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.
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