Bonding models an introduction

In Sections 2.1-2.3 we summarize valence bond (VB) and molecular orbital (MO) theories of homonuclear bond formation, and include practice in generating Lewis structures. 

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An introduction to the modeling methods can be found in refs. [22,231. The classical MD simulations reported here were performed with the modified AMBER software/241 in which the potential energy consists of harmonic deformations of bond and angles, dihedral energies, plus non-bonded interactions represented by a sum of pair wise additive coulombic and van der Waals contributions ... 

This chapter begins a series of chapters devoted to electronic structure and transport properties. In the present chapter, the foundation for understanding band structures of crystalline solids is laid. The presumption is, of course, that said electronic structures are more appropriately described from the standpoint of an MO (or Bloch)-type approach, rather than the Heitler-London valence-bond approach. This chapter will start with the many-body Schrodinger equation and the independent-electron (Hartree-Fock) approximation. This is followed with Bloch s theorem for wave functions in a periodic potential and an introduction to reciprocal space. Two general approaches are then described for solving the extended electronic structure problem, the free-electron model and the LCAO method, both of which rely on the independent-electron approximation. Finally, the consequences of the independent-electron approximation are examined. Chapter 5 studies the tight-binding method in detail. Chapter 6 focuses on electron and atomic dynamics (i.e. transport properties), and the metal-nonmetal transition is discussed in Chapter 7. 

The importance of Marcus theoretical work on electron transfer reactions was recognized with a Nobel Prize in Chemistry in 1992, and its historical development is outlined in his Nobel Lecture.3 The aspects of his theoretical work most widely used by experimentalists concern outer-sphere electron transfer reactions. These are characterized by weak electronic interactions between electron donors and acceptors along the reaction coordinate and are distinct from inner-sphere electron transfer processes that proceed through the formation of chemical bonds between reacting species. Marcus theoretical work includes intermolecular (often bimolecular) reactions, intramolecular electron transfer, and heterogeneous (electrode) reactions. The background and models presented here are intended to serve as an introduction to bimolecular processes. 

For an introduction to the structures and reactions of carbenes, see (a) Liebman, J. F. Simons, J. in Liebman, J. F. Greenberg, A., Eds. Molecular Structure and Energetics, Volume 1 Chemical Bonding Models VCH Publishers Deerfield Beach, FL, 1986 p. 51 (b) Moss, R. A. Jones, M., Jr., in Jones, M., Jr. Moss, R. A., Eds. Reactive Intermediates, Vol. 2 John Wiley Sons New York, 1981 (c) Kirmse, W. Carbene Chemistry Academic Press New York, 1964 Gilchrist, T. L. Rees, C. W. Carbenes, Nitrenes and Arynes Appleton-Century-Crofts New York, 1969 (d) Mine, J. Divalent Carbon Ronald Press New York, 1964 Bertrand, G. in Moss, R. A. Platz, M. S. Jones, M., Jr., Eds. Reactive Intermediate Chemistry John Wiley Sons Hoboken, NJ, 2004 chapter 8 (e) Jones, M., Jr. Moss, R. A. in Moss, R. A. Platz, M. S. Jones, M., Jr., Eds. Reactive Intermediate Chemistry John Wiley Sons Hoboken, NJ, 2004 chapter 7. 

Mosterman, P. J. (1997). Hybrid dynamic systems a hybrid bond graph modeling paradigm and its application in diagnosis. Ph.D. Thesis. Nashville Vanderbilt University, van der Schaft, A. J., Schuhmacher, H. (2000). An introduction to hybrid dynamical systems. No. 251 in Lecture Notes in Control and Information Sciences. London Springer. 

Borutzky, W. (2009). Bond graph modelling and simulation of multidisciplinary systems—An introduction. Simulation Modelling Practice and Theory, 77(1), 3-21. 

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