Generalized resonating valence bond method

We have used the concepts of the resonance methods many times in previous chapters to explain the chemical behavior of compounds and to describe the structures of compounds that cannot be represented satisfactorily by a single valence-bond structure (e.g., benzene, Section 6-5). We shall assume, therefore, that you are familiar with the qualitative ideas of resonance theory, and that you are aware that the so-called resonance and valence-bond methods are in fact synonymous. The further treatment given here emphasizes more directly the quantum-mechanical nature of valence-bond theory. The basis of molecular-orbital theory also is described and compared with valence-bond theory. First, however, we shall discuss general characteristics of simple covalent bonds that we would expect either theory to explain. 

RGVB resonating generalized valence bond method... 

A. F. Voter, W. A. Goddard, III, Chem. Phys. 57, 253 (1981). A Method for Describing Resonance between Generalized Valence Bond Wavefunctions. 

The Generalized Multistructural Wave Function (GMS) [1,2] is presented as a general variational many-electron method, which encompasses all the variational MO and VB based methods available in the literature. Its mathematical and physico-chemical foundations are settled. It is shown that the GMS wave function can help bringing physico-chemical significance to the classical valence-bond (VB) concept of resonance between chemical structures. The final wave functions are compact, easily interpretable, and numerically accurate. 

From the conceptual point of view, there are two general approaches to the molecular structure problem the molecular orbital (MO) and the valence bond (VB) theories. Technical difficulties in the computational implementation of the VB approach have favoured the development and the popularization of MO theory in opposition to VB. In a recent review [3], some related issues are raised and clarified. However, there still persist some conceptual pitfalls and misinterpretations in specialized literature of MO and VB theories. In this paper, we attempt to contribute to a more profound understanding of the VB and MO methods and concepts. We briefly present the physico-chemical basis of MO and VB approaches and their intimate relationship. The VB concept of resonance is reformulated in a physically meaningful way and its point group symmetry foundations are laid. Finally it is shown that the Generalized Multistructural (GMS) wave function encompasses all variational wave functions, VB or MO based, in the same framework, providing an unified view for the theoretical quantum molecular structure problem. Throughout this paper, unless otherwise stated, we utilize the non-relativistic (spin independent) hamiltonian under the Bom-Oppenheimer adiabatic approximation. We will see that even when some of these restrictions are removed, the GMS wave function is still applicable. 

The BOVB method does not of course aim to compete with the standard ab initio methods. BOVB has its specific domain. It serves as an interface between the quantitative rigor of today s capabilities and the traditional qualitative matrix of concepts of chemistry. As such, it has been mainly devised as a tool for computing diabatic states, with applications to chemical dynamics, chemical reactivity with the VB correlation diagrams, photochemistry, resonance concepts in organic chemistry, reaction mechanisms, and more generally all cases where a valence bond reading of the wave function or the properties of one particular VB structure are desirable in order to understand better the nature of an electronic state. The method has passed its first tests of credibility and is now facing a wide field of future applications. 

It was mentioned above (p. 24) that Wheland o had developed a molecular orbital treatment which allowed for overlap between adjacent atomic orbitals. He found that inclusion of overlap made little difference in the calculated resonance energies of hydrocarbons, and this is generally to be expected i for bond orders and charge densities with this class of compounds. However, with heterocyclic molecules some differences do arise. Davies applied the method to a number of heterocyclic compounds and derived values for charge densities, bond orders and free valencies. The coulombic integral for nitrogen is now written + h[y where y = p ha... 

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