GROUP THEORY IN SPECTROSCOPY

Quite a lot of what we will be talking about in this Appendix was invented by Evariste Galois. He was only 21 when he died in a duel cherchez la femmel). Galois spent his last night writing down his group theory. 

Evariste Galois (1811-1832), French mathematician, also created many fundamental ideas in the theory of algebraic equations. 

The group theory in this textbook will be treated in a practical way, as one of useful 

We will try to be concise, but examples need raplanations, there are few lovers of dry formulae. 

Imagine a set of elements R/, i = 1,2. g. We say that they form a group G of order g, if the following four conditions are satisfied  

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Thus, any representation Tcan be expressed as a function of its irreducible representations Pi. This operation is written as P = S a, Pi, where a, indicates the number of times that Pi appears in the reduction. In group theory, it is said that the reducible representation P is reduced into its Pi irreducible representations. The reduction operation is the key point for applying group theory in spectroscopy. To perform a reduction, we need to use the so-called character tables. 

Piepho S.B. Schatz, P.N. Group Theory In Spectroscopy, Wlley-Intersclence New York, 1983. 

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

Piepho, S. B. Schatz, P. N. Group Theory in Spectroscopy With Applications to Magnetic Circular Dichroism Wiley New York, NY, 1983. Stephens, P. J. Annu. Rev. Phys. Chem. 1974, 25, 201. 

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

Piepho SB, Schatz PN (1983) Group theory in spectroscopy. With applications to magnetic circular dichroism. Wiley, New York... 

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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