From Hartree–Fock and Heitler–London to chemical orbitals

For chemistry the theoretical representation of the forces connecting atoms in molecules was and is a central problem. The Atomic Orbital and the Molecular Orbital are basic building blocks in the Heitler–London (HL) and in the Linear Combination of Atomic Orbitals–Molecular Orbital (LCAO-MO) methods, which have lead to the construction of modern Valence Bond and Hartree–Fock methods (and related extensions). However, accurate predictions from non semi-empirical methods often require enormous amount of computer power, if applied to molecules of reasonable size and current chemical interest. We have critically re-examined the two basic methods and suggested a few extensions. Merging of the Hartree–Fock with the Heitler–London algorithms, as recently proposed in the Hartree–Fock–Heitler–London (HF–HL) method, reduces the length of the expansions needed in AO or MO ab initio models in the computation of binding energy; this simplification allows easy interpretation of the resulting wave function. The HF–HL method is exemplified with systematic computations on ground and excited state of the hydrides and homonuclear diatomic molecules with atoms of the first and second period of the periodic table. Further, we show that the HF–HL method is derivable from a wave function constructed with a new type of orbital, the Chemical orbital (CO), which embodies the characterization of MO near equilibrium, AO at dissociation and at the united atom. Preliminary computations with CO are included. The new method provides the conceptual origin of both the HF and VB approaches, thus the foundation of an 80 years effort in variational quantum chemistry.