Molecular structure valence bond method

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... 

Resonance theory [15] contains essentially three assumptions beyond those of the valence bond method. Perhaps the most serious assumption is the contention that only unexcited canonical forms, non-polar valence bond structures or classical structures need be considered. Less serious, but no more than intuitive, is the proposition that the molecular geometry will take on that expected for the average of the classical structures. This is extended to the measurement of stability being greater the greater the number of classical structures. These concepts are still widely used in chemistry in very qualitative ways. 

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.)... 

Quantum-chemical cluster models, 34 131-202 computer programs, 34 134 methods, 34 135-138 for chemisorption, 34 135 the local approach, 34 132 molecular orbital methods, 34 135 for surface structures, 34 135 valence bond method, 34 135 Quantum chemistry, heat of chemisorption determination, 37 151-154 Quantum conversion, in chloroplasts, 14 1 Quantum mechanical simulations bond activation, 42 2, 84—107 Quasi-elastic neutron scattering benzene... 

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 theory of resonance should not be identified with the valence-bond method of making approximate quantum-mechanical calculations of molecular wave functions and properties. The theory of resonance is essentially a chemical theory (an empirical theory, obtained largely by induction from the results of chemical experiments). Classical structure theory was developed purely from chemical facts, without any help from physics. The theory of resonance was also well on... 

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. 

We have used the concepts of the resonance methods many times in previous chapters to explain the chemical behavior of compounds and to describe the structures of compounds that cannot be represented satisfactorily by a single valence-bond structure (e.g., benzene, Section 6-5). We shall assume, therefore, that you are familiar with the qualitative ideas of resonance theory, and that you are aware that the so-called resonance and valence-bond methods are in fact synonymous. The further treatment given here emphasizes more directly the quantum-mechanical nature of valence-bond theory. The basis of molecular-orbital theory also is described and compared with valence-bond theory. First, however, we shall discuss general characteristics of simple covalent bonds that we would expect either theory to explain. 

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],... 

Nevertheless, acknowledging or denying the existence of differences between resonance theory and classical structural theory was dependent on their different assessments of the role of alternative methods to study molecular structure. Wheland equated resonance theory to the valence bond method and viewed them as alternatives to the molecular orbital method. Pauling conceded that the valence bond method could be compared with the molecular orbital method, but not with... 

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. 

A wide range of theoretical methods has been applied to the study of the structure of small metal clusters. The extremes are represented on the one hand by semi-empirical molecular orbital (Extended Huckel) (8 ) and valence bond methods (Diatomics-In-Molecules) ( ) and on the other hand by rigorous initio calculations with large basis sets and extensive configuration interaction (Cl) (10). A number of approaches lying between these two extremes have been employed Including the X-a method (11), approximate molecular orbital methods such as CNDO (12) and PRDDO (13) and Hartree-Fock initio molecular orbital theory with moderate Cl. 

Either the molecular orbital or the valence bond method may be used to analyse the interaction of substituents on the reactant, products, and transition states. Substituents which stabilise the transition state more than reactants will accelerate the reaction, while those which stabilise the reactant more than transition state will slow down the reaction. In valence bond theory, the reactants are represented hy a nucleophile lone pair as an anion (Fig. 6-21, path a) and a neutral nucleophile (path b), and the carhonyl by the covalent and ionic re.sonance structures [70]. 

The valence-bond approach plays a very important role in the qualitative discussion of chemical bonding. It provides the basis for the two most important semi-empirical methods of calculating potential energy surfaces (LEPS and DIM methods, see below), and is also the starting point for the semi-theoretical atoms-in-molecules method. This latter method attempts to use experimental atomic energies to correct for the known atomic errors in a molecular calculation. Despite its success as a qualitative theory the valence-bond method has been used only rarely in quantitative applications. The reason for this lies in the so-called non-orthogonality problem, which refers to the difficulty of calculating the Hamiltonian matrix elements between valence-bond structures. 

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. 

In the two principal approaches to the valence structure of H2—the molecular orbital and valence bond methods—the molecular wavefunc-tions are written in terms of atomic Is functions. 

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."... 

Molecular structures and lattice structures are sometimes rationalized using the the valence bond method and the Lewis modeP with the octet rule. In these cases it is necessary to invoke concepts such as resonance or mesomerism. Such models are less convenient for technologists but are nevertheless summarized because they are so often used in a qualitative way to rationalize chemical bonding. The molecular orbital model is invaluable in assigning spectra. 

---