Spin Hamiltonian Valence Bond Theory and its Applications to Organic Radicals, Diradicals, and Polyradicals

Chapter 8 introduces the semiempirical theory of spin-Hamiltonians, using respective AO-based determinants, which are eigenfunctions of the S z operator. This theory is well suited for neutral systems having one electron per site, and it provides some qualitative rules related to ground-state properties. As in Hückel MO theory (MOT), the overlaps between AOs are set to zero and the energy of an electronic state is obtained by diagonalization of a Hamiltonian matrix, which is entirely determined by the molecular graph in terms of a unique parameter g , related to the 2β S term, which is utilized in the qualitative VB theory (VBT) described in Chapter 3. The theory is applied to the spin multiplicities of alternant conjugated polyenes and provides a very simple rule to predict Hund's rule violations. It may also provide qualitative spin-densities in alternant free radicals or polyradicals, and relative stabilities for isomers of polyenes.