How the alternating degeneracy in rotational Raman spectra of CO2 and C2H2 reveals the vibrational temperature

The contribution of higher vibrational levels to the rotational spectrum of linear polyatomic molecules with a center of symmetry (CO2 and C2H2) is assessed. An apparent nuclear degeneracy is analytically formulated by vibrational averaging and compared to numerical averaging over vibrational levels. It enables inferring the vibrational temperature of the bending and asymmetric stretching modes from the ratio of even to odd peaks in the rotational Raman spectrum. The contribution from higher vibrational levels is already observable at room temperature as g e/o=0.96/0.04 for CO2 and g e/o=1.16/2.84 for C2H2. The use of the apparent degeneracy to account for higher vibrational levels is demonstrated on spectra measured for a CO2 microwave plasma in the temperature range of 300-3500 K, and shown to be valid up to 1500 K.