Fractional numbers of electrons in Kohn–Sham theory

A semi-empirical self-interaction correction, based on the fractional number of electrons qA surrounding each atom A, is investigated in generalised gradient approximation density functional theory. The correction, which involves locally scaling the exchange functional (Becke 1988) by qA0.371, leads to a significantly improved potential energy curve for H2+. It also shifts the H2 potential energy curve towards that of Hartree–Fock, and increases the barrier for the reaction H + H2→H2 + H. An alternative correction qA−0.174 leads to a much improved dissociation of H2 in a restricted formalism.