Modern valence bond theory

Modern valence bond theory is the application of valence bond theory (VBT) with computer programs that are competitive in accuracy and economy, with programs for the Hartree–Fock or post-Hartree-Fock methods. The latter methods dominated quantum chemistry from the advent of digital computers because they were easier to program. The early popularity of valence bond methods thus declined. It is only recently that the programming of valence bond methods has improved. These developments are due to and described by Gerratt, Cooper, Karadakov and Raimondi (1997);^[1] Li and McWeeny (2002); Joop H. van Lenthe and co-workers (2002);^[2] Song, Mo, Zhang and Wu (2005); and Shaik and Hiberty (2004)^[3]

While molecular orbital theory (MOT) describes the electronic wavefunction as a linear combination of basis functions that are centered on the various atoms in a species (linear combination of atomic orbitals), VBT describes the electronic wavefunction as a linear combination of several valence bond structures.^[4] Each of these valence bond structures can be described using linear combinations of either atomic orbitals, delocalized atomic orbitals (Coulson-Fischer theory), or even molecular orbital fragments.^[5] Although this is often overlooked, MOT and VBT are equally valid ways of describing the electronic wavefunction, and are actually related by a unitary transformation. Assuming MOT and VBT are applied at the same level of theory, this relationship ensures that they will describe the same wavefunction, but will do so in different forms.^[4]