## Exact quantum mechanics using classical mechanics

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.

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