A new approach to bonding in transition metal clusters

Abstract

The idea that the molecular orbitals of a cluster of atoms can be usefully classified according to their nodal structure, so that the energy increases with the number of nodes, is quantified and shown to apply in its usual form only to molecular orbitals constructed from atomic σ orbitals. The method is extended to deal with atomic π and δ orbitals by the use of vector and tensor surface harmonics respectively. In all cases the orbitals can be classified approximately in terms of angular momentum quantum numbers l and m, but in the π and δ cases there are two orbitals, with different parity, for each lm, and the energy is determined primarily by the parity. The method provides a classification scheme and an approximate energy ordering which does not depend on any point-group symmetry that the cluster may have, and therefore provides a useful framework for discussion of the bonding in cluster compounds such as the boron hydrides and the transition metal cluster carbonyls.