Beyond Molecular Orbital Theory: The Impact of Generalized Valence Bond Theory in Molecular Science

Abstract

The generalized valence bond (GVB) method was developed by William A. Goddard III in the latter half of the 1960s. The GVB wavefunction addresses the most serious deficiencies of the Hartree–Fock (HF) wavefunction and its early application led to a number of important new concepts. Unfortunately, the complexity of the GVB equations limited its application to small atoms and molecules. This limitation was overcome by the development of the GVB(PP/SO) method in the early 1970s by William J. Hunt, P. Jeffrey Hay, and W. A. Goddard III. The GVB(PP/SO) wavefunction combines the perfect pairing (PP) spin function with orthogonality between orbitals in different electron pairs (SO), leading to a greatly simplified energy expression, but also some loss of generality. The GVB(PP/SO) and associated CI methods were used to elucidate the essential features of a broad range of molecular problems in the 1970s through the early 1990s. In the late 1990s, spurred by the developments in Joseph Gerratt’s group, the full GVB method enjoyed a renaissance. The studies by Gerratt and coworkers and Dunning and coworkers have, once again, shown the importance of GVB theory as a sound theoretical foundation for understanding molecules and molecular processes. In addition, the GVB wavefunction, when cast in its natural orbital (NO) form, is a compact, yet efficient zero-order wavefunction for the treatment of dynamical correlation.