Basicity Bond valence model

In Chapter 2 it was shown that the Madelung field of a crystal is equivalent to a capacitive electric circuit which can be solved using a set of Kirchhoff equations. In Sections 3.1 and 3.2 it was shown that for unstrained structures the capacitances are all equal and that there is a simple relationship between the bond flux (or experimental bond valence) and the bond length. These ideas are brought together here in a summary of the three basic rules of the bond valence model, Rules 3.3, 3.4, and 3.5. 

A closer comparison of bond valence and electron density models is not possible because of the different underlying assumptions of the models. The forces in the bond valence model act between structureless point atoms, but the forces in the electron density model are exerted by electrons on nuclei and vice versa. This basic difference makes it difficult to compare the two models in greater detail. They are best seen as complementary, the electron density model providing important information about the nature of the bonding between the atoms, the bond valence model providing a simple tool for predicting structure and properties, particularly in cases where the structure is complex. 

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. 

In our theoretical formulation for PCET [26, 27], the electronic structure of the solute is described in the framework of a four-state valence bond (VB) model [41]. The most basic PCET reaction involving the transfer of one electron and one proton may be described in terms of the following four diabatic electronic basis... 

In Section 1.1 we described the basic bonding patterns of organic molecules and the properties of different types of localized bonds. The concepts introduced were mostly fairly classical valence bond concepts. They have definite predictive power, and that is an important measure of the value of any model. However, the picture we are about to present also has the... 

A simple connection table, consisting of a list of atoms (with types, charges, etc.) and their bonds (with bond orders). (All programs to date have operated on a basic valence model, as epitomized by the connection table.)... 

Valence band spectra provide information about the electronic and chemical structure of the system, since many of the valence electrons participate directly in chemical bonding. One way to evaluate experimental UPS spectra is by using a fingerprint method, i.e., a comparison with known standards. Another important approach is to utilize comparison with the results of appropriate model quantum-chemical calculations 4. The combination with quantum-chcmica) calculations allow for an assignment of the different features in the electronic structure in terms of atomic or molecular orbitals or in terms of band structure. The experimental valence band spectra in some of the examples included in this chapter arc inteqneted with the help of quantum-chemical calculations. A brief outline and some basic considerations on theoretical approaches are outlined in the next section. 

Further analysis is based on the idea that the characteristic experimental behavior of different classes of compounds and the suitability of those or other models used to describe this behavior is ultimately related to the extent to which the chromophores or electron groups physically present in the molecular system are reflected in these models. It is easy to notice, that the MM methods work well in case of molecules with local bonds designated in Table 1 as valence bonds the QC methods apply both to the valence bonded systems, and for the systems with delocalized bonds (referred as orbital bonds in Table 1). The TMCs of interest, however, not covered either by MM or by standard QC techniques can be physically characterized as those bearing the d-shell chromophore. The magnetic and optical properties characteristic for TMCs are related to d- or /-states of metal ions. The basic features in the electronic structure of TMCs of interest, distinguishing these compounds from others are the following ... 

In the last few years, the polarizable continuum model for the study of solvation has been extended to consider multideterminantal wavefunctions. Such novel techniques allow the study of the most important solvent effects on chemical reactions. In this context, the valence bond theory provides a way to analyze such effects through the transcription of the, generally, complicated multiconfigurational wavefunctions into sums of few selected classical structures, which are, in fact, more useful to understand the electron distribution rearrangement along a reaction path. In this chapter, the valence bond analysis of CASSCF wavefunctions calculated for chemical reactions in solution is discussed in details. By way of example, the results for some basic chemical processes are also reported. 

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