Statistical theory of electronic degrees of freedom in wave packet molecular dynamics

We derive statistical distributions for the degrees of freedom in wave packet molecular dynamics models. Specifically, a theory is developed for the width distributions of Gaussian wavepackets in both isotropic and anisotropic formulations. The resulting distribution functions show good agreement with molecular dynamics data under warm dense matter conditions, providing practical guidance for constraining the confining potential, an empirical parameter in the model. We also discuss how these distributions influence the resulting effective Coulomb interactions.