Previous work by Fermi and by Dennison has shown that the principal features of the infrared and Raman spectra of carbon dioxide may be explained by taking account of the first order perturbation terms in the potential energy expression. It was not possible to predict the positions of the levels with any high degree of accuracy, however. The present paper extends this work by introducing a second order perturbation. The formula for the second order energy correction of a general linear symmetrical triatomic molecule is initially computed. This formula is then modified in order that it may be applicable to the carbon dioxide molecule in which resonance degeneracy plays an essential rôle. A review is made of the experimental data which determine the positions of the carbon dioxide vibrational energy levels. These include the results of a recent investigation of absorption bands appearing in the spectrum of Venus, as well as new and as yet unpublished data found by Barker and Wu. In all, twenty levels have been found and out of these, eleven are required to determine the anharmonic constants of the molecule. The remaining nine levels may then be predicted, and their positions are found to agree very accurately with the values obtained experimentally. A table is given showing the positions of a number of C${\mathrm{O}}_2$ infrared bands which while accessible to observation have not as yet been reported. The recent work by Langseth and Nielsen on the Raman spectrum of C${\mathrm{O}}_2$ is discussed.

• Received 16 February 1933

DOI:https://doi.org/10.1103/PhysRev.43.716