Bridging Cultures

Two distinct cultures are competing for the description of molecular electronic structure in quantum chemistry: the molecular orbital (MO) model, which may be considered to involve density functional theory (DFT) and views the orbitals as delocalized, and the valence bond (VB) model, which deals with localized one-center hybridized orbitals. A short history of the MO and VB methods and the origin of their rivalry is first recalled. Then it is shown in a simple case that the two models are equivalent if electron correlation is fully taken into account. In the general case, many bridges exist between the VB description of bonding and the descriptions by electron-delocalized approaches. The first bridge is a direct conversion of any MO wave function, with or without configuration interaction (CI), to a linear combination of VB structures, by means of an algebraic transformation, which is always possible albeit more insightful in minimal basis set. Another bridge is provided by the possibility of localizing the MOs of a single determinant at the Hartree-Fock level, by means of unitary transformations that maximize the distances between electron pairs. This transformation, which leaves the determinant unchanged, describes a molecular system in a VB manner with local bonds and lone pairs. Still another way to extract VB information from a Hartree-Fock determinant from the electron density calculated by DFT is offered by the block-localized wave function (BLW) method. At a higher level of theory, the generalized valence bond (GVB) method yields a wave function that can display either overlapping localized atomic orbitals (AOs) or orthogonal bonding and antibonding MOs. Besides, the natural bond orbitals (NBOs) model and natural resonance theory (NRT) can interpret any MO wave function, calculated at any level of sophistication, or any electron density calculated by DFT, in terms of VB structures, which can be given a quantitative weight. VB wave functions can also be obtained from complete active space self-consistent field CASSCF MO wave functions, involving the totality of nondynamic electron correlation, by means of the complete active space valence bond CASVB methods. Finally, as a VB description of a molecular system often uses hybridized orbitals, it is shown that such a description and the very concept of hybridization are in no way conflicting with photoelectron spectra nor with any experimental result of any kind.