Vectorial correlation functions for a classical system of free asymmetric rotors

A theory is presented to calculate vectorial time correlation functions for a classical system of free asymmetric rotors. The Euler equations of a freely rotating rigid body are solved first, and Eulerian angles between the laboratory-fixed and the molecule-fixed coordinate systems are deduced. The results are expressible in terms of the Jacobi theta functions. Further calculation implies the construction of the $Q$ matrix. Its general properties are examined with the help of group theory. The final integration over the components of the angular momentum vector is in part analytical and in part numerical. The calculation is simplified by considering the properties of the Jacobi zeta function. General properties of free asymmetric rotor correlation functions and of their Fourier transforms are discussed.