  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.
