Towards a fully self-consistent embedding theory average atom model for warm dense hydrogen

Modeling warm dense matter accurately is challenging without invoking computationally expensive simulations to capture electronic and ionic interactions. Density functional theory (DFT)-based average atom models (AAMs) reduce the complex ionic system by averaging over local environments or charge states, significantly reducing computational cost while retaining accuracy properties like equations of state and mean ionization states. However, DFT-based AAMs struggle to capture a key effect in dense plasmas—the overlapping electron densities between neighboring atoms, which alter orbital energies through enforced orthogonality. To address this contribution, we have developed a self-consistent AAM that includes these interactions via the non-additive kinetic potential v^nadd as in DFT embedding theories. v^nadd can be computed using Thomas-Fermi, von Weizsäcker, or more sophisticated finite-temperature functionals. The model takes an ion-ion pair correlation function, g_II(r) as input—as computed from pseudoatom molecular dynamics—which encodes the plasma density and temperature. It then solves for a self-consistent electronic subsystem, including v^nadd; we thereby introduce a novel interaction term in existing AAMs. We apply this model to hydrogen at solid density and a few eV, examining the impact of v^nadd on electron densities, energy shifts, and mean ionization.