A new concept for an approximate MO formalism

A molecular orbital (MO) formalism avoiding the zero differential overlap (ZDO) approximation of common semiempirical methods is developed. Using the Ruedenberg approximation for diatomic overlap densities appearing in Coulomb integrals, the Fock matrix is simplified such that its construction scales with N2 instead of N4 in ab initio methods if N is the dimension of the basis set. Thus, the one-electron and two-electron Coulomb parts of the Fock matrix are formulated explicitly in an atomic orbital (AO) basis whereas the ZDO approximation is restricted to the two-electron exchange part of the Fock matrix.