Langevin equations and computed correlation functions for a rotating and translating asymmetric top

Publisher Website
Google Scholar
Abstract
The three-dimensional diffusion in condensed material of a rotating and translating asymmetric-top molecule is considered with use of three frames of reference: the laboratory frame (x,y,z), a rotating frame (1,2,3)’, and a moving frame (1,2,3). The frame (1,2,3)’ has the same origin as (x,y,z), but rotates with an angular velocity ω, the molecular angular velocity. The frame (1,2,3) is defined by the principal molecular moments of inertia, and its origin is therefore the molecular center of mass. The molecular angular velocity ω is the same in all three frames. By writing a pair of simultaneous single-molecule Langevin equations, a rotational equation in (1,2,3) and a translational equation in frame (1,2,3)’, a natural description of the molecular diffusion is obtained without the need of friction cross terms. This description introduces into the analysis the center-of-mass position vector r, and the forces obtained by transforming Newton’s equation into a noninertial frame, i.e., by the frame transformation (x,y,z)→(1,2,3)’ or vice versa.