The valence bond VB model of bonding in

Valence bond theory considers the interactions between separate atoms as they are brought together to form molecules. We begin by considering the formation of H2 from two H atoms, the nuclei of which are labelled H. and Hg, and the electrons of which are 1 and 2, respectively. When the atoms are so far apart that there is no interaction between them, electron 1 is exclusively associated with H, while electron 2 resides with nucleus Hg. Let this state be described by a wavefunction -i/ i. 

When the H atoms are close together, we cannot teU which electron is associated with which nucleus since, although we gave them labels, the two nuclei are actually indistinguishable, as are the two electrons. Thus, electron 2 could be with and electron 1 with Hg. Let this be described by the wave-function 1p2- 

Equation 2.1 gives an overall description of the covalently bonded H2 molecule / covalent linear combination of wavefunctions and ip2- The equation contains a normalization factor, N (see Box 1.4). In the general case where  

Another linear combination of V l and V 2 can be written as shown in equation 2.2. 

The bond dissociation energy (At/) and enthalpy (A/t) values for H2 are defined for the process  

Equation 1.23 gives an overall description of the covalently bonded H2 molecule V covaient linear combination of 

In terms of the spins of electrons 1 and 2, tp+ corresponds to spin-pairing, and corresponds to parallel spins (nonspin-paired). Calculations of the energies associated with these states as a function of the intemuclear separation of Ha and Hb show that, while V - represents a repulsive state (high energy), the energy curve for tp+ reaches a 

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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. 

An alternative stream came from the valence bond (VB) theory. Ovchinnikov judged the ground-state spin for the alternant diradicals by half the difference between the number of starred and unstarred ir-sites, i.e., S = (n -n)l2 [72]. It is the simplest way to predict the spin preference of ground states just on the basis of the molecular graph theory, and in many cases its results are parallel to those obtained from the NBMO analysis and from the sophisticated MO or DFT (density functional theory) calculations. However, this simple VB rule cannot be applied to the non-alternate diradicals. The exact solutions of semi-empirical VB, Hubbard, and PPP models shed light on the nature of spin correlation [37, 73-77]. 

Figure 1. Simple chemical bonding model showing that unbound or partially bound atoms on a semiconductor surface contribute states within the band gap. The states of unbound atoms (a) are split upon partial bonding (b), then further split when the fully bound species (c) is formed. Evolution of the periodic lattice broadens the bonding states to form the valence band (vb) and the antibonding orbitals to form the conduction band (cb). In the process of band formation, the unbound and partially bound states (a and b) remain between vb and cb.

A recent summary of the history and dynamics of the theoretical models of benzene39 cites a view that even though the current molecular orbital (MO) view of benzene seems complete and ultimate while the valence bond (VB) view seems obsolete, the recent findings about zr-distortivity in benzene indicate that the benzene story is likely to take additional twists and turns that will revive the VB viewpoint (see footnote 96 in ref 39). What the present review will show is that the notion of delocalized zr-systems in Scheme 1 is an outcome of both VB and MO theories, and the chemical manifestations are reproduced at all levels. The use of VB theory leads, however, to a more natural appreciation of the zr-distortivity, while the manifestations of this ground state s zr-distortivity in the excited state of delocalized species provides for the first time a physical probe of a Kekule structure .3... 

Valence bond (VB) theories or empirical valence bond (EVB) methods have been developed in order to solve this problem with bond potential functions that (i) allow the change of the valence bond network over time and (ii) are simple enough to be used efficiently in an otherwise classical MD simulation code. In an EVB scheme, the chemical bond in a dissociating molecule is described as the superposition of two states a less-polar bonded state and an ionic dissociated state. One of the descriptions is given by Walbran and Kornyshev in modeling of the water dissociation process.4,5 As... 

In the preceding section, we discussed the electron pair (2c-2e) bond and how it can be influenced by Pauli repulsion of the SOMOs with other electrons. In the three-electron (2c-3e) bond, Pauli repulsion plays an even more fundamental role, as we will see.72 The idea of the three-electron bond was introduced in the early 1930s by Pauling in the context of the valence bond (VB) model of the chemical bond.70 71 Since then, it has been further developed both in VB and in MO theory and has become a standard concept in chemistry.118-129 In VB theory,7°>71 118 123 the two-center, three-electron (2c-3e) bond between two fragments A and B is viewed as arising from a stabilizing resonance between two valence bond structures in which an electron pair is on fragment A and an unpaired electron on B (13a), or the other way around (13b) ... 

