VARIATIONAL SOLUTIONS FOR THE THERMAL AND REAL-TIME PROPAGATOR USING THE MCLACHLAN VARIATIONAL PRINCIPLE

A new approximation to the propagator is presented. The approximation as applied to the thermal propagator (coordinate space density matrix) is obtained by using an analog of the McLachlan variational principle for the solution of the Bloch equation. The approximation as applied to the real time propagator is obtained by using the McLachlan variati onal principle for the solution of the time-dependent Schrodinger equa tion. The-approximate coordinate space density matrix has the same fun ctional form of the high temperature limit of the density matrix, whil e the approximate real time propagator has-the same functional form-as the short time propagator. We present numerical results for the therm al propagator for several test systems and compare these results to pr evious work of Zhang, Levy; and Freisner [Chem. Phys, Lett. 144, 238 ( 1988)], Mak and Andersen [J. Chem. Phys. 92, 2953 (1990)], and Cao and Berne [J. Chem. Phys. 92, 7531 (1990)]. We also present numerical res ults for: the approximate real time propagator for several test system s and compare to the exact results and results obtained by Gaussian wa ve packet propagation.