Localized orbitals and short‐range molecular interactions. I. Theory

The separation of the electronic energy into Coulombic and penetration components [V. Magnasco, G. F. Musso, and R. McWeeny, J. Chem. Phys. 47, 4617 (1967)] in the case of a (closed‐shell) single determinant wavefunction of nonorthogonal localized spin bond orbitals (BO) is studied on the basis of a convenient density matrix formulation. The main correction that results when overlap is admitted consists of two terms, the first describing the energy of the density ``perturbation'' in the field of the ``unperturbed'' one‐electron operator F̂₀, the second the Coulomb‐exchange self‐interaction of the density ``perturbation.'' When the groups interacting at short range are atoms or molecules, compact closed formulas for the interaction energies can be derived, and the connection with first‐order perturbation theory is discussed. The present formalism is suitable for analyzing both nonadditivity of short‐range intermolecular forces and the nature of barriers to internal rotation in molecules.