Ab initio VB theory

Despite the VB-theoretic successes of recent decades there still seems a domination by MO theory. Ab-initio VB theory seems weak in comparison to ab-initio MO-based theory in consideration of general availability of canned programs. Semi-empirical VB theory (the simplest versions of which are the focus of the present chapter) seems weak in comparison to semi-empirical MO-based theory when consideration is made of a comprehensive semiempirical model to make quantitative estimates for heats of formation, geometries, or excitation spectra, all for a diversity of chemical species. 

In Table 1 are collected details of the major applications of ab initio VB theory over the past decade or so. A number of general comments may usefully be made. For a given basis set, a properly optimized VB calculation with non-orthogonal orbitals converges on to the result given by full interaction of all possible structures considerably more rapidly than a calculation... 

Table 1 Recent major applications of ab initio VB theory Molecule Remarks Ref.

It was questions like these that indicated to me that the existing skeleton of conceptual applied quantum chemistry had to be replaced by a different framework. It was then that I realized that ab initio VB theory had little to do with Resonance Theory, even in a qualitative sense, and that, as a result, one should expect conventional concepts (based on Resonance Theory) to be intuitive guesses rather than theoretically... 

The question is whether or not these reliable predictions of quantitative VB theory may also arise from a qualitative VB theory. Early semiempirical HLVB calculations by Wheland (14,15) and for that matter any VB calculations with only HL structures, incorrectly predict that CBD has resonance energy larger than that of benzene. Wheland, who analyzed the CBD problem, concluded that ionic structures play an important role, and that their inclusion would probably correct the VB predictions. Indeed the above mentioned successful ab initio VB calculations implicitly include ionic structures due to the use of CF orbitals in the VB descriptions of benzene, CBD, and COT. As will be immediately seen, ionic structures are indeed essential for understanding the difference between aromatic and antiaromatic species, such as benzene, CBD, and COT. Furthermore, the inclusion of ionic structures bring in some novel insight into other features of these molecules, such as ring currents, and so on (see Exercise 5.4). 

Another features in this book is the description of the main methods and programs available today for ab initio VB calculations, and how actually one may plan and run VB calculations. In this sense, the book provides a snapshot of the current VB capabilities in 2007. Regrettably, much important work had to be left out. The readers interested in technical and theoretical development aspects of VB theory may wish to consult two other monographs (4,5). 

A spin-free approach for valence bond (VB) theory, based on symmetric group techniques, is introduced in this chapter. Bonded tableaux (BT) are adopted to represent VB structures, and a paired-permanent-determinant algorithm is developed to solve the so-called IV problem in the nonorthogonal VB method, followed by the introduction of our ab initio VB program, Xiamen-99. Furthermore, applications of ab initio VB method to the resonance effect, chemical reactions, and excited states are carried out by the Xiamen package. 

With the advent of the computer era, it is now possible to reexamine and rethink the resonance theory at the ab initio level. For example, throughout Pauling and Wheland s books, benzene is supposed to be a hybrid of two Kekule structures, by noting that Dewar and other ionic structures make little contribution to the resonance in benzene. However, classical ab initio VB calculations with all possible 175 resonance structures by Norbeck et al. [51] and Tantardini et al. [3], where strictly atomic orbitals are used to construct VB functions, manifested that the five covalent Kekule and Dewar structures make even less contribution to the ground state of benzene than the other 170 ionic structures. This prompts us to reconsider the mathematical formulations for resonance structures [52]. 

This chapter is aimed at the nonexpert and designed as a tutorial for faculty and students who would like to teach and use VB theory, but possess only a basic knowledge of quantum chemistry. As such, an important focus of the chapter will be the qualitative wisdom of the theory and the way it applies to problems of bonding and reactivity. This part will draw on material discussed in previous works by the authors. Another focus of the chapter will be on the main methods available today for ab initio VB calculations. However, much important work of a technical nature will, by necessity, be left out. Some of this work (but certainly not all) is covered in a recent monograph on VB theory. ... 

The ab initio calculations of various three-electron hemibonded systems [122, 123] indicated that the inclusion of electron correlation corrections is extremely important for the calculation of three-electron bond energies. The Hartree-Fock (HF) error is found to be nonsystematic and always large, sometimes of the same order of magnitude as the bond energy. According to valence bond (VB) and MO theories, the three-electron bond is attributed to a resonance between the two Lewis structures... 

Modem valence bond (VB) theories such as Spin-Coupled theory, together with DFT and Molller-Plesset MO methods, and ab initio molecular dynamics, were employed to study structure/dynamics in representative carbonium ions. 

This is a book on ab initio valence bond (VB) theory. There is a vast literature on valence bond theory - much of it devoted to semiempirical and qualitative... 

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