Nonorthogonal orbitals; the Hartree–Fock–Heitler–London method and preliminary applications

Since the early days of quantum chemical computations, the determinantal wave function can be constructed either with orthogonal or nonorthogonal one electron functions (the orbitals). The two classical quantum mechanical methods, the Hartree–Fock (HF), and the Heitler–London (HL) are examples of the use of orthogonal, and nonorthogonal orbitals, respectively. Both models are approximations yielding approximately half of the experimental binding energy, due to the correlation error. Very extended expansions (with many thousand determinants) recover the error. The two methods have been recently merged into the Hartree–Fock–Heitler–London method (HF–HL), which systematically ensures correct molecular dissociation and a binding energy generally more correct than that obtained with the two parent models. Relatively short expansions of HL configurations yield correct binding energies, at the expense, however, of a high computational time in the optimization of the orbital expansion coefficients. In the HF–HL model, the inner shell electronic correlation is computed with a Coulomb hole functional. We compare computations at the HF, HL, and HF–HL levels, and for the latter, we consider relatively short expansions leading to reasonable binding energies. The computations compare the ground-state potential energies of the hydrides and homopolar diatomic molecules of the first and second period of the atomic table, a few excited states, and small polyatomic molecules like H2O, C2H2, and HCN. © 2012 Wiley Periodicals, Inc.