Density-functional theory-based chemical reactivity indices in the Hartree-Fock method. I. Unrestricted Hartree-Fock method for a noninteger number of electrons.

Correct evaluation of the reactivity indices, such as chemical potential, hardness, and Fukui function demands for the extension of the formalism beyond the integer particle picture. An ensemble approach is used as an extension of the unrestricted Hartree-Fock (UHF) method for noninteger electron number systems. A prescription is given for the construction of an ensemble Fock operator for a system with partially filled spin-orbitals. The comparison between the ensemble HF method and the hyper-HF method in terms of density matrices and spin-orbitals is presented. The equivalence of the equiensemble case and the ensemble UHF case with unequal weight factors is shown.