VB model

Boranes are typical species with electron-deficient bonds, where a chemical bond has more centers than electrons. The smallest molecule showing this property is diborane. Each of the two B-H-B bonds (shown in Figure 2-60a) contains only two electrons, while the molecular orbital extends over three atoms. A correct representation has to represent the delocalization of the two electrons over three atom centers as shown in Figure 2-60b. Figure 2-60c shows another type of electron-deficient bond. In boron cage compounds, boron-boron bonds share their electron pair with the unoccupied atom orbital of a third boron atom [86]. These types of bonds cannot be accommodated in a single VB model of two-electron/ two-centered bonds. 

We often refer to Heitler and London s method as the valence bond (VB) model. A comparison between the experimental and the valence bond potential energy curves shows excellent agreement at large 7 ab but poor quantitative agreement in the valence region (Table 4.3). The cause of this lies in the method itself the VB model starts from atomic wavefunctions and adds as a perturbation the fact that the electron clouds of the atoms are polarized when the molecule is formed. 

The main features of the chemical bonding formed by electron pairs were captured in the early days of quantum mechanics by Heitler and London. Their model, which came to be known, as the valence bond (VB) model in its later versions, will serve as our basic tool for developing potential surfaces for molecules undergoing chemical reactions. Here we will review the basic concepts of VB theory and give examples of potential surfaces for bond-breaking processes. 

The approach presented above is referred to as the empirical valence bond (EVB) method (Ref. 6). This approach exploits the simple physical picture of the VB model which allows for a convenient representation of the diagonal matrix elements by classical force fields and convenient incorporation of realistic solvent models in the solute Hamiltonian. A key point about the EVB method is its unique calibration using well-defined experimental information. That is, after evaluating the free-energy surface with the initial parameter a , we can use conveniently the fact that the free energy of the proton transfer reaction is given by... 

Valence bond diagrams, for SN2 reactions, 60 Valence bond (VB) model for diatomic molecules, 15-22 empirical (EVB), 58-59 EVB mapping potential, 87, 88... 

FM model (see le l i at exp. geom. 11 In parenthesis the ratio with ihe corresponding VB model values. 

We can show the relationships among the state components pictorially (see Figure 16.17). Because the VBS is a spec of its implementation, we should be able to replicate the VBS model in the implementation and show how its links are all redundant. The invariants that relate the implementation and specification models are called retrievals. 

The minimal basis calculation on the hydrogen molecule is a well-worn but eminently suitable example for our purposes. It has a convenient symmetry element and orbital basis calculations can be carried through which are quantitatively acceptable and yet not prohibitively unwiedly to report. We give below variational calculations on the H2 molecule using the familiar simplest AO basis in the one-electron-group (MO) model and the electron-pair (VB) model. These calculations have been performed explicitly to investigate the effect of symmetry constraints . 

MO or VB models. Occasionally atom-in-molecule orbital exponents are used (principally for H atoms, using 1.2) but it is unusual to see any interpretation of this fact. 

The electron transfer properties of nickel 1,2-dithiolenes Ni(R2C2S2)" have been extensively studied in recent years, but there is still much controversy concerning the nature of the bonding in these complexes. On the basis of a simple VB model neutral and binegative species (87) may be assumed to contain the metal in the oxidation state +2, mononegative species may contain either nickel(II) or nickel (III), and trinegative species are assumed to contain nickel(I). 

The frequency exaltation of the Kekule mode is mirrored by the structural manifestations in the twin states, discussed with reference to Figures 16 and 17. Thus, the repulsive jr-curve in the ground state softens the potential and thereby enables the ground-state molecule to distort along the Kekule mode when angular strain is exerted. In contrast, the attractive jr-curve in the twin excited state stiffens the potential and restores the local Deh symmetry of the benzene nucleus. The two physical effects are in perfect harmony and find a natural reflection in the VB model. 

Zhu, J., Li, H., Korchinski, M. and Fellin, P. (2005) Prediction of initial emission rates of 2-butoxyethanol from consumer products using equilibrium headspace concentrations an appliacation of the vapor pressure and boundary layer (VB) model. Environmental Science and Technology, 39, 8214-19. 

VB model, though successful for the interactions between monovalent atoms, breaks down when 71 bonds are considered. The aim of this chapter is to bring a quantitative answer to a question which can be so summarized What is the nature of the driving force which makes benzene more stable in a D6h geometry than in an alternated Dih geometry of Kekule type Exactly the same type of question applies to the allyl radical which will also be investigated and will allow the study of the effects of configuration interaction (Cl) and basis set extension. 

Here we skim over the field of semiempirical VB theory of the Jt-systems of benzenoids. Primary focus is on a systematic derivational development of a hierarchical sequence of VB models. Different VB-based models are addressed in different sections (2, 3,5, 6) here, and the overall development is summarized in the diagram at the conclusion of Sect. 7. Section 4 serves as an interlude on quantum chemical computational methods, with emphasis on the VB basis and its relationship to chemical structure — this being crucial for the following sections. Along the way we indicate some of the history and general characteristics of the models. The unifying view which emerges not only incorporates many aspects of past work but reveals avenues for future research. 

Overall the present article seeks to meld chemical graph-theoretic (chemicalbonding) ideas with conventional quantum-chemical approaches, all within the framework of traditional VB theory here extended to encompass more recent results and models. Thence use is made of some quantum-chemical nomenclature, which, however, is standard fare in any of a number of quantum chemistry texts, though they seldom seriously discuss VB models for Jt-network systems. Some effort is made to incorporate solid-state theoretic results on one of the models which has arisen with different applications in mind. As such, the present article offers a novel global perspective which (as is so often the case) emphasizes the author s own work in the area. 

The primitive VB model is defined in terms of overlap and Hamiltonian matrix elements over the basis states of eqn. (2.1.3). For fixed there are 2N possible spin-product functions so that this gives the dimension of the model s space. Indeed (though not originally formulated in this manner) the model may be mathematically represented entirely in spin space, despite the fundamental spin-free nature of the interactions. One may introduce a spin-space overlap operator by integrating out the spin-free coordinates... 

The overlap operator of the primitive VB model may be rigorously transformed away. Indeed, the eigenvalue problem of (2.2.1) is seen to be equivalent to... 

A point of some confusion is that there are different representations of the Pauling-Wheland VB model. In fact, Pauling and Wheland [1] did not represent it in the form of Eq. (3.1.10), but rather they presented it as a matrix on the Rumer basis (mentioned in Sect. 4.2 here). The appearance of (3.1.10) may be further modified through the use of the Dirac identity [25]... 

Though the exact solution of the Pauhng-Wheland VB model (or the positive-./ Heisenberg spin Hamiltonian) is generally a nontrivial matter, there are a number... 

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