Group Theory and Spectroscopy

Up to now, we have seen that many of the optical properties of active centers can be understood just by considering the optical ion and its local surrounding. However, even in such an approximation, the calculation of electronic energy levels and eigenfunctions is far from a simple task for the majority of centers. The calculation of transition rates and band intensities is even more complicated. Thus, in order to interpret the optical spectra of ions in crystals, a simple strategy becomes necessary. 

This strategy consists of analysis of the symmetry properties for the active center (i.e., the ion and its local environment) and it is extremely useful for interpreting optical spectra without tedious calculations. Indeed, the symmetry properties of the active center are also the symmetry properties of its corresponding Hamiltonian. 

among other applications, symmetry considerations are useful in solving some spectroscopic problems, such as  

An Introduction to the Optical Spectroscopy of Inorganic Solids J. Garcia Sole, L. E. Bausa, and D. Jaque 2005 John Wiley Sons, Ltd ISBNs 0-470-86885-6 (HB) 0-470-86886-4 (PB) 

It is not the purpose of the present chapter to deal with all of the aspects related to this impressive capability. Rather, we will try to give some basic concepts, so that a nonspecialist in group theory is able to calibrate its potentiality and to apply it to simple problems in optical spectroscopy. 

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GROUP THEORY AND SPECTROSCOPY Table 7.6 The character table of group D3... 

G. Racah, Group Theory and Spectroscopy, Ergebnisse der exakten Naturwissenschaften, Springer-Verlag, Berlin, 1965, 37, p. 28. 

Racah, G., 1965, Group Theory and Spectroscopy, in Springer Tracts in Modern Physics, Vol. 37, ed. G. Hohler (Ergebnisse der Exakten Na-turwissenschaften) (Springer, Berlin). 

Wulfman, C. E. (1979), Dynamical Groups in Atomic and Molecular Physics, in Recent Advances in Group Theory and Their Applications to Spectroscopy, Plenum, New York. 

Piepho S.B., Schatz P.N. (1983) in Group Theory In Spectroscopy, John Wiley and Sons, New York. 

For a more thorough discussion of group theory and vibrational spectroscopy, see Hams, D.C. Bertolucci, M. D. Symmetry and Spectroscopy, Dover New York, 1989, Chapter 3. 

B. R. Judd. Group theory in atomic spectroscopy. In E. M. Loebl (ed.) Group Theory and Its Applications, Academic Press, New York, 1968. 

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... 

S. B. Piepho and P. N. Schatz, Group Theory in Spectroscopy with Applications to Magnetic Circular Dichroism, John Wiley Sons, Inc., New York, 1983. 

Infrared radiation is only absorbed by the irradiated molecule at the appropriate frequency if the corresponding vibration results in a change in molecular dipole moment. This means that not all vibrational modes are infrared active. An analysis of which vibrational modes in a polyatomic molecule are active is based on group theory and the symmetry properties of the molecule. More details about this subject may be found in monographs devoted to spectroscopy [G4]. 

In the case of the discipline of electrocatalysis, it is important to state that the reactants, the electrons, are microscopic particles that obey the new theoretical approaches that are presented below. The term electrocatalysis as stated in Chapter 2 involves a clear participation of the metal s properties, such as the electronic configuration, that can only be understood by considering quantum mechanics. The introduction of these novel mathematical methods into quantum physics and chemistry started with the use of group theory in spectroscopy and the study of chemical bonds [1-3]. Moreover, the study of all the concepts together as an interdisciplinary science is due to the contributions of Hawkins [4] and Rechenberg [5] to group theory and quantum mechanics. 

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