that of the Yukawa fluid. The results suggest that theoretical approaches to the hard core two-Yukawa fluid (such as integral equations and perturbation theory) could provide an analytic basis for predicting the physical properties of the Lennard-Jones fluid.

The formalism and model introduced in a previous paper [1984, Molec. Phys., 51, 253] and used there to study the inhomogeneous association reaction A + B⇌AB is used here to consider the homogeneous association reaction 2A⇌A2. Two approximations are introduced to obtain an analytic theory. The first is the Percus-Yevick approximation. The second is the neglect of rigid polygonal n-mers, n ≥ 3. (These are sterically possible in our model, but can be expected in most cases to form only rarely because of their restricted geometry.) Representative quantitative results for association probabilities, association constants and radial distribution functions as functions of thermodynamic state are given and discussed. Our model has a dimension-less association parameter τ that is a combined measure of association strength and temperature; for a given atomic number density ρA there is a value of τ at which diatomic association is complete. Under the assumptions of our theory one then has a fluid of homonuclear diatomics, the hard dumbell fluid. It is found that in this case our theory reduces to the zero pole approximation of Morriss and Cummings for this fluid.

In the first paper in this series, a new integral equation approximation-the Percus-Yevick excess (PYX) approximation-was introduced and contrasted with the corrected Percus-Yevick (CPY) approximation. In the present paper, these two approximations are evaluated for a molecular fluid, the molecules of which interact via a short ranged anisotropic potential prototypical of the overlap interactions encountered between homonuclear diatomic molecules. We conclude that the CPY and PYX approximations are quite accurate; interestingly, however, they unexpectedly yield very similar results leading us to conclude that, on balance, both approximations are equally good.

Neutron diffraction measurements at 0·7 Å are reported for coexisting liquid deuterium bromide at -40°C. The results show that the deuterium bromide molecule in the liquid is little distorted as compared with the free molecule. The presence of a peak in the intermolecular pair distribution function at 3·1 Å is thought to be evidence of the formation of weak, rather long, intermolecular hydrogen bonds. As expected, both these effects are much weaker than for deuterium chloride reported in an earlier paper [2] and liquid deuterium bromide is therefore a simpler polar liquid.