Valence bond VB method

Simonetta and Heilbronner (1964) recently carried out calculations by the valence bond (VB) method for some simple cations, and compared the results obtained by this method, inter alia, with the results of Colpa and collaborators (1963) and of Koutecky and Paldus (1963). In the case of the proton addition complexes of mesitylene and cyclohepta-triene, the electron excitation energies calculated by the VB method agree very well with experiments, and also agree to a good approximation with the results of Cl calculations. The calculations also successfully reproduce the electron density of the cycloheptatriene cation. In this, a perturbation calculation allowed for the AO s adjoining the —CHg—CH2-lihkage. 

The approach used first, historically, and the one this book is about, is called the valence bond (VB) method today. Heitler and London[8], in their treatment of the H2 molecule, used a trial wave function that was appropriate for two H atoms at long distances and proceeded to use it for all distances. The ideal here is called the separated atom limit . The results were qualitatively correct, but did not give a particularly accurate value for the dissociation energy of the H—H bond. After the initial work, others made adjustments and corrections that improved the accuracy. This is discussed folly in Chapter 2. A cmcial characteristic of the VB method is that the orbitals of different atoms must be considered as nonorthogonal. 

An alternative to the SCF MO approach is the valence-bond (VB) method, which is discussed in most quantum-chemistry texts. 

Shortly after quantum mechanics evolved Heitler and London[l] applied the then new ideas to the problem of molecule formation and chemical valence. Their treatment of the H2 molecule was qualitatively very successful, and this led to numerous studies by various workers applying the same ideas to other substances. Many of these involved refinements of the original Heitler-London procedure, and within three or four years, a group of ideas and procedures had become reasonably well codified in what was called the valence bond (VB) method for molecular structure. 

A natural way to study aromaticity would be to make use of the concept of two structures, as introduced by Kekule. The first to use this view were Pauling and Wheland [47]. They used an approximate form of the valence bond (VB) method developed by Heitler and London [48], for describing the aromaticity of benzene. 

Historically, the first calculation of the electronic structure of a neutral molecule was carried out by Heitler and London [15], who treated H2 using the valence bond (VB) method. In this early paper, the molecular wave function for H2 was considered to be purely covalent, and constructed from the atomic orbitals (AO s) %a and %b of the separate atoms. Dropping the normalization constant hereafter, the wave function is given in equation 1. 

Although the emphasis in ab initio calculations in recent years has been on calculations using the MO approach, alternative methods have not been neglected, particularly Valence Bond (VB) methods of various types. Particularly promising has been the work of Goddard and co-workers with the so-called Generalized Valence Bond (GVB) method.13... 

The computational schemes of quantum chemistry are based either on molecular orbital (MO) or valence bond (VB) methods (5). MO cpt is defined as an one-electron wave function describing an electron in some effective field of nuclei and other electrons. It is usually represented as a linear combination of atomic orbitals Xk (LCAO) ... 

I was inspired too by Linus Pauling (1901-94), another polymath with humanistic concerns. His Nature of the Chemical Bond (1939) brought a new perspective to theories of molecular structure, and refuted the implication of a popular examination question of the time, Is inorganic chemistry a largely closed and finished subject Pauling s resonance theory, formally based on the quantum-mechanical valence-bond (VB) method for... 

In the present work a simple London formula for application of the valence bond (VB) method to the tree-center problem [28] is used in order to stress the importance of triplet excited states of the activating molecule in the catalysis by TM atoms and complexes. Activation of the C-H bond in methane is considered as a conceivable example illustrating essential features of spinuncoupling in catalysis. Theoretically studied reactions of hydrocarbons with the second-row TM atoms [15] are used for illustration of new features. 

The quantum mechanical methods described in this book are all molecular orbital (MO) methods, or oriented toward the MO approach ab initio and SE 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 (VB) method. Basically the MO method allows atomic orbitals (AOs) to interact to create the MO of a molecule, and does not focus on individual bonds as shown in conventional structural formulas. The VB method, on the otherhand, 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... 

In constructing the spatial part of the electronic wave function the Valence-Bond (VB) method is useful. This method (similar to the Heitler-London approach) postulates that a linear combination of several product functions (called covalent structures or ionic structures ) is appropriate... 

Slater determinants are usually constructed from molecular spinorbitals. If, instead, we use atomic spinorbitals and the Ritz variational method (Slater determinants as the expansion functions), we would get the most general formulation of the valence bond (VB) method. The beginning of VB theory goes back to papers by Heisenbeig, the first application was made by Heitler and London, and later theory was generalized by Hurley, Lennard-Jones, and Pople. The essence of the VB method can be explained by an example. Let us take the hydrogen molecule with atomic spinorbitals of type liaO and Vst (abbreviated as aa and b ) centered at two nuclei. Let us construct from them several (non-normalized) Slater determinants, for instance ... 

There are two approximate starting points in quantum chemistry the molecular orbital (MO) and valence bond (VB) methods. The MO theory derived from the Huckel treatment ignores the interactions between the electrons, whereas the VB theory forms the basis for the electron-paired chemical bond, and for the resonance concept [14]. In MO theory the electrons are delocalized (without any correlation), as contrasted to VB theory, where they are supposed to be localized. 

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