A comment on the use of redundant vibrational coordinates

The treatment of molecular vibrations in terms of redundant coordinates is discussed. It is proposed that a force-constant matrix FC for the constraints should be introduced, to give a mechanical reason why the constraint coordinates C are held at C ¼ 0: Then FC is found to be infinite, in order to give the vanishing of the compliance matrix NC in the constraints. The corresponding compliance matrix NR in the redundant coordinates R has a zero eigenvalue for each constraint. The Moore–Penrose inverse of NR in N2R ¼ Fp R; the canonical force constant matrix is the treatment of [Martı´nez Torres et al. J Chem Phys 110 (1999) 3302]. This situation is contrasted with that in Cartesian coordinates, where the force-constant matrix has a zero eigenvalue corresponding to each translation or rotation, and the compliance matrix is infinite. q 2004 Elsevier B.V. All rights reserved.