An algebraic model based on Lie-algebraic and discrete symmetry techniques is applied to the analysis of thermodynamic vibrational properties of molecules. The local anharmonic effects are described by a Morse-like potential and the corresponding anharmonic bosons are associated with the SU(2) algebra. A vibrational high-temperature partition function and the related thermodynamic functions are derived and studied in terms of the parameters of the model. The idea of a critical temperature is introduced in relation with the specific heat. A physical interpretation of a quantum deformation associated with the model is given.
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