Functional series in asymmetric-molecular-rotors theory. I. Vectorial correlation functions and spectral densities for a free classical ensemble

A new method is presented to calculate vectorial correlation functions for a system of free asymmetric-top molecules. The analytical expression of the rotation matrix of an asymmetric top is determined first by using a special set of functions. Next, this matrix is developed into a Fourier series. Final results, obtained after averaging over a canonical ensemble, appear in the form of rapidly converging series of integrals of free spherical-rotor correlation functions. This development contains no approximation and is well adapted to numerical treatment. It also represents a convenient starting point to develop rotational models for extended diffusion.