Rotational Brownian motion of spherical molecules the Fokker-Planck equation with memory

The rotational Fokker-Planck equation with memory is considered for a spherical top molecule. Angular momenta and rotational energy correlation functions and also orientational correlation functions in the high and low friction limit are calculated analytically. A convenient semianalytical method of solution of the equation through recursive relations is proposed. The method is applicable for an arbitrary memory kernel of the equation and representative calculations for the exponential memory kernel are presented to simultaneously keep track of the behavior of the angular momenta and orientational correlation functions vs. intensity and correlation time of the Brownian torques.