Resonating valence bond model

As pointed out in Chapter 7, the atomic orbital (valence bond) model regards benzene as a resonance hybrid of the two structures... 

The weak and highly polar Cl—F bond in FCIO can be rationalized in terms of either a (p—7T )a bond (see Section II, C) or a simple valence bond model (66) resulting in a resonance hybrid of the following canonical forms FCIO2 F + C102. It has been discussed in detail by Parent and Gerry (220), by Carter et al. (43), and in Section II, C of this review. 

The Yamanouchi-Kotani basis is best suited if we want to solve the Heisenberg problem in the complete spin space. However, the number of spins that can be handled this way, soon reaches an end due to the rapid growth of the spin space dimension f(S,N). Even with the present day computers, the maximum number of spins that can be treated clusters around N = 30. For larger values of N one must resort to approximate treatments, one of which, as described hereafter, is based on the idea of resonating valence bonds (RVB) coming from the classical VB model developed by Pauling and Wheland back in the early 1930 s [37, 51]. In essence,... 

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. 

Bonding. —In the valence-bond description of XeF2, Coulson has emphasized the dominance of the canonical forms (F-Xe)+F and F (Xe-F) in the resonance hybrid. This representation accounts well for the polarity FXe F , indicated by nmr, Moss-bauer, ESCA, and thermodynamic data. It is particularly impressive that the enthalpy of sublimina-tion derived for the XeFy case, by Rice and his co-workers in 1963, on the basis of the charge distribution "FXe+F , is 13.3 kcal mol , whereas the experimental value reported in 1968 is 13.2 kcal mol . It should be recognized that the Coulson valence-bond model is not, in the final analysis, significantly different from the Rundle and Pimentel three-center molecular orbital description or the Bilham and Linnett one-electron-bond description, but it does provide for a more straightforward estimation of thermodynamic stabilities of compounds than the other approaches do. 

The interaction of the bent banana bonds of the classical Coulson-Mofiit valence bond model of cyclopropane which uses methane-like sp hybrids and joins three units to form the alicyclic ring imply a resonance energy in cyclopropane of 69 kcalmol" Modern molecular orbital calculations (STO-3G) support an electron rich n system and an electron deficient cr-system for cyclopropane. 

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. 

In the valence bond model, organometallic compounds with carbanion character may be considered as resonance hybrids of two contributing structures, one purely covalent and one purely ionic (equation 5.57). 

The proton resonance spectra of the three structurally isomeric groups of bis(o-hydroxynaphthaldimine)Ni(II) are presented and the assignments discussed. A satisfactory qualitative explanation of the spin density distributions in the three isomeric groups is given in terms of a valence bond model of spin delocalization. The spin density distributions for the 2-hydroxy-1- or -3-naphthaldimine complexes and 1-hydroxy-2-naphthaldimine complexes are similar in sign to those observed for fl- and a-naphthyl groups, respectively. 

In the following section, two mainstream theoretical concepts will be briefly described, namely the resonating valence bond (RVB) theory of Anderson, and Varma s pairing model of quantum critical fluctuation (QCF), as the origin of high-Tc superconductivity. 

Powell, B.J. and McKenzie, R.H. (2005) Half-filled layered organic superconductors and the resonating-valence-bond theory of the Hubbard-Heisenberg model. Phys. Rev. Lett., 94, 047004 (4 pages). 

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