Cross correlation between rotation and translation in spherical tops

Abstract

The nature of statistical cross correlation between center-of-mass molecular translation and rotation of the same molecule is investigated for carbon tetrachloride liquid by molecular dynamics computer simulation. It is shown that rotation and translation in this $T_d$-symmetry spherical top are indeed correlated through the existence of the molecular Coriolis, centripetal, and nonuniform accelerations of the rigid molecule, thus invalidating the Debye theory of rotational diffusion under the conditions for which it was originally proposed. The simple cross-correlation function 〉ω(t${)\mathrm{v}}^T$ (0)〈/[〈${\omega }^2$(0)${〉}^{1/2}$ 〈$v^2$(0)${〉}^{1/2}$] vanishes, however, for all t and in all frames of reference for the spherical top diffusing in three dimensions in a bath of other spherical tops.