Classical Valence Bond

A single determinant MO wave function for the H2 molecule within a minimum basis consisting of a single s-function on each nucleus is given as (see also 

By including the doubly excited determinant, built from the antibonding MO, the amount of covalent and ionic terms may be varied, and be determined completely by the variational principle (eq. (4.19)). 

The 2-configurational Cl wave function (7.4) allows a qualitatively correct description of the H2 molecule at all distances, in the dissociation limit the weights of the two configurations become equal. 

The classical VB wave function, on the other hand, is build from the atomic fragments by coupling the unpaired electrons to form a bond. In the H2 case, the two electrons are coupled into a singlet pair, properly antisymmetrized. The simplest VB description, known as a Heitler-London (HL) function, includes only the two covalent terms in the HF wave function. 

Just as the single determinant MO wave function may be improved by including excited determinants, the simple VB-HL function may also be improved by adding terms which correspond to higher energy configurations for the fragments, in this case ionic structures. 

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In our laboratory we have examined the reactivity pattern of [0s3(y-H)2(C0)10], an unsaturated cluster which can be represented as possessing an osmium-osmium double bond in its classical valence bond representation. We find (2,3) that this compound undergoes a number of reactions with metal carbonyls which in some cases can be formulated as proceeding through intermediates analogous to metal olefin complexes ... 

How does this NBO description of A—F bonding compare with the classical valence-bond (VB) picture 14 Although it is evident that the NBO Lewis-structure description is very VB-like in its emphasis on localized, transferable electron-pair bonds and lone pairs of the chemist s Lewis diagram, there are important differences in mathematical detail. 

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. 

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. 

Therefore, the dependence on the coefficients does not enter the gradient expression not for fixed orbitals, which is the classical Valence Bond approach and not for optimised orbitals, irrespective of whether they are completely optimised or if they are restricted to extend only over the atomic orbitals of one atom. If the wavefimction used in the orbital optimisation differs, additional work is required. This would apply to a multi-reference singles and doubles VB (cf. [20,21]). Then we would require a yet unimplemented coupled-VBSCF procedure. Note that the option to fix the orbitals is not available in orthogonal (MO) methods, due to the orthonormality restriction. 

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

The Generalized Multistructural Wave Function (GMS) [1,2] is presented as a general variational many-electron method, which encompasses all the variational MO and VB based methods available in the literature. Its mathematical and physico-chemical foundations are settled. It is shown that the GMS wave function can help bringing physico-chemical significance to the classical valence-bond (VB) concept of resonance between chemical structures. The final wave functions are compact, easily interpretable, and numerically accurate. 

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. 

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. 

Classical Valence Bond 11.3 Dipole Moment Convergence 270... 

In Chapter 9, we found that some geometrical arrangements of nuclei do not allow an equivalent set of localized molecular orbitals to be defined. In such cases, there are non-localizable canonical m.o.s these structures are presented as resonant hybrids in the classical valence-bond description. 

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. 

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.)... 

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. 

There is a lot of delocalization in this structure, and usually these ligands are represented with a curved line to show the donation of both nitrogen lone pairs to the carbene C atom. You might prefer to include the formal + and - charges, but these compounds really do stretch the classical valence bond representation almost to breaking point, and conventionally the charges are not shown as they cancel out. 

Some typical tetrahedral orbital schemes are shown in Figure 3.10. The symmetrically bonded P04 anion contains a double system of n bonds equally distributed over all of the four linkages, whereas in POCI3 the tt-bonding resides almost wholly in the phosphoryl linkage. These cases correspond to the classical valence bond concept of resonance in the case of the PO4 anion (3.16a) and a fixed double bond in the case of POCI3 (3.16b). For alternative representations of the PO4 anion (see 5.33). 

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