The Application of Group Theory to Chemistry

Group theory is often used only as a pedagogical tool in the undergraduate mathematical curriculum, with limited applicability. A good Physical or Inorganic Chemistry course can expose students to the use of groups in solving chemical problems such as orbital shapes and geometric properties, but the development of these techniques often lacks rigor. This paper serves as a bridge between the theory of groups and these applications. The actual links are isomorphisms between the geometric concept of a symmetry group and the algebra of matrix representations. Different paths are taken, including the development of linear operators acting in a function space. A discussion of equivalence and reducibility of different representations ends with the Great Orthogonality Theorem. This theorem greatly simplifies the creation of character tables, which make vibrational analyses and SALC\u27s possible