Spectral moments of the rotational correlation functions for the first- and second-rank tensors of asymmetric top molecules

A method of evaluating the spectral moments M^l _2k of the rotational correlation functions for the first- and second-rank tensors of rigid asymmetric top molecules is developed. It is based on the calculation of the coefficients of a Taylor series expansion of the vector and tensor orientational correlation functions about t = 0 with the help of angular momentum theory, and is applicable to a pair intermolecular interaction potential with arbitrary dependence on the angular variables. Equations for the second (M^l ₂), fourth (M^l ₄), and sixth (M^l ₆) spectral moments are obtained as a demonstration of the ability of the method. The results for (M^l ₂) and M^l ₄ coincide with previously known values and the equation for M^l ₆ is new. As particular cases, the theory contains the results for classical ensembles of symmetric tops, spherical tops, and linear molecules.