B.C. Freasier

An efficient microcanonical sampling method

Abstract A new microcanonical sampling procedure is presented which incorporates much of the simplicity and efficiency of the canonical procedures. Comparison with previous procedures indicates that the gain in efficiency is substantial. The relevance to numerical simulation of rate processes and equilibrium systems is noted.

Ergodic collision theory of intermolecular energy transfer

Abstract We present a simple theory of collisional energy transfer between molecules based on the assumption of ergodic collisions, i.e., the final state distri

Hard dumbells: Monte Carlo pressures and virial coefficients

The equation of state was determined by Monte Carlo simulation for 108 dumb-bells subject to periodic boundary conditions. The isotropic fluid-solid phase transition was observed. An orientational phase transition was not observed. Virial coefficients through B5 were calculated.

A generalized van der Waals model for solvation forces between solute particles in a colloidal suspension

A model for solvation forces between two solute particles in a colloidal suspension is solved within the framework of the generalized van der Waals model (GvdW) of fluids. The results for this approximation are compared to machine simulations for a subcritical solvent. Density profiles, adsorption excess, and force of interaction are studied. Particular attention is paid to the phenomenon of liquid film formation between the particles as a function of interparticle distance. Theory and simulation are found to be in good overall agreement.

A test of RRKM theory against numerical simulation for classical chain molecules. I. Method and preliminary results

Abstract A systematic investigation of the internal part of the unimolecular reaction dynamics of one-dimensional chain molecules has been undertaken to examine the validity of RRKM theory. The basic aims, means and scope of this program of research are reported here together with results for uniform chains. Classical mechanics is used and the atoms in the chain interact by Morse pair potentials acting between neighbouring particles. The simulation method described here consists of a very efficient Monte Carlo sampling of microcanonical initial states coupled with a predictor-corrector molecular dynamics algorithm. Time-dependent and best fitting time-independent decay rate coefficients can be extracted from the set of lifetimes to dissociation observed in the simulation. These are then compared to the corresponding rate coefficients predicted by the usual form of RRKM theory where anharmonic contributions ot the density of states are neglected or to a more rigorous implementation where the anharmonic contributions are accounted for. Calculations for uniform chains reported here establish a pattern of deviations from RRKM prediction which will be explored and explained in greater detail in this program of research.

Generalized van der Waals theory of hard sphere oscillatory structure

The recently developed generalized van der Waals (GvdW) theory, a free energy density functional theory based on cell theory and van der Waals approximations, is here applied to the prediction of hard sphere oscillatory structures at a hard wall, between two hard walls, and around a hard sphere. Three different functional forms of the crucial free volume factor are compared. The results confirm that the fine‐grained GvdW theory containing a nonlocal entropy functional yields structures reproducing packing oscillations not only qualitatively but to quantitative accuracy. The error depends on the choice of free volume factor and can be made small except at high density where the range and magnitude of oscillations are overestimated. Evidence of early onset of a hard sphere freezing transition is seen.

Simulation of microscopic chemical processes.: I. De-energization of bromine in argon

Abstract This is the first in a series of articles devoted to the study of fundamental chemical processes by numerical simulation. The main aim of this work is to facilitate the development of accurate chemical reaction rate theories. We report here the results of an investigation of the collisional de-energization of highly vibrationally excited bromine by a heatbath of argon atoms at 295 K. A molecular dynamics calculation has been carried out for a cell containing one bromine molecule and 106 argon atoms at pressures of about 20 and 100 atmospheres. On the average the bromine molecule loses about 0.4 kcal/mole per collision but the relaxation is dominated by collisions removing about 3 kcal/mole. Detailed statistics on the energy transfer including collision lifetimes and their correlation with the strength of the collision is provided. Comparing the relaxation rate for the two pressures we find a 20% deviation from the binary collision scaling law.

Isotropic hard core dumbell fluid: Equation of state

Abstract A monte-Carlo calculation has been made for 108 hard core dumbbells of the compressibility factor in the isotropic density range. These compressibility factors are compared to several approximate theories, and comments are made on the utility of these approximate theories.

Ergodic collision theory of intermolecular energy transfer II. Quantum effects in the harmonic approximation

Abstract An efficient numerical implementation of the ergodic collision theory is described and used to evaluate the average energy transfer per collision relevant to several reactant species undergoing unimolecular reaction. The full effect due to vibrational quantization in the harmonic approximation is included and found to cause only a minor shift in the results previously obtained in a quasi-classical approximation. A much simplified computational method based on the use of specific heat data for the molecules concerned is suggested and shown to account for most of this shift.

Simulation of microscopic chemical processes.: II. De-energization of bromine in argon at high pressures

Abstract The collisional de-energization of very highly vibrationally excited bromine in an argon medium has been studied by molecular dynamics calculation at 295 K and pressures up to 1200 atm. This note is concerned, in particular, with the validity of the scaling laws for the relaxation rate obtained on the basis of the independent binary collision theory. The relaxation rate is found to increase faster than predicted by independent binary collision theory so that the deviation at 1200 atm amounts to a factor of two.