The Dunham Calculation Of Highly-excited Vibrational Energy Levels For Triatomic Molecules

Dunham firstly deduced the expansion expression of rovibrational energy levels of diatomics in 1932. From then on, the Dunham expansion method was extensively applied in the studies of rovibrational energy levels of diatomics, it becomes one of effective methods used to study the rovibrational energy levels of diatomics. By means of Dunham expansion expression, not only can we calculate the rovibrational energy levels, but also can we calculate some valuable physical values such as the force constants etc.Dunham expansion method is effective for the studies of rovibrational energy levels of diatomics, meanwhile, it can also be applied to study the vibrational energy levels of triatomic molecules, and even can be employed to study the vibrational energy levels of tetratomic molecules. In this article, according to Dunham expansion method of triatomic molecules, Fermi resonance interaction and Darling-Dennison resonance interaction considered, using Fortran language the calculation procedure was coded. The vibrational energy levels of the H2O, H2S, D2O, D2S molecule were fitted using our code respectively, and the spectral parameters were obtained. Using these spectral parameters, the highly excited vibrational energy levels of these four triatomic molecules were calculated respectively. The theoretical values of parts of highly-excited vibrational energy levels of these molecules were given which were not detected experimentally.The whole paper was divided into five chapters.In the first chapter, the history of molecule spectroscopy was firstly reviewed, and then the current experimental technique levels and theoretical development levels of molecule spectroscopy were summed up concisely. At last, the current situation of the Dunham expansion theory was presented.To help understand the Dunham expansion theory of triatomic molecules, first of all, the basic theories and models of diatomics were summarized concisely in chapter 2, including the common Born-Oppenheimer approximation, the harmonic oscillator model, non-harmonic oscillator model, the rigid rotator model, non-rigid rotator model, vibration rotator model and Dunham expansion theory. On the basis of the chapter 2, the Dunham expansion expression, Fermi resonance and Darling-Dennison resonance on the triatomic molecules were presented. The vibrational quantum numbers were explained simply, some concrete problems of our code were presented as well. In chapter 4, using our code, the experimental data of H2O, H2S,D2O, D2S molecule were fitted respectively, the spectral parameters were obtained, and employing these spectral parameters, we calculated the vibrational energy levels of these molecules respectively, in addition, parts of highly excited vibrational energy levels were predicted, which can provide beneficial help for the future spectral data analyses.In the last chapter, all the work in this paper was summarized concisely, and the applications of Dunham expansion method in other fields were briefly predicted.