The powerful interpretative framework of the Valence Bond (VB) theory has been exploited in several couplings and extensions with continuum models. We mention here the most relevant in the present context. 

The valence bond method with polarizable continuum model (VBPCM) method (55) includes solute—solvent interactions in the VB calculations. It uses the same continuum solvation model as the standard PCM model implemented in current ab initio quantum chemistry packages, where the solvent is represented as a homogeneous medium, characterized by a dielectric constant, and is polarizable by the charge distribution of the solute. The interaction between the solute charges and the polarized electric field of the solvent is taken into account through an interaction potential that is embedded in the... 

In the valence-bond (VB) model, this effect results from the fact that radicals of this type can be stabilized by resonance (Table 1.1, right). In the MO model, the stabilization of radical centers of this type is due to the overlap of the n system of the unsaturated substituent with the 2pz AO at the radical center (Figure 1.5). This overlap is called conjugation. 

Pauling always favored the Valence Bond (VB) theory over the Molecular Orbital (MO) theory for the description of the electronic structure of molecules, because the VB model resembles more the pre-quantum theoretical models of chemical bonding. However, modem quantum chemistry is dominated by MO theory, which has clearly prevailed in the computational applications. Nevertheless, a number of terms and concepts of VB theory still play an important role when it comes to the interpretation of the results of a quantum chemical calculation. 

In the empirical valence bond (EVB) model [304, 349, 370] a fairly small number of VB functions is used to fit a VB model of a chemical reaction path the parameterisation of these functions is carried out to reproduce experimental or ab initio MO data. The simple EVB Hamiltonian thus calibrated for a model reaction in solution can subsequently be used in the description of the enzyme-ligand complex. One of the most ingenious attributes of the EVB model is that the reduction of the number of VB resonance structures included in the model does not introduce serious errors, as would happen in an ab initio VB formulation, due to the parameterisation of the VB framework which ensures the reproduction of the experimental or other information used. This computationally efficient approach has been extensively used with remarkable success [305, 306, 371, 379] A similar method presented by Kim and Hymes [380] considers a non-equilibrium coupling between the solute and the solvent, the latter being treated as a dielectric continuum. 

The valence bond (VB) model grew out of the qualitative Tewis electron-pair model in which the chemical bond is described as a pair of electrons that is localized between two atoms. The VB model constructs a wave function for the bond by assuming that each atom arrives with at least one unpaired electron in an AO. The resulting wave function is a product of two one-electron wave functions, each describing an electron localized on one of the arriving atoms. The spins of the electrons must be paired to satisfy the Pauli exclusion principle. 

The valence bond picture for six-coordinate octahedral complexes involves d sp hybridization of the metal (Fig. 11.1c. d). The specific d orbitals that meet the symmetry requirements for the metal-ligand o-bonds are the four-coordinate t/ complexes discussed above, the presence of unpaired electrons in some octahedral compounds renders the valence level (n — )d orbitals unavailable for bonding. This is true, for instance, for paramagnetic [CoFJ (Fig. I l.lc). In these cases, the VB model invokes participation of n-level d orbitals in the hybridization. 

The two-form model has its roots in the valence-bond charge-transfer (VB-CT) model derived by Mulliken [84] and used with minor modifications by Warshel et al. for studying reactions in solutions [114]. Goddard et al. applied this VB-CT model to study the nonlinear optical properties of tire charge-transfer systems. [27, 59]. The analysis of the relationship between electronic and vibrational components of the hyperpolarizabilities within the two-state valence-bond approach was presented by Bishop et al. [17]. Despite the limitations of the VB-CT model, it is very simple and gives some insight into mutual relationships between nonlinear optical responses through the various orders. 

Another very important facet of theoretical considerations is interpretation of the phenomena under study. This is accomplished by quantum mechanical models, which yield simplified but quintessential picture of the molecular behavior [32]. In order to rationalize ortho-para directional ability of OH group let us make an inspection of the valence bond (VB) resonance structure of the benzenium ion (Fig.2). It appears that a depletion... 

Considerations like these mean that the VB model, although it has seen a considerable resurgence of interest over the past few years with several key breakthroughs being made, is still predominantly perceived as a specialist area with applications confined to smcJl numbers of electrons. The so-called Generalised Valence Bond (GVB) method which is a self-consistent development of the Heitler-London model is developed in Chapter 22 and, for the moment, this is as far as we shall go with the details of the more classical VB model until we have been able to develop the tools necessary to continue in Chapter 21. 

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