Valence bond theory classical

A single-determinant MO wave function for the H2 molecule within a minimum basis consisting of a single i -function on each nucleus is given in eq. (7.1) (see also Section 4.3). 

We have here ignored the normalization constants. The Slater determinant may be expanded in AOs, as shown in eq. (7.2). 

This shows that the HF wave function consists of equal amounts of ionic (XaXa and XbXb) and covalent (xaXb and XbXa) terms. In the dissociation limit only the covalent terms are correct, but the single-determinant description does not allow the ratio of covalent to ionic terms to vary. In order to provide a correct description, a second determinant is necessary. 

By including the doubly excited determinant I i, built from the antibonding MO, the amounts of the covalent and ionic terms may be varied, and this is determined completely by the variational principle (eq. (4.20)). 

This two-configurational Cl wave function allows a qualitatively correct description of the H2 molecule at all distances and in the dissociation Unfit, where the weights of the two configurations become equal. 

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Recognition has been made of some rather strongly worded criticism, from various sides, of the treatment of resonance of molecules among alternative valence-bond structures, as presented in earlier editions of this book, on the basis of its idealistic and arbitrary character, by the introduction of a section (Sec. 6-6) in which it is pointed out that the theory of resonance involves only the same amounts of idealization arid arbitrariness as the classical valence-bond theory. 

R. McWeeny, Int. J. Quant. Chem. 74, 87 (1999). An Ab Initio Form of Classical Valence Bond Theory. 

In classical Valence Bond theory, a bond is simply defined as a singlet coupled orbital (electron) pair. Thus, a single bond is obtained using ... 

There are many texts that make the point very clearly that the bonding in a molecule such as SFfi has very little to do with the availability of d atomic orbitals, but this is normally done in the context of MO theory, whereas the general ideas of utilizing d orbitals are much more closely allied with the ideas of classical valence bond theory. This, perhaps, is one of the reasons for the continued survival of such models. The purpose of this Chapter is to describe various calculations which have been performed using modern valence bond theory, in its spin-coupled form, resulting in a useful aide memoire which we term the democracy principle. We argue that there are no significant qualitative differences between the hypercoordinate nature of first-row, second-row and noble gas atoms in appropriate chemical environments. 

The basic idea of valence bond (VB) theory is very simple the wavefunctions for the electrons in a molecule are constructed directly from the wavefunctions of the constituent atoms. This implements in a very clear cut way a large part of the experience of chemistry. (For a review of classical valence bond theory, the reader should consult Ref. 1, for example.)... 

This paper attracted Pauling s attention, who recognized that the Heitler-London procedure could not only be extended to larger molecules but also serve as a bridge between Lewis classical idea of chemical bond and the new quantum theory. In a series of papers ", where he introduced the concepts of hybridization, resonance, electronegativity, etc., and also in a famous book that influenced many generations of chemists, Pauling developed his ideas which formed the basis of the classical Valence-Bond theory. 

It is important to appreciate clearly the distinction between SC theory and the older or classical valence bond theory. In classical VB theory, the orbitals are taken to be predetermined, either as simple atomic orbitals or hybrids of atomic orbitals. These hybrids, moreover, are fixed, for example, either as sp, sp, or sp, etc., -type orbitals. In SC theory, in contrast, no such preconceptions are imposed. The orbitals are optimized as linear combinations of basis functions (usually approximate AOs) much as in MO-based approaches. However, in common with classical VB theory, the SC orbitals in general overlap with one another (except, of course, in the case of orbitals of different symmetry), or, since the SC orbitals are often localized, by virtue of the physical separation between them. Generally speaking no constraints, apart from normalization, are applied to the SC orbitals and as a result they may be as localized or as delocalized as the situation demands. Bearing in mind that the SC orbitals are always singly occupied, this last means that their shapes are determined by whatever produces the optimum balance between the greatest extent of avoidance of the electrons in different orbitals and quantum interference effects, which arise from the overlap between orbitals. In practice, we have found that this invariably means that the SC orbitals turn out to be localized and indeed often resemble atomic or hybrid atomic orbitals, or semi-localized, meaning that the SC orbitals spread over two or, at most, three centres. 

It is not possible to write down a single, satisfactory, classical bonding diagram for S4N4 and, in valence-bond theory, numerous resonance hybrids must be considered of which the following are typical ... 

D. J. Klein, in Valence Bond Theory, D. L. Cooper, Ed., Elsevier, Amsterdam, The Netherlands, 2002, pp. 447-502. Resonating Valence Bond Theories for Carbon ir-Networks and Classical/Quantum Connections. 

R. McWeeny, Theor. Chim. Acta 73, 115 (1988). Classical Structures in Modern Valence Bond Theory. 

Most chemists still tend to think about the structure and reactivity of atomic and molecular species in qualitative terms that are related to electron pairs and to unpaired electrons. Concepts utilizing these terms such as, for example, the Lewis theory of valence, have had and still have a considerable impact on many areas of chemistry. They are particularly useful when it is necessary to highlight the qualitative similarities between the structure and reactivity of molecules containing identical functional groups, or within a homologous series. Many organic chemistry textbooks continue to use full and half-arrows to indicate the supposed movement of electron pairs or single electrons in the description of reaction mechanisms. Such concepts are closely related to classical valence-bond (VB) theory which, however, is unable to compete with advanced molecular orbital (MO) approaches in the accurate calculation of the quantitative features of the potential surface associated with a chemical reaction. 

The complete active space valence bond (CASVB) method [1,2] is a solution to this problem. Classical valence bond (VB) theory is very successful in providing a qualitative explanation for many aspects. Chemists are familiar with the localized molecular orbitals (LMO) and the classical VB resonance concepts. 

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. 

Resonating Valence-Bond theories for carbon -networks and classical/quantum connections... 

The structures of two binuclear carbonyls, Mn2(CO)i0 and Fe2(CO)9, are shown in Figure 10-2 note the carbonyl bridges in these molecules. In addition, the metal atoms in each molecule are close enough to each other so there is significant metal-to-metai bonding interaction. The stabilities of such binuclear carbonyls and similar but more complex carbonyl derivatives cannot be convincingly rationalized by the classical valence-bond approach. It is here that molecular orbital theory must be invoked. 

Pauling, L. (1960). The Nature of the Chemical Bond, Cornell University Fhess, Ithaca, NY. Another science classic by one of the original heroes of quantum chemistry. Heavily slanted towards Pauling s views on resonance and valence-bond theory. 

The purpose of this review is to give an account of approaches of this type. That is to say we examine methods where non-orthogonal orbitals enter directly into the wavefunctions. The fundamental prototype is of course the classical valence bond (VB) theory and accordingly we begin with a survey of the description it provides of molecular electronic structure, and of its important conceptual role in the description of many fundamental molecular processes. 

It is generally conceded that simple valence bond theory cannot adequately explain the bonds between the carbon atoms in benzene. This classic conundrum is often resolved by stating that there is a sort of... 

A more elaborate example than those shown above is the anionic compound SiFg2- (Figure 1.2), which adopts a classical octahedral shape that we will meet also in many metal complexes. Silicon lies below carbon in the Periodic Table, and there are some limited similarities in their chemistry. However, the simple valence bond theory and octet rule that... 

It is also possible to find relations between the MO and VB approaches on an intermediate level, as shown by Heilbronner [96]. His rather extreme view was that resonance theory expressed molecular orbital results in a different language. The "classical" valence bond model would emerge again quite recently in applications by Durand and Malrieu [97] using the Heisenberg Hamiltonian, and Bemardi, Olivucci and Robb [98], modelling photochemical reactions. 

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