Application of Quantum Mechanical Methods

4 Applications of quantum mechanical methods Carbon nitride 

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This paper is dedicated to Gaston Berthier, from whom I have learned a lot. Although Berthier s publications have mostly dealt with applications of quantum mechanical methods to chemical problems, he never liked black boxes or unjustified approximations even if they appeared to work. The question why the quantum chemical machinery does so well although it often lies on rather weak grounds has concerned him very much. I am therefore convinced that he will appreciate this excursion to applied mathematics. 

The application of quantum-mechanical methods to the prediction of electronic structure has yielded much detailed information about atomic and molecular properties.13 Particularly in the past few years, the availability of high-speed computers with large storage capacities has made it possible to examine both atomic and molecular systems using an ab initio variational approach wherein no empirical parameters are employed.14 Variational calculations for molecules employ a Hamiltonian based on the nonrelativistic electrostatic nuclei-electron interaction and a wave function formed by antisymmetrizing a suitable many-electron function of spatial and spin coordinates. For most applications it is also necessary that the wave function represent a particular spin eigenstate and that it have appropriate geometric symmetry. 

Applications of quantum mechanical methods to polymers has become increasingly iiq>ortant over the last decade. One of the several reasons for that is the parallel improvement of experimental techniques for investigating electronic properties of polymers like hotoelectron Spectroscopy (PS) and especially X-... 

In this book, the main focus is on the application of quantum-mechanical methods to elucidate the geometric and electronic structures of minerals, so that detailed discussion of the relative merits of the different approaches is not appropriate. Nonetheless, it is important for the reader to appreciate some of the major controversies that have arisen between theoreticians in the field. 

APPLICATION OF QUANTUM-MECHANICAL METHODS TO SIMPLE INORGANIC MOLECULES OF RELEVANCE TO MINERALOGY, AND TO OXIDE MINERALS... 

The success of the application of quantum mechanical methods to the description of physical and chemical properties of molecules is evident in every facet of modern chemical research and is well documented. It may be of special interest to point out some of the very recent uses of quantum chemical approaches applied as a tool in the study of molecular structure and interactions. The examples below were not selected for their relative importance in the field of quantum chemistry nor for the use of the most advanced methodology. Each represents one of many illustrations of a specific application. 

In the preceding examples on the application of quantum-mechanical methods to the study of conformational problems in biochemistry, we have centered our attention essentially on results obtained by the PCILO method. The reason for this situation resides in the first place in the fact that the results obtained by this procedure are by far the most abundant. A second reason is, however, that they appear also the most satisfactory, being in particular superior to those obtained by the Extended Huckel Theory, which comes next after PCILO in the amount of work carried out. (For practical reasons, very few calculations have been performed in this field using the CNDO/2 method.)... 

Theoretical aspects of the thermal and general chemical reactions of oxi-rans have been treated by the application of quantum-mechanical methods to the study of the reactions of the triplet states of isomers. ... 

The repulsion of fully occupied orbitals in model systems received attention in the earliest application of quantum mechanical methods. From those studies an exponential representation of the energy-distance curve was obtained. This functional form has been used extensively in the simulation of both solids and molecular systems. Also derived from early quantum mechanical results were potentials using inverse power repulsive forms (see, e.g.. Refs. 49 and 50). Such potentials have also been employed with success in the simulation of liquids, molecular solids, and ionic systems. 

Important applications of quantum mechanical methods concern the thermochemistry accompanying chemical transformations A + B +... Products. On the laboratory scale, of course, the final results are a blend of energy changes pertaining i) to molecules at equilibrium (i.e., molecules in their hypothetical vibrationless state at O K) and ii) to contributions arising from vibrational, rotational and translational energies. The evaluation of the latter contributions - which requires, namely, calculation of the fundamental vibrational frequencies of both the reactants and the products - clearly represents a problem which should be treated in isolation. Here we concentrate on the equilibrium properties of molecules at O K. 

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