Embedding Theory Average Atom Model: Implementation and Application to Warm Dense Hydrogen*

Accurate modeling in the Warm Dense Matter regime is a persistent challenge with the most detailed models being immensely computationally expensive. Density Functional Theory (DFT)-based Average Atom Models (AAM) offer significant speed-ups in calculation times while still retaining fair accuracy in evaluating equations of state, mean ionizations, and more. Despite their success, AAMs struggle to precisely account for electronic interactions – in particular, they do not account for effects on the kinetic energy arising from overlaps in neighboring atom densities. We aim to enhance these models by including such interactions via the non-additive kinetic potential V^NAD as in DFT embedding theories. V^NAD can be computed using Thomas-Fermi, von Weizsäcker, or more sophisticated kinetic energy functionals. The proposed model includes interactions beyond the central atom and introduces V^NAD as a novel interaction term in existing AAMs. We have applied this model to hydrogen at solid density and a few eV temperatures and investigated the effects of V^NAD on electron densities, energy shifts, and mean ionization.