Accelerating Embedding Potential Optimization by Reconstructing the Pseudo-Valence Electron Density

Density functional embedding theory (DFET) enables use of electronic structure methods with higher accuracy than density functional theory in a local region, with applications thus far ranging from (photo/electro)catalysis to reactions in solution. DFET partitions a large collection of atoms into smaller groups that interact via a shared embedding (interaction) potential V_emb, determined via functional optimization. The optimized effective potential (OEP) process used to optimize V_emb is time-consuming and becomes a computational bottleneck due to sharp, oscillating features of V_emb near nuclei. Here, similar to pseudopotential theory, by reconstructing electron densities used in the OEP process from smoother pseudo-valence-only (PVO) electron densities as proxies for total densities of the full system and subsystems, we can retain accuracy in the embedded electronic structure calculations while potentially reducing the overhead of V_emb construction, within the projector augmented-wave (PAW) formalism. We explore three different chemical reactions as exemplars to test PVO-DFET, namely, H₂ dissociative adsorption on a Cu(111) surface, H₂O adsorption on a Pt(111) surface, and aqueous [Ca²⁺-SO₄^2-] ion-pair formation. The PVO approximation works well for all three systems with minimal loss of accuracy (∼10-70 meV error relative to the original exact-derivative (ED) approach) while accelerating V_emb generation for the Cu and Pt systems respectively by 20× and 5×. Given proper numerical convergence parameters, the spatial distributions of differences between PVO- and ED-based V_emb outside the core regions are small, explaining the exceptional agreement between the two approaches. We anticipate that this more efficient PVO-DFET approximation will be useful whenever computation of V_emb is much more expensive than subsequent embedded high-level electron correlation calculations.