  Wave packet molecular dynamics (WPMD) has recently received a lot of
attention as a computationally fast tool to study dynamical processes in warm
dense matter beyond the Born-Oppenheimer approximation. These techniques,
typically, employ many approximations to achieve computational efficiency while
implementing semi-empirical scaling parameters to retain accuracy. We
investigate three of the main approximations ubiquitous to WPMD: a restricted
basis set, approximations to exchange, and the lack of correlation. We examine
each of these approximations in atomic and molecular hydrogen in addition to a
dense hydrogen plasma. We find that the biggest improvement to WPMD comes from
combining a two Gaussian basis with a semi-empirical correction based on the
valence-bond wave function. A single parameter scales this correction to match
experimental pressures of dense hydrogen. Ultimately, we find that
semi-empirical scaling parameters are necessary to correct for the main
approximations in WPMD. However, reducing the scaling parameters for more
ab-initio terms gives more accurate results and displays the underlying physics
more readily.
