Group theory and its applications

Every molecule possesses symmetry and hence has symmetry operations and symmetry elements. From symmetry properties of a system we can deduce its significant physical results. Consequently it is essential to operations of a system forms a group. Group theory is an abstract mathematical tool that underlies the study of symmetry and invariance. By using the concepts of symmetry and group theory, it is possible to obtain the members of complete set of known basis functions of the various irreducible representations of the group. I practice this is achieved by applying the projection operators to linear combinations of atomic orbital (LCAO) when the valence electrons are tightly bound to the ions, to orthogonalized plane waves (OPW) when valence electrons are nearly free and to the other given functions that are judged to the particular system under consideration. In solid state physics the group theory is indispensable in the context of finding the energy bands of electrons in solids. Group theory can be applied to free electron energy bands and also in photoemission spectroscopy to derive basis functions by projection operator method. Group theory has many applications in physics and chemistry, for example, this is used to classify crystal structures, the symmetry of molecules and to determine physical properties such as polarity, spectroscopic properties useful for Raman spectroscopy and infrared spectroscopy and to construct molecular orbital. This book explains in detail how to determine the symmetry operations and elements of different molecules and then goes on to present how to determine the character tables of different groups with examples illustrating the procedure in full detail. It is written for physicists at an introductory level, keeping in view that a beginner will be able to understand the concepts which are relevant to the treatments of problems in physics.