Humanizing Science and Mathematics by Commemorating March Anniversaries

Raman selection rules for vibration-rotation transitions in symmetric top molecules

“…In this paper the equivalent selection rules for Raman transitions are discussed. These results have been previously discussed by Placzek and Teller [2], and by Placzek [3], and by Teller [4], and for certain point groups the selection rules are quoted by Herzberg [5] ; however, none of these authors give the ( + l) and ( -l) selection rules with generality, and Herzberg--who is the only author to give the results in the modern notation--actually quotes the correct selection rules only for molecules whose highest-fold symmetry axis is C 3 or C 4. In particular, the selection rules for the point group Dee (which are necessary, for example, to interpret the vibration-rotation Raman spectrum of the allene molecule) do not appear to have been previously derived.…”

“…t These selection rules are correctly stated by Placzek and Teller[2] (p. 233) and by Placzek[3] (p. 34I) : however, Teller[4] (p. 133), like Herzberg[5], appears to give the correct selection rules only for the case of C3 molecules. Downloaded by [Michigan State University] at 17:58 02 January 2015…”

“…We now return to the exceptional point groups Dna with n even, and S m with 89 even, for which the dipole selection rules are given by (4). From two successive dipole transitions we can, again, achieve AK=0, + 1, or +2, but in this case the correlation with A0 will be as follows:…”