Localized orbitals for polyatomic systems (I)

Adams and Gilbert independently derived a rigorous generalization of the Hartree‐Fock equation which enables one to obtain localized orbitals in any polyatomic system with closed shells or which may be represented by a single Slater determinant. This generalization is approximately valid in any polyatomic system which one may approximate by a single Slater determinant. Kunz transformed the Adams‐Gilbert equation into another form and analyzed the equation in powers of overlap. We re‐examine the Adams‐Gilbert equation and transform it into a considerably simple form by use of a non Hermitian localization operator. Development in powers of the overlap yields equations identical to those found by Kunz. However our equations are valid in the more general case where the orbitals localized about a given site are non orthogonal. We also develop several perturbation iteration solutions of the Adams‐Gilbert equation.