Frequency moments of the spectral density of an atomic-displacement time-correlation function of a three-dimensional Lennard-Jones crystal in the classical and quantum regimes

An expression for the memory function appearing in the Mori's memory function formalism has been derived using two plausible approximations. The resulting expression is of the [Formula: see text] form. The parameters a, b and ν are such that sum rules up to the sixth order of an appropriate time correlation function are exactly satisfied. The sech (bt) and the [Formula: see text] forms of the memory function have been used and derived earlier. But these satisfy sum rules only up to the fourth order and are special cases corresponding to ν = 1 and ν = 2. It is found that ν varies from 1.1 to 1.7 for Lennard–Jones fluids, investigated over wide ranges of densities and temperatures for the velocity auto-correlation function. We have also derived expressions for the shear viscosity and the thermal conductivity by using this approach. The results obtained for the shear viscosity and the thermal conductivity for Lennard–Jones fluids at various densities and temperatures have been found to be in good agreement with molecular dynamics (MD) results.

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Rate Constants, Reactive Flux

10.1093/oso/9780198805014.003.0005 ◽

2018 ◽

Author(s):

Niels Engholm Henriksen ◽

Flemming Yssing Hansen

Keyword(s):

Correlation Function ◽

Rate Constant ◽

Cross Sections ◽

Time Correlation ◽

Time Correlation Function ◽

Exact Expression ◽

Reaction Cross ◽

Dividing Surface ◽

Definition Of ◽

Reactive Flux

This chapter discusses a direct approach to the calculation of the rate constant k(T) that bypasses the detailed state-to-state reaction cross-sections. The method is based on the calculation of the reactive flux across a dividing surface on the potential energy surface. Versions based on classical as well as quantum mechanics are described. The classical version and its relation to Wigner’s variational theorem and recrossings of the dividing surface is discussed. Neglecting recrossings, an approximate result based on the calculation of the classical one-way flux from reactants to products is considered. Recrossings can subsequently be included via a transmission coefficient. An alternative exact expression is formulated based on a canonical average of the flux time-correlation function. It concludes with the quantum mechanical definition of the flux operator and the derivation of a relation between the rate constant and a flux correlation function.

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Two-body dynamics in fluids as probed by interaction-induced light scattering

Canadian Journal of Physics ◽

10.1139/p81-199 ◽

1981 ◽

Vol 59 (10) ◽

pp. 1504-1509 ◽

Cited By ~ 5

Author(s):

U. Balucani ◽

R. Vallauri

Keyword(s):

Correlation Function ◽

Light Scattering ◽

Time Correlation ◽

Time Correlation Function ◽

Simulation Experiments ◽

Particle Pairs ◽

Body Dynamics ◽

Atomic Fluids ◽

Relative Dynamics

The relative dynamics of particle pairs in fluids is investigated both theoretically and by simulation experiments. The physical implications of this analysis are important in all interaction-induced phenomena and illustrated in the case of the pair time correlation function relevant to collision-induced light scattering in atomic fluids.

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