Generalized resonating valence bond

Finally, in 1986 Voter and Goddard carried out a generalized resonating valence bond (GRVB) calculation for square cyclobutadiene. As perhaps expected, the function... 

The generally accepted theory of electric superconductivity of metals is based upon an assumed interaction between the conduction electrons and phonons in the crystal.1-3 The resonating-valence-bond theory, which is a theoiy of the electronic structure of metals developed about 20 years ago,4-6 provides the basis for a detailed description of the electron-phonon interaction, in relation to the atomic numbers of elements and the composition of alloys, and leads, as described below, to the conclusion that there are two classes of superconductors, crest superconductors and trough superconductors. 

Within weeks of the confirmation of the discovery of high temperature superconductivity in the cuprates by Bednorz and Muller, Anderson[l] suggested an explanation of the phenomena and called it resonating valence bonds (RVB). Despite an enormous theoretical effort by the international scientific community, systematic or consistent theoretical results have been hard to obtain on this idea for the model proposed by Anderson for the cuprates. When some specific predictions were made based on the general ideas or approximate calculations, experiments did not conform. 

The hypothesis that electron-pair donation from the a atom will stabilize this transition state leads to the difficulty that the attacking atom must carry more bonds than conventional valence bond symbolism admits. Despite this problem, the general idea is expressed by 7 and its relationship to 6 by resonance. It is possible that transition state stabilization can be obtained in this way by rehybridization of the entire molecule. Klopman et al. suggest that the a effect arises from... 

The NRT resonance weights, bond orders, and valencies are generally comparable to those of the older Pauling-Wheland theory (particularly for species of low ionicity) and can be used to rationalize chemical phenomena in a similar fashion. Pauling s classic, The Nature of the Chemical Bond, brilliantly illustrates such reasoning. 

Resonance is by no means restricted to organic molecules. The following sets of valence-bond structures represent the hybrid structures of nitrate ion, NO30, carbonate ion, CO320, and nitrous oxide, NaO. These are only representative examples. We suggest that you check these structures carefully to verify that each member of a set conforms to the general rules for resonance summarized above. 

We have used the concepts of the resonance methods many times in previous chapters to explain the chemical behavior of compounds and to describe the structures of compounds that cannot be represented satisfactorily by a single valence-bond structure (e.g., benzene, Section 6-5). We shall assume, therefore, that you are familiar with the qualitative ideas of resonance theory, and that you are aware that the so-called resonance and valence-bond methods are in fact synonymous. The further treatment given here emphasizes more directly the quantum-mechanical nature of valence-bond theory. The basis of molecular-orbital theory also is described and compared with valence-bond theory. First, however, we shall discuss general characteristics of simple covalent bonds that we would expect either theory to explain. 

RGVB resonating generalized valence bond method... 

A. F. Voter, W. A. Goddard, III, Chem. Phys. 57, 253 (1981). A Method for Describing Resonance between Generalized Valence Bond Wavefunctions. 

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. 

From the conceptual point of view, there are two general approaches to the molecular structure problem the molecular orbital (MO) and the valence bond (VB) theories. Technical difficulties in the computational implementation of the VB approach have favoured the development and the popularization of MO theory in opposition to VB. In a recent review [3], some related issues are raised and clarified. However, there still persist some conceptual pitfalls and misinterpretations in specialized literature of MO and VB theories. In this paper, we attempt to contribute to a more profound understanding of the VB and MO methods and concepts. We briefly present the physico-chemical basis of MO and VB approaches and their intimate relationship. The VB concept of resonance is reformulated in a physically meaningful way and its point group symmetry foundations are laid. Finally it is shown that the Generalized Multistructural (GMS) wave function encompasses all variational wave functions, VB or MO based, in the same framework, providing an unified view for the theoretical quantum molecular structure problem. Throughout this paper, unless otherwise stated, we utilize the non-relativistic (spin independent) hamiltonian under the Bom-Oppenheimer adiabatic approximation. We will see that even when some of these restrictions are removed, the GMS wave function is still applicable. 

The BOVB method does not of course aim to compete with the standard ab initio methods. BOVB has its specific domain. It serves as an interface between the quantitative rigor of today s capabilities and the traditional qualitative matrix of concepts of chemistry. As such, it has been mainly devised as a tool for computing diabatic states, with applications to chemical dynamics, chemical reactivity with the VB correlation diagrams, photochemistry, resonance concepts in organic chemistry, reaction mechanisms, and more generally all cases where a valence bond reading of the wave function or the properties of one particular VB structure are desirable in order to understand better the nature of an electronic state. The method has passed its first tests of credibility and is now facing a wide field of future applications. 

Basis-set optimization is thus the hallmark of the present author s approach. Nevertheless, GMCSC wavefunctions can otherwise be viewed as more flexible versions of Resonating Generalized Valence Bond (R-GVB) wavefunctions [9]. The extra flexibility arises from GMCSC s freedom from the constraint of... 

In practice, the valence bond picture has probably exerted more influence on how chemists actually think than the HMO picture. However most early applications were primarily qualitative in nature. This qualitative VB picture can be summarized under die name of resonance theory [10]. The basic concept is that in general the more ways one has of arranging the spin pairing in the VB wave function, the more stable the molecule is likely to be. Thus, VB theory predicts that phenanthrene with 14 carbon atoms and 5 Kekule structures should be more stable than anthracene with 14 carbon atoms but just 4 Kekule structures, in complete accord with the experimental evidence. It also predicts that benzenoid hydrocarbons with no Kekule structures should be unstable and highly reactive, and in fact no such compounds are knowa Extensions of this qualitative picture appear, for example, in Clar s ideas of resonant sextets [11], which seem to be very powerful in rationalizing much of the chemistry of benzenoid aromatic hydrocarbons. The early ascendancy of HMO theory was thus largely based on the ease with which it could be used for quantitative computations rather than on any inherent superiority of its fundamental assumptions. 

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