A General Method of Obtaining Molecular Symmetry Coordinates

A general method of obtaining molecular symmetry coordinates based on the algebra of group representation theory is described. The method is direct and involves no trial and error. It presupposes a knowledge of the irreducible representations of the molecular symmetry group rather than merely of their characters. The orthogonality properties of the symmetry coordinates are derived. As an example, the method is applied to boron trifluoride (D3h), with the use of both internal and Cartesian coordinates.