Langevin equation method for the rotational Brownian motion and orientational relaxation in liquids

A theory of orientational relaxation for the inertial rotational Brownian motion of a linear molecule (rotator in space) is developed in the context of the Langevin equation method without recourse to the Fokker–Planck equation. The general term in the time-dependent infinite hierarchy of differential-recurrence relations for the orientational correlation functions describing the relaxation behaviour of the system is derived by averaging the corresponding Euler–Langevin equation. The solution of this hierarchy is obtained in terms of continued fractions. The correlation times and the spectra of the orientational correlation functions are calculated for typical values of the model parameters.