A comment on the use of redundant vibrational coordinates

✍ Scribed by James K.G. Watson

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 104 KB
• Volume: 695-696
• Category: Article
• ISSN: 0022-2860
• DOI: 10.1016/j.molstruc.2003.10.033

✦ Synopsis

The treatment of molecular vibrations in terms of redundant coordinates is discussed. It is proposed that a force-constant matrix F C for the constraints should be introduced, to give a mechanical reason why the constraint coordinates C are held at C ¼ 0: Then F C is found to be infinite, in order to give the vanishing of the compliance matrix N C in the constraints. The corresponding compliance matrix N R in the redundant coordinates R has a zero eigenvalue for each constraint. The Moore-Penrose inverse of N R in N 2 R ¼ F p 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.