Forward-Backward Semiclassical Dynamics with Linear Scaling

A forward-backward semiclassical method is presented for calculating correlation functions of polyatomic systems. Unlike conventional semiclassical theories, this formulation does not require evaluation of the prefactor that contains a determinant with elements defined by the stability matrix. It is shown rigorously that the contribution of the semiclassical prefactor in the present formulation can be absorbed in the semiclassical phase and initial density if the momentum jump at the end of the forward propagation is chosen to be one-half of that dictated by the classical equations of motion. As a consequence, the number of equations of motion to be solved in its implementation is linearly proportional to the number of degrees of freedom. The method is applied to the dynamics of water clusters which involve strongly anharmonic interactions.