  We perform on-the-fly non-adiabatic molecular dynamics simulations using the
symmetrical quasi-classical (SQC) approach with the recently suggested
molecular Tully models: ethylene and fulvene. We attempt to provide benchmarks
of the SQC methods using both the square and the triangle windowing schemes as
well as the recently proposed electronic zero-point-energy correction scheme
(so-called the gamma correction). We use the quasi-diabatic propagation scheme
to directly interface the diabatic SQC methods with adiabatic electronic
structure calculations. Our results showcase the drastic improvement of the
accuracy by using the trajectory-adjusted gamma-corrections, which outperform
the widely used trajectory surface hopping method with decoherence corrections.
These calculations provide useful and non-trivial tests to systematically
investigate the numerical performance of various diabatic quantum dynamics
approaches, going beyond simple diabatic model systems that have been used as
the major workhorse in the quantum dynamics field. At the same time, these
available benchmark studies will also likely foster the development of new
quantum dynamics approaches based on these techniques.
