In recent years the chemistry community has demonstrated the numerical power of semiclassical initial value representation (SCIVR) approximations. However, the theoretical basis was at times questionable. The accuracy of the approximations, their parametrization and the specific forms to be used were of intense debate. The SCIVR class of approximation was known to fail for deep quantum tunneling.
In this talk we will present the SCIVR series representation of the exact quantum propagator, showing that the SCIVR approximation is just the first term in a perturbation series. Examples will be presented showing that it is straightforward to compute additional terms in the series and that typically only one or two terms are needed to obtain the quantum dynamics with acceptable numerical accuracy.
We will also show that the SCIVR series method deals correctly with deep quantum tunneling which is now represented in terms of coherent classical paths. These are classical trajectories which have a small number of discontinuities. Adjacent trajectories are related to each other through coherent state overlaps. Results for deep tunneling through an Eckart barrier will be presented. Both thermal and energy dependent rates will be analyzed.
The formalism of the SCIVR series method will also be used to present new derivations of SCIVR approximations without prefactors as well as a general class of thawed SCIVR propagators.
Finally, we shall show how short time numerically exact quantum dynamics may be used to compute eigenvalues and tunneling splittings. The implications for ab-initio chemistry computations will be discussed.