Computation of molecular wave functions in terms of localised molecular orbitals

Abstract

A preliminary investigation of a new Localised Molecular Orbital (LMO) method is presented and applied to the molecules HCN, CO, N2, H2O, NH3 and CH4. The LMOs are called Perfectly Localised Molecular Orbitals (PLMOs) and are obtained in the one-determinant Hartree-Fock Molecular Orbital-Linear Combination of Atomic Orbitals (MO-LCAO) approximation in a minimal AO basis. The PLMOs are obtained from a starting set of occupied Canonical Molecular Orbitals (CMOs) by applying a general orthogonal transformation to the sigma valence CMOs and by minimising the energy sacrificed in restricting the transformed MOs to basis AOs on one and two centres only. The atomic centres upon and between which the lone pair and bond PLMOs reside is decided largely by an energy criterion alone. The resulting set of PLMOs are non-orthogonal. In the example molecules, the energy difference between the canonical wave function and that constructed from the PLMOs is found to be small. The PLMOs, expressed in terms of normalised hybrid atomic orbitals (HAOs) on each atom, are found to reflect a normal valence description of the molecules in which the overall level of hybridisation is low. This is possible because a substantial degree of non-orthogonality among the HAOs on each atom is found. The PLMOs yield satisfactory bond and lone pair moments and electronic populations, and are also shown, to have a satisfactory behaviour at non-experimental geometries of the water molecule. It is concluded that the small sacrifice in accuracy that results from completely localising LMOs by the PLMO method is outweighed by the advantages of dealing with one and two-centre LMOs. It is also suggested that the differences in the properties of LMOs generated by different orthogonal transformation criteria is dependent on the relative amounts of delocalisation from bond and lone pair LMOs.