Quantum mechanical concepts

The experimental trends in bonding and structure which we have discussed in the previous chapter cannot be understood within a classical framework. None of the elements and only very few of the thousand or more binary AB compounds are ionic in the sense that the electrostatic Madelung energy controls their bonding. And even for ionic systems, it is a quantum mechanical concept that stops the lattice from collapsing under the resultant attractive electrostatic forces the strong repulsion that arises as the ion cores start to overlap is direct evidence that Pauli s exclusion principle is alive and well and hard at work  

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As noted in the previous section, spin is a purely quantum-mechanical concept there is no classical-mechanical analog. 

Chapter 4 discusses the well-known VSEPR model. Although this model can be regarded as an empirical model that does not directly use quantum mechanical ideas, its physical basis is to be found in the Pauli principle. This dependence on a quantum mechanical concept has not always been clearly understood, so we emphasize this aspect of the model. We have tried to give a rather complete and detailed review of the model, which has been somewhat modified over the years since it was first proposed in 1957. 

For the description of systems with conjugated double bonds force field calculations of the kind described here are not very useful since, in principle, they only allow the description of relatively localised valence effects and of pairwise nonbonded interactions. Effects of delocalisation as occurring in conjugated vr-systems represent a new element for whose description quantum-mechanical concepts are appropriate. 

The problem of a priory assessment of stable structure formation is one of the main problems of chemical physics and material science. Its solution, in turn, is directly linked with the regularities of isomorphism, solubility and phase-formation in general. Surely, such problems can be cardinally solved only based on fundamental principles defining the system of physical and chemical criteria of a substance and quantum-mechanical concepts of physics and chemistry of a solid suit it. 

These were bold and simple statements. To put them in a modern context, the discovery of triphenylmethyl combined the novelty of something like bucky balls with the controversial nature of something like polywater or cold fusion. Thus Gomberg was soon to find that the triphenylmethyl problem was attractive and complex enough to occupy him and many others for a long time. A first period lasted until about 1911 when the phenomena observed had been clarified to the satisfaction of a majority of the research community. Theoretically, little understanding was possible before the advent of the electron pair bond and, in particular, theory based on quantum mechanical concepts. This meant that the theory available... 

The models of optical properties in this book are strictly classical. However, modern theoretical work aimed at understanding in detail the microphysics of optical properties is mostly quantum mechanical. Therefore, in this section we briefly discuss a few relevant quantum-mechanical concepts and also show that there is an analogy between the classical and quantum-mechanical descriptions of optical properties. 

The concepts which we need for understanding the structural trends within covalently bonded solids are most easily introduced by first considering the much simpler system of diatomic molecules. They are well described within the molecular orbital (MO) framework that is based on the overlapping of atomic wave functions. This picture, therefore, makes direct contact with the properties of the individual free atoms which we discussed in the previous chapter, in particular the atomic energy levels and angular character of the valence orbitals. We will see that ubiquitous quantum mechanical concepts such as the covalent bond, overlap repulsion, hybrid orbitals, and the relative degree of covalency versus ionicity all arise naturally from solutions of the one-electron Schrodinger equation for diatomic molecules such as H2, N2, and LiH. 

Atomic structure is fundamental to inorganic chemistry, perhaps more so even than organic chemistry because or the variety or elements and their electron configurations that must be dealt with. It will be assumed that readers will have brought with them from earlier courses some knowledge oT quantum mechanical concepts such as the wave equation, the particle-in-a-box. and atomic spectroscopy. 

The methodological section is intended for readers who are not very familiar with the theoretical details. Accordingly, only part of the formalism is presented in the form of equations however, the general quantum mechanical concepts that allow the computation of NMR observables from first-principles theory, as well as some important technical details, are outlined. Readers who are not interested in methodological details may skip Sects. 2.2 - 2.9, since the subsequent sections do not make excessive references to the methodology part. 

J. D. McGervey, Quantum Mechanics—Concepts and Applications, Academic Press, New York, 1995. 

Molecular mechanical calculations which are based on classical Newtonian mechanics [260—262], but use quantum mechanical concepts to formulate empirical equations. The parameters used are based entirely on experimental data. 

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