Quantum Theory of Chemical Bonds

The observation [22] that several carbon atoms may be united by means of one, two or three valencies C-C, C=C, C=C, has also been incorporated, at face value, into electronic theories of chemical bonding and provided with a quantum gloss. In many cases, actual relationships within molecules are too complicated to be represented by simple graphs, and the supposed quantum effects assumed to be at work in these situations led to the invention of pseudo-scientific concepts such as hybridization and resonance. This patch-work is still featured as the quantum theory of chemical bonding. 

Raymond Daudel, Quantum Theory of Chemical Bonding (The Chemist, No. 4), Presses Univ. de France, Paris, 1971. 

Masaaki Ogasawara and Hiroto Tachikawa, Introduction to Quantum Theory of Chemical Bonds, Sankyo Shuppan Co. Ltd., Tokyo, 1994. 

Coulson, C. A. (1961). Valence, Oxford University Press, London. Somewhat dated but a classic introduction to quantum theory of chemical bonding. 

One of the key concepts of Pauling s quantum theory of chemical bonding, introduced in 1931, was resonance In many cases an ion or molecule could not be represented, conceptually or on paper, as one classical structure, but required what he called a hybridization of two or more of these structures. The single classical structure simply did not describe the chemical bond(s). In less than a decade he had transformed the earlier, somewhat simplistic theory of the chemical bond into a powerful, highly sophisticated theory and research tool. 

S. S. Shaik, P. C. Hiberty,A Chemist s Guide to Hjfe ceBond77ieo/y, Wiley, New York (2007) S. Wilson, M. Raimondi, D. L. Cooper, eds.. Quantum Theory of Chemical Bonding, Special Issue in Memory of Joseph Gerratt, International Journal of Quantum Chemistry, 74 (2) (1999)... 

Since this book is about the periodic table of the elements, rather than compounds, the quantum theory of chemical bonding is not discussed. For a historical account of developments in molecular quantum chemistry, interested readers may consult J. Servos, Physical Chemistry from Ostwald to Pauling, Princeton University Press, Princeton, NJ, 1990. 

As the reader will note, this case is somewhat intermediate in terms of epistemological and ontological reduction as I have defined them here. It may be described as ontological in the sense that it deals with issues of causation and in particular downward causation. However what McLaughlin appeals to as the final arbiter are the details of current theories, namely the quantum theory of chemical bonding, which is surely an epistemological issue. 

The problem in educating student chemists—and in educating ourselves— is to decide what kind of theory and how much of it is desirable. In other words, to what extent can the experimentalist afford to spend time on theoretical studies and at what point should he say, Beyond this I have not the time or the inclination to go The answer to this question must of course vary with the special field of experimental work and with the individual. In some areas fairly advanced theory is indispensable. In others relatively little is useful. For the most part, however, it seems fair to say that molecular quantum mechanics, that is, the theory of chemical bonding and molecular dynamics, is of general importance. 

This book is composed of three Parts. Part I, consisting of the first five chapters, reviews the basic theories of chemical bonding, beginning with a brief introduction to quantum mechanics, which is followed by successive chapters on atomic structure, bonding in molecules, and bonding in solids. Inclusion of the concluding chapter on computational chemistry reflects its increasing importance as an accessible and valuable tool in fundamental research. 

The theory of chemical bonding is overwhelmed by a host of insurmountable obstacles the real orbitals and hybrids of LCAO have no physical, chemical or mathematically useful attributes - certainly not in the quantum-mechanical sense the distribution of electron density between atoms, in the form of spin pairs, is an overinterpretation of the empirical rules devised to catalogue chemical species the structures, assumed in order to generate free-molecule potential fields, are only known from solid-state diffraction experiments the assumption of directed bonds is a leap of faith, not even supported by crystal-structure analysis. The list is not complete. 

D. K. Belashchenko, Physical Chemistry Section on the Principles of Quantum Mechanics and the Theory of Chemical Bonding. Course of Lectures, Mosk. Inst. Stali Splavov, Moscow, 1976. 

