Empirical VB

An alternative stream came from the valence bond (VB) theory. Ovchinnikov judged the ground-state spin for the alternant diradicals by half the difference between the number of starred and unstarred ir-sites, i.e., S = (n -n)l2 [72]. It is the simplest way to predict the spin preference of ground states just on the basis of the molecular graph theory, and in many cases its results are parallel to those obtained from the NBMO analysis and from the sophisticated MO or DFT (density functional theory) calculations. However, this simple VB rule cannot be applied to the non-alternate diradicals. The exact solutions of semi-empirical VB, Hubbard, and PPP models shed light on the nature of spin correlation [37, 73-77]. 

EVB Empirical VB. A method used to construct the free energy profiles in enzymatic reactions. 

In the MO theory, the most reliable approach for the study of reaction pathways perhaps is CASSCF [12, 13], but multi-VBSCF is essentially at the same level with CASSCF [14]. Since a VB wave function can be expanded into the combination of numerous Slater determinants that are used to define configurations in the MO theory, the VB theory provides a very compact, accurate description for chemical reactions. While both MO and VB theories have their own advantages as well as disadvantages, in our opinions, there are some areas where the VB theory is particularly superior to the MO theory 1) the refinement of molecular mechanics force field 2) the development of empirical or semi-empirical VB approaches 3) the impact of intermolecular charge transfer or intramolecular electron delocalization on the structure and properties 4) the validation of classical chemical theories and concepts at the quantitative level 5) the elucidation of chemical reactions and excited states intuitively. 

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. 

While in this contribution we focused attention to k-Clar structures, and to their relation to the Hemdon-Hosoya type Clar structures, one can anticipate a number of interesting problems to emerge from the proposed innovation for Jt-aromatic sextets. It would be of interest to see, for instance, how k-Clar structures as a basis for semi-empirical VB... 

VB functions have been championed by Warshel and his co-workers for use in studying reactions in enzymes and in solution. The method, which they term the empirical VB (EVB) method, supposes that the wave-function for a particular problem, i/>,can be written as a linear combination of the wavefunctions of resonant forms, v i, which are postulated to be important in the process. For example, for a bond breaking reaction, AB — A+ + B, which produces ionic products, the contributing resonant forms could be the covalent, AB, and ionic, A B+,states that dissociate to atoms and ions respectively. The total wavefunction is ... 

The status of cyclobutadiene as a putative member of the aromatic series was now able to be studied by a method free of the gross approximations of the empirical VB and MO methods. It was already known that cyclooctatetraene, the next in the series of 4n electron systems, was not aromatic, that it behaved as a poly-olefin, but the situation was confused by the fact that there was non-planarity forced by the a-framework. Wheland [209] had shown that in cyclobutadiene the empirical descriptions by MO and VB methods were in conflict in a unusual way. The VB picture was that cyclobutadiene was stabilized by resonance, with a (Pauling)... 

The VB approach has been particularly popular for studies of 7r-electron systems, mostly using semi-empirical techniques. We shall, however, concentrate on a few of the semi-empirical VB treatments that have been used to obtain potential surfaces for reactive systems. 

Zeiri et al. have reported an ambitious application of a semi-empirical VB formalism to dissociative electron transfer on ionic surfaces They studied electron transfer from a charged AgBr surface to Ag ions and from Br"" ions to AgBr surface holes. With very few VB structures it is possible to describe such complex processes quite well. 

As mentioned above, a detailed comparison between such a semi-empirical VB method and a DIM calculation for a system such as K -f- Brj would be very worth while to ascertain the relative merits of these approaches. 

Alternatively, the height of the crossing point can be calculated with any MO-based method, by determining the energy of the reactant wave function at zero iteration (see Appendix 23A), by constrained optimization of block-localized wavefunctions [44], or by an energy decomposition scheme of the Morokuma-analysis type [45]. Lastly, the height of the crossing point can be computed by means of molecular mechanical methods [46], or related empirical VB calculations [47,48]. 

Valence bond theory enables a very straightforward account of environmental effects, such as those imparted by solvents and/or protein pockets. A major contribution to the field was made by Warshel who created an empirical VB (EVB) method. By incorporating van der Waals and London interactions... 

What keeps various graph theoretical and semi-empirical VB models alive is that the concepts involved in these models are expressed by a language that is commonly understood in chemistry, which includes such basic structural elements as atoms, bonds, rings, and various molecular fragments, such as the bay region or the pharmacophores, which are of interest in structure—bioactivity studies. In this article we will focus on aromaticity in hydrocarbons, and in particular the aromaticity of benzenoid hydrocarbons, and will see that there is some theoretical justification to expect the fully benzenoid 6n 7r-elec-tron systems of Clar to be the most aromatic polycyclic hydrocarbons. The reason that we have confined our attention to conjugated hydrocarbons is... 

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