Ensemble averages for Smoluchowski–Debye rotational diffusion in the presence of a two-angle-dependent reorienting force

An approximate method of solving the Smoluchowski–Debye equation for rotational diffusion of molecules subjected to the action of a two-angle-dependent external driving field within the Kasprowicz–Kielich and Kielich method is proposed. This calculation method, introduced in the Kielich papers for the case of `weak molecular reorientationʹ, describes molecular relaxation in various non-linear electro-optical effects for an external reorienting field dependent on the polar angle only. Taking advantage of the properties of spherical harmonic functions, the Kielich method is extended to the case of reorienting fields dependent on the azimuthal and polar angles.