Donald D. Fitts

Monte Carlo and hypernetted chain equation of state for the square‐well fluid

Results of Monte Carlo and hypernetted chain theory calculations are reported for both the radial distribution function and the equation of state of the square‐well fluid for the particular case where the potential is cut off at 1.5σ, where σ is the hard sphere diameter. At high densities, substantial errors are found in the hypernetted chain equation results at all temperatures. However, these errors are very nearly independent of temperature. The hypernetted chain theory accounts for the perturbing effects of the attractive forces with good accuracy despite appreciable errors in the treatment of the repulsive forces.

Percus–Yevick equation of state for the two‐dimensional Lennard‐Jones fluid

Values of the radial distribution functions and thermodynamic properties for the two‐dimensional Lennard‐Jones fluid are obtained from the Percus–Yevick theory. Results are reported for a wide range of temperatures and densities and are compared with computer simulations. The energy equation of state is found to give the best agreement with the computer simulations. The reduced critical temperature as predicted by the Percus–Yevick theory from the compressibility equation is about 0.495.

Integral-equation perturbation theory for the radial distribution function of simple fluids

The radial distribution function (RDF) for a fluid whose molecules interact according to the Lennard-Jones potential is calculated by means of statistical-mechanical perturbation theory using the Percus-Yevick (PY) and hyper-netted-chain (HNC) theories to approximate the perturbation corrections. In both cases the infinite perturbation series can be summed in closed form. The contribution of the attractive part of the pair potential to the RDF is treated as a perturbation to a reference system whose molecules interact according to the repulsive part of the potential. The RDF of the reference system is expanded about RDF for a fluid of hard spheres of diameter d. Five criteria for the determination of d are presented and tested. Excellent agreement between the calculated RDF and computer simulations are obtained over a wide range of densities from the HNC perturbation treatment for the attractive intermolecular forces and the PY perturbation expansion for the repulsive forces with the hard-sphere diameter ...

Perturbation theory and the radial distribution function of fluids with nonspherical potentials

Abstract A perturbation expansion for the radial distribution function of fluids with nonspherical pair potentials is discussed. Numerical calculations are presented for dipolar hard-sphere and quadrupolar hard-sphere fluids. Agreement with the computer simulation results is excellent, even at high dipole and quadrupole moments.

Statistical Mechanics of Transport Processes. XIV. Linear Relations in Multicomponent Systems

A classical treatment of the time dependence of a phase‐space distribution function for a system near equilibrium is presented. The nonequilibrium distribution function is expressed as a stationary zero‐order function plus a perturbation term and is used to obtain the diffusion and heat fluxes by averaging the appropriate dynamical variables. When only terms linear in the gradients of the local temperature, the chemical potentials, and the velocity of the local centers of mass are retained, the usual linear relations result and explicit expressions for the phenomenological coefficients are obtained. These expressions agree with the results of Mori and of Green and are shown to obey the Onsager reciprocal relations.

Perturbation theory for the radial distribution functions of dipolar and quadrupolar hard-sphere fluids

The radial distribution functions for the dipolar and the quadrupolar hard-sphere fluids are calculated by means of statistical-mechanical perturbation theory to third order using the hypernetted-chain (HNC) theory to approximate the perturbation terms. For both fluids the perturbation expansions through third order disagree with computer simulations, indicating that the expansion converges slowly. On the other hand, a Pade approximant, constructed from the second and third-order HNC terms, for each radial distribution function agrees excellently with the computer simulations.

Reference system selection and average Mayer-function perturbation theory for molecular fluids

A perturbation theory for molecular fluids due to Smith, and Perram and White is analysed and equations are presented in a computationally convenient form for determining the full angular-dependent pair correlation function. The discussion centres on the most appropriate choice of reference system and we use the Mayer function as expansion functional. The implications of the resulting RAM (reference system average Mayer-function expansion) theory are discussed.

Semiempirical SCF‐LCAO—MO Treatment of Furan

The self‐consistent field—molecular orbital method including configuration interaction is utilized for the study of the π‐electronic structure of the five‐membered heterocyclic molecule furan. The calculation proceeds through the density matrix formalism of McWeeny. A judicious choice of the two empirical core parameters for oxygen, along with the semiempirical approximations of Pariser and Parr, leads to a satisfactory description of the ionization potential, electronic spectra, and chemical reactivity of furan.

Perturbation theory for the radial distribution function for simple polar fluids

Abstract The radial distribution function for a fluid whose molecules interact according to the Stockmayer potential was calculated by means of thermodynamic perturbation theory using two different approximations for the perturbation term and was compared with computer simulation results. The approximation based on the Percus-Yevick equation was found to be in much better agreement with the simulations than was the “simplified superposition approximation” to the perturbation term.

Physical adsorption of a heteronuclear diatomic molecule onto a solid surface: a theoretical approach

A theoretical study is made of the physical adsorption of the heteronuclear diatomic molecule H35Cl on a solid crystalline argon surface. The potential energy of interaction between the adsorbate molecule and adsorbent is computed by a lattice summation over the requisite number of individual HCl...Ar “pair” interactions, described using an equation developed by Neilson and Gordon. Adsorption is considered at four sites on the (111) face of the argon cubic close-packed lattice: the tetrahedral (T) hole, the octahedral (O) hole, above a surface atom (A); and the saddle point (SP). Values of the potential energy are evaluated as a function of location and orientation of the adsorbate relative to the adsorbent surface. The results indicate that adsorption is preferred at the T and O sites and that the adsorbate can be considered localized at temperatures < 30 K. The preferred molecular orientation for adsorption at a T or O site is perpendicular to the surface with the H end pointing downward while at an A site the molecule prefers an orientation parallel to the surface. The Schrodinger equation is solved for the rotational-librational energy levels of an adsorbed H35Cl molecule above the tetrahedral hole of the argon surface. At temperatures below 10–15 K the adsorbate molecules can be considered confined to their ground rotational-librational energy states.