Relation of dipole and angular velocity autocorrelation functions

Abstract

A truncated Mori expansion for the angular velocity autocorrelation function is used as a starting-point to calculate the orientational auto-correlation function for a disk and a sphere using the newly developed methods of Lewis et al. [9]. Assuming the angular velocity to be a gaussian process, one obtains for a spherical top the first few terms of a development in powers of time. In the free rotor and Debye limits this series can be rearranged to agree with the corresponding terms of the expansion in powers of time of the known limiting expressions. A closed form is obtained for the disk which does the same. It becomes clear that this three-variable Kivelson/Keyes formalism [3] when used for the angular velocity is equivalent to the inertia-corrected itinerant oscillator in two dimensions [24]. Thus it is possible now to relate analytically a realistic, oscillatory angular velocity autocorrelation function to a realistic orientational autocorrelation function for the same molecular symmetry.