VB theory, classical

The purpose of this review is to discuss the main conclusions for the electronic structure of benzenoid aromatic molecules of an approach which is much more general than either MO theory or classical VB theory. In particular, we describe some of the clear theoretical evidence which shows that the n electrons in such molecules are described well in terms of localized, non-orthogonal, singly-occupied orbitals. The characteristic properties of molecules such as benzene arise from a profoundly quantum mechanical phenomenon, namely the mode of coupling of the spins of the n electrons. This simple picture is furnished by spin-coupled theory, which incorporates from the start the most significant effects of electron correlation, but which retains a simple, clear-cut visuality. The spin-coupled representation of these systems is, to all intents and purposes, unaltered by the inclusion of additional electron correlation into the wavefunction. 

For a system consisting of six electrons with a net spin of zero, = 5. For our present purposes, it is probably most useful to consider the modes of spin coupling in terms of the traditional basis of Rumer functions used in classical VB theory. For a discussion of different spin functions, and of the relationships between them, see... 

At first sight, the concepts presented in this chapter may seem a little odd if compared to classical VB theory. However, in adopting these new concepts, we can bring physico-chemical significance to the resonance concept, establishing a common line of reasoning with MO theory. This is important because once one begins to increase the sophistication of the calculations, the numerical differences between MO and VB theories tend to... 

The HF wavefunction takes the form of a single Slater determinant, constructed of spin-orbitals, the spatial parts of which are molecular orbitals (MOs). Each MO is a linear combination of atomic orbitals (LCAOs), contributed by all atoms in the molecule. The wavefunction in classical VB theory is a linear combination of covalent and ionic configurations (or structures), each of which can be represented as an antis5nnmetrised product of a string of atomic orbitals (AOs) and a spin eigenfunction. The covalent structures recreate the different ways in which the electrons in the AOs on the atoms in the molecule can be engaged in bonding or lone pairs. An ionic structure contains one or more doubly-occupied AOs. Each of the structures within the classical VB wavefunction can be expanded in terms of several Slater determinants constructed from atomic spin orbitals. 

In contrast to MO approaches, having more than one basis function on an atomic centre is a major problem for classical VB theory. For example, if in the above-mentioned 7t-only VB description of benzene we decide to switch f rom a single- to a double-C basis, the number of covalent structures increases from 5 to 2 X 5 = 320 and, according to Weyl s dimension formula which gives the number of linearly independent configurations for N electrons distributed between M orbitals,... 

In the following section we present a general framework in which non-orthogonal orbitals are used to expand the exact wavefunction. This serves to explain the spin-coupled VB theory which is the basic motif of this chapter, and also to show how this reduces to classical VB theory on the one hand, and to the Cl expansion on the other. 

In Section IV results obtained so far by the spin-coupled VB theory are surveyed and in Section V we return somewhat briefly to classical VB theory. 

One conclusion that emerges from this survey is that the most useful features of the classical VB theory are utilized not necessarily in ab initio work, but in providing a framework for semi-empirical theories. These last are proving to be of real value in the interpretation of results of beam scattering experiments, and in the provision for dynamical studies of potential surfaces which possess the correct general features. 

The last sections are devoted to the application of VB theory to inter-molecular interactions. Since van der Waals forces are so weak compared to chemical forces, it is intuitively obvious that classical VB theory has much to offer in this context rather than a supermolecule approach. 

One of the most unacceptable features of classical VB theory is the proliferation of physically unreasonable ionic structures, whose role is to provide for deformation of the atomic functions when the molecule forms. As shown particularly clearly here, these are now unnecessary the spin-coupled wavefunction for benzene incorporates all the deformation required. 

The concept of resonance was introduced by Pauling in classical Valence-Bond (VB) theory, to take into account the fact that in some cases more than one Lewis stmcture can be written for a molecule. The most typical example of this situation is the benzene molecule which, in classical VB theory, is represented by a superposition (resonance) of the two Kekule stmctures ... 

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