About the symmetries of the rotation-vibration wavefunction of molecules

Abstract

The importance recently given to the 3.39 μm methane line, on account of its near-coincidence with a helium-neon laser line, has drawn attention to a discrepancy between different symmetry notations for the vibration-rotation levels of tetrahedral molecules: this line has been denoted F 1 or F 2, depending on the author. The purpose of this note is to point out that either notation may be used, but that it is necessary in all theories to employ some trick to avoid the use of translational wavefunctions. First, I shall make some general comments on the use of group theory.