Basic Valence Bond Theory

Chapter 3 teaches the basic principles of valence bond theory (VBT) and how to write suitable valence bond (VB) wave functions for a variety of molecular interactions. The two-electron/two-center case is treated first, with its covalent and ionic bonding singlet VB structures and the repulsive triplet one. The wave functions are written in terms of Slater determinants constructed with localized or semilocalized atomic orbitals. These principles are extended to polyelectronic cases and to configuration interaction between VB structures. The VB formalism using the exact Hamiltonian is described, allowing one to compute the energies of VB structures and the Hamiltonian matrix elements between the structures. A qualitative VBT is also outlined, using an effective Hamiltonian in terms of overlaps and reduced resonance integrals, allowing one to easily calculate the energies of VB structures, bonding energies, repulsive interactions, and nonbonded interactions. Some bridges are presented between VBT and molecular orbital theory (MOT).