Improving the efficiency of the Herman-Kluk propagator by time integration

A method is presented that reduces the number of trajectories needed to achieve accurate results with the Herman-Kluk method and similar initial value semiclassical propagation techniques that involve integration over phase space. It is shown that a time average over motion may be inserted into these integrals with the result that their numerical convergence is accelerated. This technique is applied to two systems with encouraging results, especially for long-time propagation.