Langevin equation method for the rotational Brownian motion and orientational relaxation in liquids: spherical top molecules

A solution of the infinite hierarchy of differential-recurrence relations for the statistical moments (orientational correlation functions) governing the inertial rotational Brownian motion and the dielectric relaxation of an assembly of spherical top molecules is obtained in terms of a continued fraction. It is shown analytically that the solution based on this approach agrees with that of Sack [Proc. Phys. Soc. Lond. B 70 (1957) 414] (with a corrected misprint) and Fixman and Rider [J. Chem. Phys. 51 (1969) 2425] obtained from the corresponding Fokker-Planck equation.