Projected Hybrid Density Functionals: Method and Application to Core Electron Ionization

This work presents a new class of hybrid density functional theory (DFT) approximations, incorporating nonlocal exact exchange in predefined states such as core atomic orbitals (AOs). These projected hybrid density functionals are a flexible generalization of range-separated hybrids. This work derives projected hybrids using the Adiabatic Projection formalism. One projects the electron-electron interaction operator onto the chosen predefined states, reintroduces the projected operator into the noninteracting Kohn-Sham reference system, and introduces a density functional approximation for the remaining electron-electron interactions. Projected hybrids are readily implemented existing density functional codes, requiring only a projection of the one-electron density matrices and exchange operators entering existing routines. This work also presents a first application: a core-projected Perdew-Burke-Ernzerhof hybrid PBE0c70, in which the fraction of nonlocal exact exchange is increased from 25% to 70% in core AOs. Automatic selection of the projected AOs provides a black-box model chemistry appropriate for both core and valence electron properties. PBE0c70 predicts core orbital energies that accurately recover core-electron binding energies of second- and third-row elements, without degrading PBE0's good performance for valence-electron properties.