Group theory and electronic structure

The author would like to thank all the group members in the past and present who carried out all the researches discussed in this chapter Drs. C. Zhu, G. V. Mil nikov, Y. Teranishi, K. Nagaya, A. Kondorskiy, H. Fujisaki, S. Zou, H. Tamura, and P. Oloyede. He is indebted to Professors S. Nanbu and T. Ishida for their contributions, especially on molecular functions and electronic structure calculations. He also thanks Professor Y. Zhao for his work on the nonadiabatic transition state theory and electron transfer. The work was supported by a Grant-in-Aid for Specially Promoted Research on Studies of Nonadiabatic Chemical Dynamics based on the Zhu-Nakamura Theory from MEXT of Japan. 

Puska, M. J., Nieminen, R. M., and Manninen, M. (1981). Physical Review B24,3037. Sutton, A. P. (1993). Electronic structure of materials. Oxford University Press. Tinkham, M. (1964). Group theory and quantum mechanics. McGraw-Hill, New York. Vitek, V. and Srolovitz, D. J. (eds) (1989). Atomistic simulations of materials beyond pair potentials. Plenum, New York. 

Spectroscopic methods can yield the required understanding of the complexes. Especially optical spectroscopy provides very detailed information about electronic and vibronic structures, in particular, when highly resolved spectra are available. However, without the development of suitable models, which are usually based on perturbation theory, group theory, and recently also on ab-initio calculations, a thorough understanding of the complexes is very difficult to achieve. In this volume and in a subsequent one some leading researchers will show that such a detailed description of... 

Molecular vibrations, as detected in infrared and Raman spectroscopy, provide useful information on the geometric and electronic structures of a molecule. As mentioned earlier, each vibrational wavefunction of a molecule must have the symmetry of an irreducible representation of that molecule s point group. Hence the vibrational motion of a molecule is another topic that may be fruitfully treated by group theory. 

In the theory of electronic structure of crystals, we also use the molecrdar-cluster model being based on physical reasons we choose a molecular fragment of a crystal and somehow try to model the influence of the rest of a crystal on the cluster chosen (for example, by means of the potential of point charges or a field of atomic cores). Prom the point of view of symmetry such a model possesses only the symmetry of point group due to which it becomes impossible to estabhsh a connection of molecular-cluster electronic states with those of a boundless crystal. At the same time, with a reasonable molecular-cluster choice it is possible to describe well enough the local properties of a crystal (for example, the electronic structure of impurity or crystal imperfections). As an advantage of this model it may also be mentioned an opportunity of application to crystals of those methods of the account of electronic correlation that are developed for molecules (see Chap. 5). 

This book is far from being the first to describe the electron energy spectrum peculiarities of high-temperature phases. However, earlier books and reviews considered either separate groups of the systems under discussion (Calais, 1977 Neckel, 1983), or attention was focused on particular effects, such as the presence of vacancies (Ivanovsky, Gubanov, Shveikin and Kurmaev, 1983). The latest achievements in the development of both computational methods of the quantum chemistry of solids and experimental techniques have resulted in the rapid accumulation of new results, which are sometimes of principal importance for understanding the properties of carbides and nitrides. This has allowed us to proceed to the next step in the creation of a comprehensive theory of electronic structure of refractory phases, that is, to the consideration of the peculiarities of the properties of real crystals with defects and impurities, as well as to the development of new methods for the description and, if possible, prediction of their properties. 

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