Orbital Exchange Calculations: An Alternative View of the Chemical Bond

Contemporary quantum chemistry methods assume that the two orbitals of the bonding pair are unambiguously identifiable. This work does not make that assumption. The purpose of this paper is to explore a model of the chemical bond which does not assume that the orbitals of the bonding pair can be unambiguously identified with either of the bonding atoms when their orbitals overlap to bond. To provide maximum flexibility in the definition of the bonding orbitals, the orbitals have been represented as spatial arrays and the calculations performed numerically. This model of the chemical bond assumes that the identifiability of the bonding orbitals is a function of 1-(overlap/(1+overlap)) where the overlap of the two bonding orbitals is calculated in the usual manner. The kinetic energy of the bonding electron pair and the energy required to meet the orthogonality requirements, mandated by the Pauli principle, are a function of overlap/(1+overlap). The model assumes that the bonding orbitals are straight-forward atomic orbitals or hybrids of these atomic orbitals. The results obtained by applying this simple approach to eleven di-atomics and seven common poly-atomics are quite good. The calculated bond lengths are generally within 0.005Å of the measured values and bond energies to within a few percent. Except for molecules with polarized symmetrical 1s or 2s sigma bonding orbitals, bond lengths are determined, independent of bond energy, at that point where overlap/(1+overlap) equals 0.5.