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∞h and N2O of symmetry type C∞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.

The aim of this work is to study the highly excited vibrational states of Hydrogen Cyanide HCN in exact vibron model and with mean field approximation in vibron model. Considering the     44 UU  spectrum generating algebra for linear triatomic molecules the standard Hamiltonian is constructed by the linear and quadratic combination of Casimir operators. For higher order correction, the quadratic contributions of Casimir operators are used to construct the Hamiltonian. Using this Hamiltonian the higher excited vibrational levels of HCN are calculated in local mode approximation. The energy levels are observed as a function of vibron number N. The best fit is obtained for N=184 (N1= 139, N2=45) with r.m.s. deviation 5.598 cm-1. The intermodal coupling within the same polyad is studied and addressed properly by introducing Majorana operator. The r.m.s. deviation is then reduced to 4.755 cm -1 . The modification is negligible which indicates the local nature of HCN. In this work, 35 experimental levels are taken for fit. Out of which only two sets of levels are accidentally degenerate. The Fermi resonances of the accidentally degenerate levels are studied using the Fermi operator and r.m.s. deviation becomes 4.835. The coefficient of Majorana and Fermi coupling for different levels are obtained by diagonalzing the Majorana and Fermi matrices for each polyad. The Majorana and Fermi matrices for each polyad are diagonalized with MATRIX CALCULATOR program. The algebraic parameters are evaluated by a least square fit against the experimental data using MATLAB R2015a. Using this model, a set of energy levels is predicted up to 30000cm-1, with a very good accuracy.HCN is chosen for this study, because, it's vibrational states can be fairly described without any modification due to Fermi resonance. The fundamental vibrational levels of HCN are again calculated, using mean field approximation (MFA) and compared them to that are obtained using vibron model. A good agreement is observed.

No abstract