Construction of orbital-specific hybrid functional by imposing the linearity condition for orbital energies in density functional theory

We propose a new scheme to construct an orbital-specific (OS) hybrid functional so as to satisfy the linearity condition that the second derivative of the total energy with respect to the occupation number in Kohn-Sham density functional theory (KS-DFT) is zero. Numerical assessment confirms that the orbital energies exhibit a significantly small fractional-occupation-number dependence for NH₃ molecule. The newly proposed OS hybrid functional accurately reproduces ionization potentials (IPs) of core and valence orbitals for molecules containing second and third row atoms in the sense of Koopmans' theorem.