The extension of the Kramers theory of the escape rate of a Brownian particle from a potential well to the entire range of damping proposed by Mel'nikov and Meshkov [J. Chem, Phys. 85, 1018 (1986)] is applied to the rotational Brownian motion of fixed axis rotators in a double well cosine potential. The procedure yields an expression for the Kramers escape rate valid for all values of the dissipation including the very low damping (VLD), very high damping (VHD), and crossover regimes. This equation provides a good asymptotic estimate of the correlation time tau(parallel to) of the longitudinal dipole moment correlation function calculated by solving the underlying Langevin equation using the matrix-continued fraction method. Moreover, for low barriers, where the Mel'nikov and Meshkov approach is not applicable, analytic equations for tau(parallel to) in the VLD and VHD limits are derived and a simple extrapolating equation that is valid for all values of the damping is proposed. (C) 2004 American Institute of Physics.