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**Extra info for Electronic Absorption Spectra and Geometry of Organic Molecules. An application of molecular orbital theory**

**Sample text**

The operation which is to be applied first is written in the top row, and the following operation in the first left-hand column. The result is found at the intersection of the row and column. Any set of elements which multiply according to the multiplication table of a group is said to form a representation of the group. The set of elements which form a representation may be a set of numbers and may be a set of matrices. * The dimension of a matrix of a representation is called the dimension of the representation.

If φ1 and φ2 are doubly degenerate wavefunctions, the results of 44 3. 8) where the a's are constants. 10) The set of matrices of the transformations for all the symmetry operations of the point group makes up an irreducible representation of the group. The set of doubly degenerate wavefunctions φ± and φ2 is said to form a basis for that doubly degenerate irreducible representation. The character of a degenerate representation for a symmetry operation R is the sum of the diagonal elements of the corresponding matrix A(R).

8) where the a's are constants. 10) The set of matrices of the transformations for all the symmetry operations of the point group makes up an irreducible representation of the group. The set of doubly degenerate wavefunctions φ± and φ2 is said to form a basis for that doubly degenerate irreducible representation. The character of a degenerate representation for a symmetry operation R is the sum of the diagonal elements of the corresponding matrix A(R). In the above example, the character of the representation for the operation R is