Clustering of continuous distributions of charge

Abstract

An investigation is carried out of the association and clustering of equimolar mixtures of oppositely charged Gaussian charge distributions (CDs) of the form ∼ exp ( − r2 /2α2), where r is the separation between the centres of charge and α governs the extent of charge spreading (α→0 is the point charge limit). The results of molecular dynamics (MD) and Ornstein–Zernike integral equation with the mean spherical approximation (MSA) and hypernetted-chain (HNC) closures are compared for these systems. The MD and HNC radial distribution functions, g(r), agree very well for not too small α. The MD and MSA, g(r), also agree well for α ≈ 1 and greater. The potential energy per particle for the three methods also agrees well over a wider range of α values, better than might be expected from inspection of the radial distribution functions, because the dominant contributions to U come predominantly from intermediate and long distance ranges where there is good agreement between the g(r) from the MSD and HNC closures. The nature of the association and clustering of the charges as a function of α is explored through the mean nearest neighbour distance for unlike and like species and the mean and root-mean-square force. The velocity and force autocorrelation functions are also calculated; they show increasingly oscillatory behaviour in the small α limit, originating in vibrations of a pair of CDs of opposite sign.