Coordination compounds are usually symmetrical molecules with degenerate orbitals. Hence, the individual multiplet states arising from open-shell configurations can, in general, not be expressed by a single determinant. We have therefore exploited symmetry to the largest possible extent in order to simplify the relation between the multiplet splitting and single-determinant energies and thus developed a new method based on vector coupling to keep the computational effort to a minimum. A system of computer programs working on both mainframe and personal computers has been developed, carrying out for any desired point group the required group theoretical manipulations. The description of the method is illustrated by considering three practical examples. © 1994 John Wiley & Sons, Inc.