Generalised valence bond

Extended Hiickel theory Generalised valence bond model Hartree-Fock... 

One widely used valence bond theory is the generalised valence bond (GVB) method of Goddard and co-workers [Bobrowicz and Goddard 1977]. In the simple Heitler-London treatment of the hydrogen molecule the two orbitals are the non-orthogonal atomic orbitals on the two hydrogen atoms. In the GVB theory the analogous wavefunction is written ... 

Resonating Generalised Valence Bond (GVB) calculations were performed on cyclobutadiene by Voter and Goddard [54], They find a resonance energy of -22 kcal/mol for this molecule. According to them its geometry cannot easily be predicted, and is determined by the interaction between resonance and bond strain. 

Fig. 4. Generalised Valence Bond Configuration Interaction relative free energies for the addition of olefin to Cr02Cl2 showing that addition across a single Cr=0 bond is favoured. (Derived from Fig. 10 of Ref. 95a)...

Considerations like these mean that the VB model, although it has seen a considerable resurgence of interest over the past few years with several key breakthroughs being made, is still predominantly perceived as a specialist area with applications confined to smcJl numbers of electrons. The so-called Generalised Valence Bond (GVB) method which is a self-consistent development of the Heitler-London model is developed in Chapter 22 and, for the moment, this is as far as we shall go with the details of the more classical VB model until we have been able to develop the tools necessary to continue in Chapter 21. 

The generalised valence bond (GVB) method, developed by Goddard in 1970, is one of the simplest and oldest valence bond methods that use flexible orbitals in a general way. The generalised Coulson-Fischer theory for the hydrogen molecule mentioned above is used to describe every electron pair in a molecule. The orbitals for each electron pair are expanded in terms of the full basis set and are non-orthogonal. Orbitals from different pairs are forced to be orthogonal. This condition simplifies the calculations but may lead to some difficulties [160,161],... 

Hunt WJ, Hay PJ, Goddard WA (1972) Self-consistent procedures for generalised valence bond wavefunctions. Applications H3, BH, H2O, C2H6 and O3. J Chem Phys 57 738-748... 

S. Clifford, M. J. Bearpark and M. A. Robb A hybrid MC-SCF method generalised valence bond (GVB) with complete active space SCF (CASSCF), Chem. Phys. Lett. 256, 320-326 (1996). 

The London equation has in addition been the progenitor of semi-empirical (or semi-theoretical) valence-bond methods of which Moffitt s method of atoms in molecules (95) and Ellison s method of diatomics in molecules(96), the latter not in fact being a direct generalisation of the former, are the most important. It is beyond the scope of this article to give the details of these methods and their modifications and the reader is referred to other reviews that encompass them (85, 97). It is however important to emphasize that they work by using relatively simple polyatomic wavefunctions and introducing corrections to the resulting Hamiltonian matrix... 

When the new orbitals are determined, the Valence Bond function is redetermined using Eq. (2), and the procedure is repeated until convergence is obtained, i.e. all by s in Eq. (6) are zero and the Generalised Brillouin theorem (Eq. (4)) is satisfied. 

Texts on alternative types of valence-bond theory include those of references 1 and 2. Reference 3 provides a review of modern ab initio methods and classical valence-bond approaches to electronic structure. References 4 and 5 provide reviews of generalised and spin-coupled valence-bond theory. Both of these theories can use delocalised orbitals that involve more than two atomic centres to accommodate the active-space electrons. In references 6-8, overviews are presented of aspects of increased-valence theory. 

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