Quantum mechanics qualitative concepts

Appealing and important as this concept of a molecule consisting of partially charged atoms has been for many decades for explaining chemical reactivity and discussing reaction mechanisms, chemists have only used it in a qualitative manner, as they can hardly attribute a quantitative value to such partial charges. Quantum mechanical methods (see Section 7.4) as well as empirical procedures (see... 

The modern approach to chemical education appears to be strongly biased toward theories, particularly quantum mechanics. Many authors have remarked that classical chemistry and its invaluable predictive rules have been downgraded since chemistry was put into orbit around physics. School and undergraduate courses as well as textbooks show an increasing tendency to begin with the establishment of theoretical concepts such as orbitals and hybridization. There is a continuing debate in the chemical literature on the relative merits of theory as opposed to qualitative or descriptive chemistry 1-6). To quote the late J. J. Zucker-man who supported the latter approach (3). 

The problems which the orbital approximation raises in chemical education have been discussed elsewhere by the author (Scerri [1989], [1991]). Briefly, chemistry textbooks often fail to stress the approximate nature of atomic orbitals and imply that the solution to all difficult chemical problems ultimately lies in quantum mechanics. There has been an increassing tendency for chemical education to be biased towards theories, particularly quantum mechanics. Textbooks show a growing tendency to begin with the establishment of theoretical concepts such as atomic orbitals. Only recently has a reaction begun to take place, with a call for more qualitatively based courses and texts (Zuckermann [1986]). A careful consideration of the orbital model would therefore have consequences for chemical education and would clarify the status of various approximate theories purporting to be based on quantum mechanics. 

The reader already familiar with some aspects of electrochemical promotion may want to jump directly to Chapters 4 and 5 which are the heart of this book. Chapter 4 epitomizes the phenomenology of NEMCA, Chapter 5 discusses its origin on the basis of a plethora of surface science and electrochemical techniques including ab initio quantum mechanical calculations. In Chapter 6 rigorous rules and a rigorous model are introduced for the first time both for electrochemical and for classical promotion. The kinetic model, which provides an excellent qualitative fit to the promotional rules and to the electrochemical and classical promotion data, is based on a simple concept Electrochemical and classical promotion is catalysis in presence of a controllable double layer. 

The triple bond structure appears in the third place with spherical AOs and standard tableaux functions, but is not among the first four with HLSP ffinctions. This is actually misleading due to the arbitrary cutoff at four ffinctions in the table. The HLSP function triple bond has a coefficient of 0.09182, only slightly smaller that function 4 in the table. The appearance of the triple bond structure in this wave function is the quantum mechanical manifestation of the V back-bonding phenomenon invoked in qualitative arguments concerning bonding. We thereby have a quantitative approach to the concept. 

Real space algorithms (section 4) allow for mappings between present day computer programs and strict molecular quantum mechanics [10,11]. It is the separability of base molecular states that permits characterizing molecular states in electronic Hilbert space and molecular species in real space. This feature eliminates one of the shortcomings of the standard BO scheme [6,7,12]. Confining and asymptotic GED states are introduced. In section 5 the concept of conformation states in electronic Hilbert space is qualitatively presented. 

Quantum mechanics has made important contributions to the development of theoretical chemistry, e.g. the concept of quantum mechanical resonance in the interpretation of the perturbation in the excited states of polyelectronic systems, the concept of exchange in the formation of a covalent bond, the concept of non-localized bonds (though, in my view, unsatisfactory and only arising from a neglect of electronic repulsions), the concept of dispersion forces etc., but it is noteworthy that all these ideas owe their success and justification to their ability to account qualitatively for previously unexplained experimental facts rather than to their quantitative mathematical aspect. 

We have used the concepts of the resonance methods many times in previous chapters to explain the chemical behavior of compounds and to describe the structures of compounds that cannot be represented satisfactorily by a single valence-bond structure (e.g., benzene, Section 6-5). We shall assume, therefore, that you are familiar with the qualitative ideas of resonance theory, and that you are aware that the so-called resonance and valence-bond methods are in fact synonymous. The further treatment given here emphasizes more directly the quantum-mechanical nature of valence-bond theory. The basis of molecular-orbital theory also is described and compared with valence-bond theory. First, however, we shall discuss general characteristics of simple covalent bonds that we would expect either theory to explain. 

The concept of (approximately) transferable, localized electron-domains provides a link between quantum physics and classical chemical theory and serves to clarify, from the viewpoint of physics, the status of classical chemical concepts. This link provides a chemist, therefore, with an intuitive understanding of quantum mechanical relations, in the sense that it permits one to guess qualitatively, through the use of classical chemical theory, what answers rigorous applications of the quantum mechanical formalism would give when applied to simple chemical problems 157>. Through the Correspondence Principle, the electron-... 

Successful model building is at the very heart of modern science. It has been most successful in physics but, with the advent of quantum mechanics, great inroads have been made in the modelling of various chemical properties and phenomena as well, even though it may be difficult, if not impossible, to provide a precise definition of certain qualitative chemical concepts, often very useful ones, such as electronegativity, aromaticity and the like. Nonetheless, all successful models are invariably based on the atomic hypothesis and quantum mechanics. The majority, be they of the ah initio or semiempirical type, is defined via an appropriate non-relativistic, Born-Oppenheimer electronic Hamiltonian on some finite-dimensional subspace of the pertinent Hilbert or Fock space. Consequently, they are most appropriately expressed in terms of the second quantization formalism, or even unitary group formalism (see, e.g. [33]). 

Valence bond theory is one of the two quantum mechanical approaches that explain bonding in molecules. It accounts, at least qualitatively, for the stability of the covalent bond in terms of overlapping atomic orbitals. Using the concept of hybridization, valence bond theory can explain molecular geometries predicted by the VSEPR model. However, the assumption that electrons in a molecule occupy atomic orbitals of the individual atoms can only be an approximation, since each bonding electron in a molecule must be in an orbital that is characteristic of the molecule as a whole. 

A qualitative quantum-chemical concept of the elementary polymerization act is proposed as a development of the concepts of the polymerization mechanism on the basis of the available experimental data generalizes in the framework of quantum-mechanical concepts. Up to the present, this concept has been based on five postulates. 

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. 

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