The perfect-pairing valence bond model for the water molecule

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Abstract
Optimized orbitals for the water molecule have been obtained within the perfect‐pairing valence bond model by an ab inito self‐consistent field calculation. Each split pair is optimized by approximating the remaining electron distribution with a localized doubly‐occupied orbital sea. In addition, the overlaps between orbitals of different pairs are optimized by considering higher order pair–pair interactions. The expansion of the energy in the cumulative order of intrapair orbital splittings converges rapidly. The total energy obtained is 49.0 kcal/mole below restricted Hartree–Fock, thus accounting for 21.0% of the correlation energy. The orbitals are well localized into a 1s core pair on oxygen, two equivalent O–H bond pairs and two equivalent lone pairs on oxygen. The hybridization of these orbitals differs considerably from what is expected on the basis of ordinary chemical intuition, the split lone pair orbitals being sp0.56 and sp1.83 and the bonding orbital centered on oxygen being sp1.84. No artificial orthogonality restrictions are imposed on the orbitals in this method. The interpair orbital overlaps are typically on the order of 0.0–0.3, rising to over 0.7 for the overlap between the diffuse orbitals of each lone pair! The energy lowering over a valence bond calculation carried out with a strong orthogonality constraint is small (3.4 kcal/mole). However, the nonorthogonal orbitals are the appropriate ones for transferring from one molecule to another and for chemical interpretation in general. Furthermore, the artificial radial nodes that appear in the strongly orthogonal orbitals hamper the perturbation calculation of correlation energies and the application of pseudopotential techniques as well.