CCL: How to calculate the independent degrees of freedom of a molecule?

[Sten Nilsson Lill <stenil===chalmers.se>]

 Sent to CCL by: Sten Nilsson Lill [stenil,chalmers.se]
 Hello Jun Zhang,
 I hope this paper by Pople and colleagues is helpful:
 J. A. Pople, Y. A. Sataty and E. A. Halevi, The Number of Independent Internal
 Coordinates in Symmetrical Molecules, Israel J. Chem. 19, 290 (1980).
 Hope it helps,
 Sten
 Ph.D. Sten Nilsson Lill
 Dep. of Chemistry
 University of Gothenburg
 SE-412 96 Gothenburg, Sweden
 e-mail: stenil,,chem.gu.se
 Phone: +46-31 786 9103
 Fax: +46-31-772 3840
 ________________________________________
 > From: owner-chemistry+stenil==chem.gu.se,,ccl.net
 [owner-chemistry+stenil==chem.gu.se,,ccl.net] On Behalf Of Jun Zhang coolrainbow
 * yahoo.cn [owner-chemistry,,ccl.net]
 Sent: Saturday, December 03, 2011 2:11 AM
 To: Nilsson Lill, Sten
 Subject: CCL: How to calculate the independent degrees of freedom of a molecule?
 Hello everyone:
 For a nonlinear N-atom molecule there are 3N-6 internal degrees of freedom, of
 course.  However, for a point group-constraint molecule, such as C2v H2O, there
 are only 2 independent degrees of freedom. So, is there a systematic way to
 determine the number and the contents of independent degrees of freedom of an
 arbitarily symmetry-constraint molecule? I heard that some knowledge like Polya
 theorem are requied, but I am not sure. It will be better if some reviews can be
 reccommended.
 Thank you in advance. Any suggestions will be appreciated.
 Best regards!
 ----------------------------------------------------------------
 Jun Zhang (coolrainbow^-^yahoo.cn)
 Computational Chemistry Group
 No.94, Weijinlu
 Nankai University
 Tianjin, China