And group theory

Other techniques that work well on small computers are based on the molecules topology or indices from graph theory. These fields of mathematics classify and quantify systems of interconnected points, which correspond well to atoms and bonds between them. Indices can be defined to quantify whether the system is linear or has many cyclic groups or cross links. Properties can be empirically fitted to these indices. Topological and group theory indices are also combined with group additivity techniques or used as QSPR descriptors. 

Vincent, A. (2000) Molecular Symmetry and Group Theory, 2nd edn., John Wiley, Chichester. 

KinR81 King, R. B. Chemical applications of topology and group theory. 9. The symmetries of coordination polyhedra. Inorg. Chem. 20 (1981) 363-372. 

We do not, in general, have to depend on conceptual approaches or on qualitative generalizations. Symmetry and group theory have provided us with a general method, called symmetry analysis, of determining the number of Raman active vibrations, the number of infrared active vibrations, and... 

Actually this statement is not quite correct because a state of the physical system is represented by each observer not by a vector in his (private) Hilbert space, but by a ray, since the normalization and phase of the state is not pertinent to the description of the state. What one has, therefore, is a correspondence between rays rather them between vectors. We shall, however, ignore this fact in the interests of simplicity. Its relevance to the present discussion is fully treated by E. P. Wigner, Nuovo Cimento, 3, 517 (1956) Rev. Mod. Phys., 29, 255 (1957) and Group Theory, Academic Press, New York, 1959. 

It should now be apparent how the species A1( A2, Bv and B2 arise. Character tables have been worked out and are tabulated for all the common point groups. Presenting all the tables here would go beyond the scope of the discussion of symmetry and group theory as used in this book. However, tables for some common point groups are shown in Appendix B. 

Harris, D. C., and Bertolucci, M. D. (1989). Symmetry and Spectroscopy. Dover, New York. Chapter 1 presents a good summary of symmetry and group theory. 

The allowed values are all the integers between -J and +J. However, in general, this is a rather complicated problem, and group theory offers a complete and straightforward solution. This problem is called the labeling problem. 

Alhassid, Y., Giirsey, F., and Iachello, F. (1983a), Potential Scattering, Transfer Matrix, and Group Theory, Phys. Rev. Lett. 50, 873. 

Derflinger, G. (1991) Chirality and group theory. In Chirality. From weak bosons to the a-helix, Janoschek, R. (ed.), Springer-Verlag, pp. 34—58. 

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