[GAP Forum] group theory and molecular spectroscopy

Roman Schmied rschmied at Princeton.EDU
Wed Apr 21 03:11:54 BST 2004

Hello GAP forum:

I thought it might be of interest for some of you to know that group 
theory is being used regularly in molecular spectroscopy. I have just 
had a GAP4-based note accepted by the Journal of Molecular Spectroscopy; 
you can download it at

In essence, we use permutations to represent the effect of symmetry 
operations on identical atoms in molecules. The character of the total 
molecular wavefunction can be computed from the spin-statistics theorem 
of quantum mechanics: the wavefunction must change sign under any odd 
permutation of Fermions, and stay the same under any other permutation 
(even permutations and/or Bosons). This leads to experimentally 
observable effects in the temperature-dependent populations of molecular 
energy eigenstates.

All this has been known for a long time, but it is very valuable to have 
a tool like GAP on our hands now.

Thanks for all the help, especially to Alexander Hulpke and Dmitrii 
Pasechnik for improving my GAP code!


Roman Schmied       Department of Chemistry
Princeton University    Princeton, NJ 08544
office (609) 258-3357, lab -4975, fax -6665

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