Empirically measured parameters are additional solvent properties, which have been developed through the efforts of physical chemists and physical organic chemists in somewhat different, but to some extent related, directions. They have been based largely on the Lewis acid base concept, which was defined by G. N. Lewis. The concept originally involved the theory of chemical bonding which stated that a chemical bond must involve a shared electron pair. Thus, an atom in a molecule or ion which had an incomplete octet in the early theory, or a vacant orbital in quantum mechanical terms, would act as an electron pair acceptor (an acid) from an atom in a molecule or ion which had a complete octet or a lone pair of electrons (a base). Further developments have included the concepts of partial electron transfer and a continuum of bonding from the purely electrostatic bonds of ion-ion interactions to the purely covalent bonds of atoms and molecules. The development of the concept has been extensively described (see Ref. 11 for details). 

In the LCAO MO description, the H2 molecnle in its ground state has a pair of electrons in a bonding MO, and thus a single bond (that is, its bond order is 1). Later in this chapter, as we describe more complex diatomic molecules in the LCAO approximation, bond orders greater than 1 are discussed. This quantum mechanical definition of bond order generalizes the concept first developed in the Lewis theory of chemical bonding—a shared pair of electrons corresponds to a single bond, two shared pairs to a double bond, and so forth. 

This review is dedicated to the memory of Carl Johan Ballhausen, our scientific grandfather so to speak. We have both received our formal training in quantum chemistry from Jens Peder Dahl, a former graduate student of Ballhausen, and one of us (NEH) was personally introduced to Carl Johan Ballhausen around 1980 - at that time already the grand old man of quantum chemistry in Denmark. Towards the end of his scientific career - after his seminal contributions to the theory of chemical bonding - Carl Ballhausen considered various nonstationary time-dependent problems in molecular quantum mechanics. That is, topics which are related to this review and to the dynamics of the chemical bond. 

The Lewis theory of chemical bonding, although useful AND easy to apply, DOES NOT TELL US HOW AND WHY BONDS FORM. A proper understanding of bonding comes from quantum mechanics. Therefore, in the second part of this chapter we will APPLY quantum mechanics TO THE STUDY OF THE GEOMETRY AND STABILITY OF MOLECULES. 

Theories of chemical bonding based on the properties of degenerate states with fixed I assume independent behaviour of the electrons in these states. In particular, for three electrons in the three-fold degenerate /i-state with 1=1, they are assumed to have distinct values of m, without mutual interference. To make this distinction it is necessary to identify some preferred direction in which the components of angular momentum are quantized. By convention this direction is labeled as Cartesian Z. If the electrons share the degenerate p-state with parallel spins, they must share the same direction of quantization. This being the case, only one of the electrons can have the quantum number m = 0, characteristic of the real function (7). 

The first quantum-mechanical treatment of the hydrogen molecule was by Heitler and London in 1927. Their ideas have been extended to give a general theory of chemical bonding, known as the valence-bond (VB) theory. The valence-bond method is more closely related to the chemist s idea of molecules as consisting of atoms held together by localized bonds than is the molecular-orbital method. The VB method views molecules as composed of atomic cores (nuclei plus inner-shell electrons) and bonding valence electrons. For H2, both electrons are valence electrons. 

In order to design a more rigorous theory of chemical bonds consistent with both Quantum Mechanics and chemical experience it is necessary to invoke an external mathematical theory able to extract qualitative information from quantitative. The topological analysis of the gradient vector field of a local function which carries the physical information is the well-established mathematical approach to handle this problem[19]. 

The modern theory of chemical bonding begins with the article The Atom and the Molecule published by the American chemist G. N. Lewis in 1916 [1], In this article, which is still well worth reading, Lewis for the first time associates a single chemical bond with one pair of electrons held in common by the two atoms "After a brief review of Lewis model we turn to a quantum-mechanical description of the simplest of all molecules, viz. the hydrogen molecule ion H J. Since this molecule contains only one electron, the Schrodinger equation can be solved exactly once the distance between the nuclei has been fixed. We shall not write down these solutions since they require the use of a rather exotic coordinate system. Instead we shall show how approximate wavefunctions can be written as linear combinations of atomic orbitals of the two atoms. Finally we shall discuss so-called molecular orbital calculations on the simplest two-electron atom, viz. the hydrogen molecule. 

Frederick Hund (1896-1997). German physicist. Hund s work was mainly in quantum mechanics. He also helped to develop the molecular orbital theory of chemical bonding. 

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