Valence-bond formalism

The classic HLSP-PP-VB (Heitler-London-Slater-Pauling perfect-pairing valence-bond) formalism and its chemical applications are described by L. Pauling, The Nature of the Chemical Bond. 3rd edn. (Ithaca, NY, Cornell University Press, 1960 G. W. Wheland, The Theory of Resonance (New York, John Wiley, 1944) and H. Eyring, J. Walter, and G. E. Kimball, Quantum Chemistry (New York, John Wiley, 1944). 

The physical and chemical properties of pyrrole and its benzo fused congeners are undeniably those expected of aromatic systems, although the extent of aromaticity has been the subject of much debate (vide Section 3.04.5.2). In the valence-bond formalism, pyrrole... 

Silver8 adopted a similar approach, and proposed a further category of unfeasible reactions in which neither individual orbital correlation rules nor total symmetry correlation rules (Wigner-Witmer rules) were obeyed. Silver and Karplus87 have shown how to derive W-H symmetry rules using a simple valence-bond formalism. 

VALENCE BOND FORMALISM USING THE EXACT HAMILTONIAN... 

VALENCE BOND FORMALISM USING AN EFFECTIVE HAMILTONIAN 49... 

In the present chapter, we explore the Pauling ideas in the context of an ab initio valence bond formalism. We do so by admitting extra orbitals in the constituent atoms of molecular systems, and devising the new types of VB structures that can be set allowing the atoms to form more bonds than their "atomic valences" admit. We will see that these Pauling s structures, as we named them, are important to describe some kinds of delocalized bonds and that they give some information about possible processes of charge transfer in the molecular systems. 

We note that the four electrons problem, a cluster of four hydrogen atoms, is a prototype for testing correlation methods in electronic structure. McWeeny [2] had already addressed this problem in the context of a valence bond formalism and here we tackle the problem in a quite unusual range of intermolecular separations. 

Following Pauling, we have admitted extra orbitals on monovalent atoms involved in molecular systems with some metallic character or very delocalized bonds. In conjunction with a spin-free valence bond formalism, these extra orbitals have allowed us to devise new kinds of VB structures, the Pauling s structures, as we call them. These structures permit the monovalent atoms to form two covalent bonds simultaneously, as a consequence of electron transfer from neighbors and, thus, give information about delocalization of charge in the system, that is not directly inferred from the usual Kekule or ionic structures. Therefore, the Pauling s structures complement the VB description of molecular systems. 

Charge Theories An Entropy Valence Bond Formalism and Relationships to Previous Models. 

In these type of carbocations the positive charge can be delocalized by a-aryl -conjugation as in 5a 5b and by P-silyl a-hyperconjugation depicted in valence bond formalism as 6a o 6b. 

Although the bis(dithiocarbamate) complexes of Fe(II) are relatively unstable to air oxidation, early studies (12, 15) produced stable adducts of NO and CO. Both 5-coordinate [Fe(NO)(I dtc)2] and 6-coordinate [Fe(NO)2(R2dtc)2] complexes are known. There has been considerable interest in the mode of attachment of the NO molecule, as there are six possibilities (see Scheme 4). (A) and (B) represent valence-bond structures of the linear Fe-NO bond. Structure (C) involves a symmetric Fe-NO TT-bond. Structure D illustrates the bent mode of attachment, in which nitrosyl is coordinated to the metal through the nitrogen atom, but the Fe-NO bond-angle differs greatly from 180°. Structures (E) and (F) are valence-bond formalisms of an unsymmetrical, metal-NO 7r-bond. The structure of [Fe(NO)(R2dtc)2] (R = Me or Et) has been shown (230,231) to be square pyramidal, with four sulfur atoms in... 

The second mechanism involves the wave-mechanical effect of electron-deloceilization, but we can present it in a crude valence-bond formalism. Atom B has a lone pair of electrons, which we show on the right-hand oxygen atom of (23). We can also write the alternative bond-diagram (24). 

These simple ideas were formulated before the advent of wave mechanics. Quantum theory not only justifies their use but enables us to refine and extend them. In attempting quantitative quantum-mechanical treatment of chemical bonds, approximations must be made. Traditionally, there have been two broad groups of approximations, called the valence bond (VB) and the molecular orbital (MO) treatments. The former is essentially a direct attempt to invest the qualitative ideas just outlined with quantum-mechanical validity, and it is therefore logical to continue the discussion with a summary of the valence-bond formalism, including such concepts as resonance, valence states and hybridization that arise within this framework. The molecular-orbital formalism will be presented in a following Section. 

Abstract The wave function of Coulson and Fischer is examined within the context of recent developments in quantum chemistry. It is argued that the Coulson-Fischer ansatz establishes a third way in quantum chemistry, which should not be confused with the traditional molecular orbital and valence bond formalisms. The Coulson-Fischer theory is compared with modern valence bond approaches and also modern multireference correlation methods. Because of the non-orthogonality problem which arises when wave functions are constructed from arbitrary orbital products, the application of the Coulson-Fischer method to larger molecules necessitates the introduction of approximation schemes. It is shown that the use of hierarchical orthogonality restrictions has advantages, combining a picture of molecular electronic structure which is an accord with simple, but nevertheless empirical, ideas and concepts, with a level of computational complexity which renders praetieal applications to larger molecules tractable. An open collaborative virtual environment is proposed to foster further development. 

The definition of oxidation state used herein is the charge left on the central metal after the ligands have been removed in their normal closed shell configurations. Inasmuch as this definition is based on valence-bond formalism, there are several instances of indefinite oxidation state (see Section III). It is recognized that oxidation state is not a measurable physical quantity. However, the concepts of oxidation state and d-electron configuration which are used throughout this chapter are generally useful... 

Morales J, Martinez TJ (2001) Classical fluctuating charge theories the maximum entropy valence bond formalism and relationships to previous models. J Phys Chem A 105(12) 2842-2850... 

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