Roots of VB Theory

The roots of VB theory in chemistry can be traced to the famous paper of Lewis The Atom and The Molecule / which introduces the notions of electron-pair bonding and the octet rule. Lewis was seeking an understanding of weak and strong electrolytes in solution, and this interest led him to formulate the concept of the chemical bond as an intrinsic property of the molecule that varies between the covalent (shared-pair) and ionic situations. Lewis paper predated the introduction of quantum mechanics by 11 years, and constitutes 

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The notion of resonance was based on the work of Heisenberg, who showed that, since electrons are indistinguishable particles then, for a two-electron system, with two quantum numbers n and m, there exist two wave 

The success of the HL model and its relation to Lewis model, posed a wonderful opportunity for the young Pauling and Slater to construct a general quantum chemical theory for polyatomic molecules. They both published, in the same year, 1931, several seminal papers in which they each developed the notion of hybridization, the covalent-ionic superposition, and the resonating benzene picture.Especially effective were Pauling s papers that linked the new theory to the chemical theory of Lewis, and that rested on an encyclopedic command of chemical facts. In the first paper, Pauling presented the electron-pair bond as a superposition of the covalent HL form and the two 

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Modem quantum-mechanical Valence-Bond (VB) theory has firm roots back to classical ideas even of a century and a half ago. These connections are of special interest, especially if greater general insight and extension of the classical concepts can be made. The interconnecting simpler semiempirical approaches, such as are of the prime focus here, are historically inextricably mixed with that of the ab initio theory, and the development has been via a peculiarly torturous road toward quantitative relevance. Thence here some brief historical commentary which also sets some nomenclature and ideas is first made. 

Valence-Bond (VB) and Molecular-Orbital (MO) theories both were clearly formulated by the end of the first decade of quantum mechanics. Of course VB theory is connected to early conceptual roots in chemistry, as emphasized by Rumer [1] and more particularly by Pauling, in a review [2] and then in his masterwork [3] The Nature cfiJte Chemical Bond. Thence for some jjeriod of time VB theory seems in the chemical community to have been viewed quite favorably. 

It has been found that the square root of the last coefficient of the characteristic polynomial in Hiickel molecular orbital theory [4], which can be computed as the determinant of the HMO matrix, gives the number of Kekule valence structures of benzenoid hydrocarbons. This is one of a few very intriguing relationships connecting the valence bond (VB) method and molecular orbital (MO) method of quantum chemistry [5,6]. 

In this paper a method [11], which allows for an a priori BSSE removal at the SCF level, is for the first time applied to interaction densities studies. This computational protocol which has been called SCF-MI (Self-Consistent Field for Molecular Interactions) to highlight its relationship to the standard Roothaan equations and its special usefulness in the evaluation of molecular interactions, has recently been successfully used [11-13] for evaluating Eint in a number of intermolecular complexes. Comparison of standard SCF interaction densities with those obtained from the SCF-MI approach should shed light on the effects of BSSE removal. Such effects may then be compared with those deriving from the introduction of Coulomb correlation corrections. To this aim, we adopt a variational perturbative valence bond (VB) approach that uses orbitals derived from the SCF-MI step and thus maintains a BSSE-free picture. Finally, no bias should be introduced in our study by the particular approach chosen to analyze the observed charge density rearrangements. Therefore, not a model but a theory which is firmly rooted in Quantum Mechanics, applied directly to the electron density p and giving quantitative answers, is to be adopted. Bader s Quantum Theory of Atoms in Molecules (QTAM) [14, 15] meets nicely all these requirements. Such a theory has also been recently applied to molecular crystals as a valid tool to rationalize and quantitatively detect crystal field effects on the molecular densities [16-18]. 

The method is referred to simply as GMCSC when a fixed basis set is used. In this case, it can be viewed as a non-orthogonal variant of the Multiconfiguration Self-Consistent Field (MCSCF) approach. However, GMCSC s methodological roots are firmly planted in the Modem VB camp, and more specifically in the late Joe Gerratt s Spin-Coupled theory [3]-[4]. 

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