Hybrid prefactor Semiclassical Initial Value Series Representation of the quantum propagator

One of the central advantages of the Herman Kluk Semiclassical Initial Value Representation (SCIVR) of the quantum propagator is that through its prefactor it approximately conserves unitarity for relatively long times. Its main disadvantage is that the prefactor appearing in the SCIVR propagator is expensive to compute as the dimensionality of the problem increases. When using the SCIVR series method for computation of the numerically exact quantum dynamics, the expense becomes even larger, since each term in the series involves a product of propagators, each with its own prefactor. This expense can be eliminated if one uses prefactor free propagators; however, these do not conserve unitarity as well as the HK propagator. As a compromise, we suggest the use of a hybrid propagator, in which the system variables are treated with the Herman-Kluk prefactor, while the bath variables are treated as prefactor free. Numerical application to a quartic oscillator coupled bilinearly to five harmonic bath oscillators demonstrates the viability of the hybrid method. The results presented are also a first application of the SCIVR series method to a system with six degrees of freedom. Convergence to the numerically exact answer using Monte Carlo sampling is obtained with at most the first two terms in the SCIVR series.