Application of Group Theory to Molecular Systems

Part of a three-volume set covering applications of group theory to physics. The articles by McIntosh and by Wulfman are well worth reading. They contain relatively short and self-contained presentations of material about symmetries of atomic and molecular systems that is difficult to find elsewhere in comparably accessible form. 

In this review we will first describe two approaches which we have used to represent atomic and molecular systems without resorting to the B-0 approximations. Next, we will describe two numerical applications of the theory, which led to determining interesting non-adiabatic contributions. In the last section we will consider future theoretical work on a general non-adiabatic approach to an N-particle system with any isotropic interaction potential, including coulombic interaction, which is presently being developed in our group. 

Such comparisons apply in quantum mechanics, too. Recognizing the symmetry of an atomic or molecular system allows one to simplify the quantum mechanics, sometimes dramatically. We have already seen some aspects of symmetry odd and even functions, the spherical nature of the hydrogen atom s Is orbital, the cylindrical shape of H2 and H2. All these are applications of symmetry. In this chapter, we will develop a general understanding of symmetry using a mathematical tool called group theory. Then, we can see how symmetry applies to some aspects of quantum mechanics. 

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