Orbital perspective of the nature of chemical bonds and potential energy surfaces: 55 years after Wahl's molecular orbital representation of homopolar diatomic molecules

To elucidate the molecular electronic energy variation and to simultaneously track the topography of a potential energy surface (PES) such as the potential basin, transition states, and potential barriers in the study of chemical bond formation and relevant chemical reactions, we devise ENOX as an extension of the ENO (energy natural orbital). The total sum of the ENOX orbital energies exactly matches the PES energy, that is, the sum of the electronic energy and nuclear-nuclear repulsion energy. ENOX gives a one-electron (orbital) energy representation, enabling to track the potential energy surface with the ENOX orbital energies alone. The ENOX extracts an orbital view of energy structure from the highly accurate wavefunctions in ground and excited states, electronic states delocalized across multiple potential energy surfaces (breaking the Born-Oppenheimer approximation), time-dependent wavepacket states, and so on. Here in this paper we apply ENOX to the ground state homopolar diatomic molecules in the second row (Li₂ to F₂) to anatomize their chemical bond formations and thereby update, after 55 years, the monumental molecular orbital studies by Wahl.