Symmetry of cross-correlation tensors in molecular dynamics: Rotation and translation in condensed matter

Abstract

The three-dimensional diffusion of an asymmetric-top molecule is described in terms of the linked translational and rotational Langevin equations both written in the moving frame of reference. The terms appearing in these equations suggest the existence of cross-correlation tensors in the moving frame (1,2,3) and in the laboratory frame (x,y,z). Their existence has been confirmed by molecular-dynamics computer simulation both in the absence and presence of a strong external electric field of force. The symmetry group to which the cross-correlation tensors belong depends on the variables being correlated, and changes when the field is applied. The latter is capable of generating cross-correlations which otherwise have no existence, and may therefore be used experimentally to isolate the cross-correlation functions from the ever-present autocorrelation functions which form the ‘‘background’’ to the ensemble molecular dynamics. It is shown that some off-diagonal elements exist in frame (x,y,z) in the absence of the field, thus invalidating the basic hypothesis of the theory of rotational diffusion.