NONLINEARLY COUPLED GENERALIZED FOKKER-PLANCK EQUATION FOR ROTATIONALRELAXATION

We have investigated the stochastic dynamics of a one dimensional roto r with C3 symmetry and zero barrier to rotation about the symmetry axi s. Angular momentum correlation functions derived from various stochas tic dynamics models were compared to the corresponding correlation fun ctions obtained from a molecular dynamics simulation [G. Widmalm, R. W . Pastor, and T. E. Bull, J. Chem. Phys. 94, 4097 (1991)]. None of the existing classical models agrees with the simulation; and we have sho wn in general that no linearly coupled generalized Langevin equation w ith Gaussian random noise can reproduce the simulation results. A quan tum stochastic dynamics model [T. E. Bull, Chem. Phys. 143, 381 (1990) ] extrapolated to the classical limit does, however, agree with the co mputer simulations. But this model is limited to very small molecules because the matrices involved become prohibitively large for even mode rately sized molecules. In order to address some of these limitations, we have constructed a nonlinearly coupled rotor-bath model for the ro tor. The form of the nonlinear coupling between the rotor and bath is determined by the symmetry of the rotor. A classical nonlinearly coupl ed generalized Langevin equation and its corresponding nonlinearly cou pled Fokker-Planck equation were derived from this microscopic rotor-b ath model using the projection operator formalism. In the limit of whi te noise, these equations reduce to the standard equations derived wit h linear coupling. With colored noise, however, the linearly and nonli nearly coupled equations are distinct. Angular momentum correlation fu nctions calculated with this nonlinearly coupled Fokker-Planck equatio n are in excellent agreement with the simulations both in terms of the short time Gaussian decay and long time exponential tail and in terms of the magnitudes of the correlation functions. Collision operators d erived from this model should therefore provide a more accurate connec tion between experimentally measured quantities and the underlying mic roscopic dynamics.