Orbital overlap and chemical bonding

The chemical bonds in the diatomic molecules Li₂-F₂ and Na₂-Cl₂ at different bond lengths have been analyzed by the energy decomposition analysis (EDA) method using DFT calculations at the BP86/TZ2P level. The interatomic interactions are discussed in terms of quasiclassical electrostatic interactions ΔE_elstat, Pauli repulsion ΔE_Pauli and attractive orbital interactions ΔE_orb. The energy terms are compared with the orbital overlaps at different interatomic distances. The quasiclassical electrostatic interactions between two electrons occupying 1s, 2s, 2p(σ), and 2p(π) orbitals have been calculated and the results are analyzed and discussed. It is shown that the equilibrium distances of the covalent bonds are not determined by the maximum overlap of the σ valence orbitals, which nearly always has its largest value at clearly shorter distances than the equilibrium bond length. The crucial interaction that prevents shorter bonds is not the loss of attractive interactions, but a sharp increase in the Pauli repulsion between electrons in valence orbitals. The attractive interactions of ΔE _orb and the repulsive interactions of ΔȨ_Pauli are both determined by the orbital overlap. The net effect of the two terms depends on the occupation of the valence orbitals, but the onset of attractive orbital interactions occurs at longer distances than Pauli repulsion, because overlap of occupied orbitals with vacant orbitals starts earlier than overlap between occupied orbitals. The contribution of ΔE_elstat in most nonpolar covalent bonds is strongly attractive. This comes from the deviation of quasiclassical electron-electron repulsion and nuclear-electron attraction from Coulomb's law for point charges. The actual strength of ΔE _elstat depends on the size and shape of the occupied valence orbitals. The attractive electrostatic contributions in the diatomic molecules Li₂-F₂ come from the s and p(σ) electrons, while the p(π) electrons do not compensate for nuclear-nuclear repulsion. It is the interplay of the three terms ΔE_orb, ΔE_Pauli, and ΔE_elstat that determines the bond energies and equilibrium distances of covalently bonded molecules. Molecules like N₂ and O₂, which are usually considered as covalently bonded, would not be bonded without the quasiclassical attraction ΔE_elstat.