Virial coefficients of hard, homonuclear dumbbells in two- to four-dimensional Euclidean spaces.

Abstract

We calculated virial coefficients up to the eighth order for hard dumbbells in two-, three-, and four-dimensional Euclidean spaces employing Mayer-sampling Monte Carlo simulations. We improved and extended available data in two dimensions, provide virial coefficients in R^{4} in dependence on their aspect ratio, and recalculated virial coefficients for three-dimensional dumbbells. Highly accurate, semianalytical values for the second virial coefficient of homonuclear, four-dimensional dumbbells are provided. We compare the influence of the aspect ratio and the dimensionality to the virial series for this concave geometry. Lower-order reduced virial coefficients B[over ̃]_{i}=B_{i}/B_{2}^{i-1} depend in first approximation linearly from the inverse excess part of their mutual excluded volume.