Some exact results for rotational correlation functions at short times

Expressions are derived for several of the coefficients in the Taylor series expansion for rotational correlation functions in powers of time. Classical ensembles of symmetric tops, spherical tops, and linear molecules are treated. Coriolis coupling terms are included in the coefficients for the angular correlation functions of symmetric tops; and angular velocity correlations are discussed as well as orientational correlation functions. Expressions are obtained for the first three non-zero coefficients of the orientational correlation functions for hindered rotors (up to and including t 6). Formal expressions are obtained for all coefficients of freely rotating molecules, and a number of these expressions are explicitly evaluated. A gaussian approximation to the memory function is proposed for the angular velocity correlation function; curves calculated from the resulting expression are compared with several simulated correlation functions.