Studies On The Full Vibrational Energy Spectra Of Diatomic Molecular Ions

There are five parts in this dissertation. Part one and part two briefly describe the significance, the progress, the physical models and several physical methods used to study the vibrational energy spectra of electronic states for diatomic molecules and its ions. In part three, the algebraic method (AM), which is proposed, by Prof. W.GSun and Dr.S.L.Hou, to study the accurate vibrational spectroscopic constants and the full vibrational energy spectra of diatomic molecules, is introduced. In part four,the AM is applied to obtain accurate vibrational spectroscopic constants and full vibrational energy spectra {E_v} for some electronic states of five diatomic molecular cations.These states are BeH⁺ -X¹âˆ‘⁺ state, CO⁺ - X²âˆ‘⁺ state, F₂⁺-X²âˆ_g state, Li₂⁺ - X²âˆ‘_g⁺ state and O₂⁺ - A²âˆ_u state. Simultaneously, the physical properties of different vibrational energy subsets are studied using the AM and taking the X¹âˆ‘⁺ state of BeH⁺ and the X²âˆ‘⁺ state of CO⁺ as examples. The studies show that since the accuracy of the AM full vibrational spectrum is determined by the accuracy of the input experimental energies, the AM and the physical requirements therein can be used as the physical method and criterion of determining the correctness and accuracy of different experimental vibrational energy sets for a diatomic electronic state. Moreover, the correct potential energy curves of F₂⁺ -X²âˆ_g state is generated by AM vibrational spectroscopic constants which proved to be more accurate than other experimental and theoretical data. Lastly, all the research works are summarized in part five.