The vibrational spectra of carbon dioxide and nitrous oxide: A Lie algebraic study

The infrared vibrational levels of nitrous oxide (N2O) and carbon dioxide (CO2) are studied in the framework of Lie algebra. The aim of this work is to compare the frequency obtained in two algebraic models: "the vibron model" and "the mean field approximation of the vibron model". To compare the two models we choose two triatomic molecules: CO2 of symmetry type D-infinity h and N2O of symmetry type C-infinity v. To construct the energy levels in the vibron model, the vibron numbers N for the two molecules are estimated from the harmonic frequency and the anharmonicity constant. After the proper estimation of N, the algebraic interaction parameters for both the molecules are evaluated against a least square fit with the experimental values using MATLAB R2015. Using the algebraic interaction parameters, the vibrational frequencies for the two molecules are calculated. Because CO2 is a linear symmetric triatomic molecule, the higher vibrational levels are largely affected by the mode mixing due to accidental degeneracy. The accidental degeneracy is studied introducing the Majorana and Fermi interaction parameters and the rms deviations are observed. The effects of accidental degeneracy for each of the molecules are not equal. In the second part of this report, the harmonic frequencies of CO2 and N2O are calculated using the mean field approximation. It is found that the results show good agreement.