Extraction of the bridge function for simple liquids from a molecular dynamics simulation and its application for correcting the pair distribution function.

Abstract

Isokinetic molecular dynamics (MD) simulations have been performed for 4000 and 32 000 particles interacting via a model potential that is appropriate to liquid aluminum and the Lennard-Jones potential. Using the hypernetted-chain approximation to extrapolate the pair distribution function (PDF) obtained by the MD simulations, the bridge function is extracted for different cutoff radii of the pair potential and system sizes. We find that the extracted bridge function is almost independent of the cutoff radius used in the MD simulation. Furthermore, the bridge function is efficiently obtained by taking the extrapolating distance to be short, about 3 to 4 interatomic spacings, even in the case of the small-size simulation, with a discarding of the PDF data outside of that distance. By solving the integral equation coupled with the correctly extracted bridge function, the PDF for the pair potential without any truncation is calculated for liquid aluminum, whose effective ion-ion potential is accompanied by a long-ranged Friedel oscillation. It is found that this integral equation successfully corrects the error, if any exists, in the MD PDF caused by the truncation of the pair potential, resulting in a good agreement with that from a large-size simulation for a sufficiently large cutoff radius. Thus, we have shown a method for obtaining the PDF for the full potential from the small-size simulation with a short cutoff potential, on the basis of the fact that the bridge function is insensitive to the truncation of the potential. At the same time, this method gives an alternative procedure to extend the MD PDF to the whole range of distances.