Minimizing propagated density errors of atomic core-electron for simultaneously accurate bandgaps and lattice constants in closed-shell Copper semiconductors

Density functional theory struggles to accurately determine electron density of atoms, whose error is inevitably encoded into the pseudopotential and propagated into solid-state calculations. However, little is known about how this affects accuracy nor how to remedy it. In this work, through a systematic study of the effect of Cu atomic density on bandgap and lattice constants of over 50 Cu-containing simple closed-shell semiconductors, we find that core-electron density can drastically affect nuclear attraction to valence electrons and subsequent charge distribution and energy position of Cu 3$d$ electrons. The error can be eliminated at its source by employing modified Hartree-Fock pseudopotentials for Cu core while retaining (semi-)local functionals for valence electrons. This real-space partitioning approach leads to simultaneous high-accuracy in bandgap and lattice constants across the entire material class.