Valence bond method, electronic structure

There are two principal methods available for the quantum mechanical treatment of molecular structure, the valence bond method and the molecular orbital method. In this paper we shall make use of the latter, since it is simpler in form and is more easily adapted to quantitative calculations.3 We accordingly consider each electron... 

Most of the commonly used electronic-structure methods are based upon Hartree-Fock theory, with electron correlation sometimes included in various ways (Slater, 1974). Typically one begins with a many-electron wave function comprised of one or several Slater determinants and takes the one-electron wave functions to be molecular orbitals (MO s) in the form of linear combinations of atomic orbitals (LCAO s) (An alternative approach, the generalized valence-bond method (see, for example, Schultz and Messmer, 1986), has been used in a few cases but has not been widely applied to defect problems.)... 

Under the Born-Oppenheimer approximation, two major methods exist to determine the electronic structure of molecules The valence bond (VB) and the molecular orbital (MO) methods (Atkins, 1986). In the valence bond method, the chemical bond is assumed to be an electron pair at the onset. Thus, bonds are viewed to be distinct atom-atom interactions, and upon dissociation molecules always lead to neutral species. In contrast, in the MO method the individual electrons are assumed to occupy an orbital that spreads the entire nuclear framework, and upon dissociation, neutral and ionic species form with equal probabilities. Consequently, the charge correlation, or the avoidance of one electron by others based on electrostatic repulsion, is overestimated by the VB method and is underestimated by the MO method (Atkins, 1986). The MO method turned out to be easier to apply to complex systems, and with the advent of computers it became a powerful computational tool in chemistry. Consequently, we shall concentrate on the MO method for the remainder of this section. 

The precise quantum cluster calculations of the electronic structure of SC ceramics were performed in Refs. [13,17,21]. Guo et al. [13] used the generalized valence bond method, Martin and Saxe [17] and Yamamoto et al. [21] performed calculations at the configuration interaction level. But in these studies the calculations were carried out for isolated clusters, the second aspect of the ECM scheme, see above, was not fulfilled. The influence of crystal surrounding may considerably change the results obtained. 

In the valence-bond method, a wave equation is written for each of various possible electronic structures that a molecule may have (each of these is called a canonical form), and the total is obtained by summation of as many of these as seem plausible, each with its weighting factor ... 

The second method of discussing the electronic structure of molecules, usually called the valence-bond method, involves the use of a wave function of such a nature that the two electrons of the electron-pair bond between, two atoms tend to remain on the two different atoms. The prototype of this method is the Heitler-London treatment of the hydrogen a olecule, which we shall now discuss. 

IN the past twenty years the electronic structures of many organic molecules, particularly benzene and related compounds, have been discussed in toms of the molecular orbital and valence bond methods.1 During the same period the structures of inorganic ions have been inferred from the bond distances f a bond distance shorter than the sum of the conventional radii has been attributed to the resonance of double bonded structures with the single bonded or Lewis structure. 

The valence bond method has not been used as widely as the molecular orbital approach. With the inclusion of polar structures, however, the valence bond method gives correct orientation for electrophilic substitution and a calculated dipole moment close to the experimental value.100 An application of the one-center method of the 7r-electron system of pyrrole gives electron densities of 1.612, 1.167, and 1.028 on the nitrogen atom and the a- and /3-carbon atoms, respectively.101 Transition energies and the dipole moment by this method are in accord with the observed values. 

The quantum mechanical methods described in this book are all molecular orbital (MO) methods, or oriented toward the molecular orbital approach ab initio and semiempirical methods use the MO method, and density functional methods are oriented toward the MO approach. There is another approach to applying the Schrodinger equation to chemistry, namely the valence bond method. Basically the MO method allows atomic orbitals to interact to create the molecular orbitals of a molecule, and does not focus on individual bonds as shown in conventional structural formulas. The VB method, on the other hand, takes the molecule, mathematically, as a sum (linear combination) of structures each of which corresponds to a structural formula with a certain pairing of electrons [16]. The MO method explains in a relatively simple way phenomena that can be understood only with difficulty using the VB method, like the triplet nature of dioxygen or the fact that benzene is aromatic but cyclobutadiene is not [17]. With the application of computers to quantum chemistry the MO method almost eclipsed the VB approach, but the latter has in recent years made a limited comeback [18],... 

G. W. Wheland, Proc. R. Soc. London, Ser. A 159, 397 (1938). The Electronic Structure of Some Polyenes and Aromatic Molecules. V—A Comparison of Molecular Orbital and Valence Bond Methods. 

P. C. Hiberty, in Modern Electronic Structure Theory and Applications in Organic Chemistry, E. R. Davidson, Ed., World Scientific, River Edge, NJ, 1997, pp. 289-367. The Breathing Orbital Valence Bond Method. 

On the theoretical side the H20-He systems has a sufficiently small number of electrons to be tackled by the most sophisticated quantum-chemical techniques, and in the last two decades several calculations by various methods of electronic structure theory have been attempted [77-80]. More recently, new sophisticated calculations appeared in the literature they exploited combined symmetry - adapted perturbation theory SAPT and CCSD(T), purely ab initio SAPT [81,82], and valence bond methods [83]. A thorough comparison of the topology, the properties of the stationary points, and the anisotropy of potential energy surfaces obtained with coupled cluster, Moller-Plesset, and valence bond methods has been recently presented [83]. 

In MO theory the orbitals are usually very delocalised, containing contributions from many, if not all, of the atoms in the system. This contradicts the intuitive notion that the electronic structure for the full system should be only slightly perturbed from that of its constituent atoms. Valence bond methods seek to correct this by using orbitals that are highly localised and which often resemble atomic orbitals. Wavefunctions constructed from such orbitals have the conceptual advantage that they can often be identified di-... 

Molecular orbital theory differs from valence bond theory in that it does not require the electrons involved in a bond to be localized between two of the atoms in a molecule. Instead, the electron occupies a molecular orbital, which may be spread out over the entire molecule. As in the valence bond approach, the molecular orbital is formed by adding up contributions from the atomic orbitals on the atoms that make up the molecule. This approach, which does not explicitly model bonds as existing between two atoms, is somewhat less appealing to the intuition than the valence bond approach. However, molecular orbital calculations typically yield better predictions of molecular structure and properties than valence bond methods. Accordingly, most commercially available quantum chemistry software packages rely on molecular orbital methods to perform calculations. 

The use of the valence-bond method sheds an interesting light on the situation. Applying this method leads to the electronic structure shown in Figure 1.20. Since... 

Quantum theory provides us with two fundamental methods for the study of the electronic structure of molecules the valence-bond method, whose simplified qualitative version is referred to frequently as the resonance theory, and the molecular-orbital method. Both represent approximate procedures for obtaining approximate solutions of the Schrddinger equation relative to molecules. This equation is the basic equation of the quantum theory and its resolution provides the electronic energy levels and the distribution of the electronic cloud in chemical systems. Approximate procedures are needed because we are unable, at present, to solve rigorously the Schro-dinger equation for any atomic or molecular system beyond the very simplest ones. 

Cooper, D. L. Cerratt, J. Raimondi, M. Nature 1986,323,699 reported a spin-coupled valence bond method for calculation of molecular electronic structure and concluded that "our results suggest that the Kekule description of benzene, as expressed in the classic VB form, is in fact much closer in reality than is a description in terms of delocalized molecular orbitals."... 

---