A generalised friction model for the evaluation of angular momentum auto correlation functions

A theory of brownian motion where the friction coefficient is a finite correlation function of molecular torque is used to derive an expression for the angular velocity autocorrelation function, ψ(r). This is related to the orientational a.c.f., φ(t), using an analysis of bandshapes due to Kubo and extended by Shimizu. Both functions φ(t) and ψ(t) contain inherent weaknesses since ψ(t) has a MacLaurin expansion even up to t⁴ only, and π(t) does not reduce to the Kummer function for an ensemble of free rotors in the so-called limit of vanishing friction. Reasons for this behaviour are discussed.