Valence-bond method modern

P. C. Hiberty, in Modern Electronic Structure Theory and Applications in Organic Chemistry, E. R. Davidson, Ed., World Scientific, River Edge, NJ, 1997, pp. 289-367. The Breathing Orbital Valence Bond Method. 

P. C. Hiberty, S. Shaik, Theor. Chem. Acc. 108, 255 (2002). BOVB—A Modern Valence Bond Method That Includes Dynamic Correlation. 

A modern valence-bond description of the Diels-Alder reaction has been presented. The method of reaction classification by similarity has been expanded to include the effect of steric congestion in the classification of cycloaddition reactions. ... 

R.D. Harcourt in (a) Valence Bond Theory and Chemical Structure, D.J. Klein, N. Trinajstic, (eds.) Elsevier New York 1990, p. 251. (b) Quantum Mechanical Methods in Main-Group Chemistry, (T.M. Klapotke, A. Schulz) Wiley, Chichester 1998, p. 217. (c) Pauling s Legacy- Modern Theory (Modelling) of Chemical Bonding, Z.B. Maksic, W.J. Orville-Thomas, (eds.) Elsevier, New York 1999, p. 443. 

We overview our valence bond (VB) approach to the ir-electron Pariser-Parr-Pople (PPP) model Hamiltonians referred to sis the PPP-VB method. It is based on the concept of overlap enhanced atomic orbitals (OEAOs) that characterizes modern ab initio VB methods and employs the techniques afforded by the Clifford algebra unitary group approach (CAUGA) to carry out actual computations. We present a sample of previous results, sis well sis some new ones, to illustrate the ability of the PPP-VB method to provide a highly correlated description of the ir-electron PPP model systems, while relying on conceptusilly very simple wave functions that involve only a few covalent structures. 

Modem views of atomic structure are, as we have seen, based largely on the applications of wave mechanics to atomic systems. Modern views of molecular structure are based on applying wave mechanics to molecules such studies provide answers as to how and why atoms combine. The Schrodinger equation can be written to describe the behaviour of electrons in molecules, but it can be solved only approximately. Two such methods are the valence bond approach, developed by Heitler and Pauling, and the molecular orbital approach associated with Hund and MuUiken ... 

A lot of the modern research in quantum chemistry is focused on improving the valence bond and molecular orbital methods for calculating molecular properties. Different underlying approximations and different orbital functions are tried, and the results are compared with previous calculations and with experimental data to determine which methods give the best results. It is often the case that the best choice of quantum chemical method depends on the particular molecule or molecular property being studied. SEE ALSO Atomic Structure Computational Chemistry Molecular Structure Theoretical Chemistry. 

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. 

This is the focus of the present work which reviews modern methods of o—7i separation. We shall discuss here our methods devised for semiempirical and ab initio all-electron calculations at the self-consistent field (SCF) MO levels, correlated MO levels, and valence bond (VB) levels. The o—7i separation meth-... 

For a classical presentation of resonance theory, see G. W. Wheland, Resonance Theory in Organic Chemistry, Wiley, New York, 1955. Models of molecular structure based on mathematical descriptions of valence bond theory have been developed F. W. Bodrowicz and W. A. Goddard III, in Modern Theoretical Chemistry, Methods of Electronic Structure Theory, H. F. Schaefer III (ed.). Plenum Press, New York, 1977, Vol. 3, Chapter 4 A. Voter and W. A. Goddard III, Chem. Phys. 57, 253 (1981) N. D. Epiotis, Unified Valence Bond Theory of Electronic Structure, Springer-Verlag, Berlin, 1983. 

Although the VB method is not part of the standard arsenal of current quantum chemistry methods, its modern forms have their strong adherents, who point out that VB theory provides valuable conceptual insights and that the computational efficiency of VB methods is increasing. Some reviews of classical and modem valence-bond theory are S. Shaik and P. C. Hiberty in K. B. Lipkowitz et al. (eds.). Reviews in Computational Chemistry, vol. 20, Chapter 1, 2004, Wiley-VCH P. C. Hiberty and S. Shaik, J. Comput. Chem., 28, 137 (2007) A. Shurki, Theor. Chem. Acc., 116, 253 (2006) S. Shaik and P. C. Hiberty, A Chemist s Guide to Valence Bond Theory, Wiley, 2007 Shaik and Hiberty, WIREs Comput. Mol. ScL, 1,18 (2011) W. Wu et al., Chem. Rev., Ill, 7557 (2011) P. Su and W. Wu, WIRES Comput. Mol. ScL, 3, 56 (2013). 

Bobrowicz, F. W., 8c Schaefer H. R, III. (1977). The self-consistent field equations for generalized valence bond and open-shell Hartree-Fockwave functions. In H. F. Schaefer III (Ed.)> Methods of electronic structure theory (modern theoretical chemistry) (Vol. 3, pp. 79-127). New York/London Plenum. 

Texts on alternative types of valence-bond theory include those of references 1 and 2. Reference 3 provides a review of modern ab initio methods and classical valence-bond approaches to electronic structure. References 4 and 5 provide reviews of generalised and spin-coupled valence-bond theory. Both of these theories can use delocalised orbitals that involve more than two atomic centres to accommodate the active-space electrons. In references 6-8, overviews are presented of aspects of increased-valence theory. 

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