C <sub> 6 </ Sub> H <sub> 6 </ Sub> Molecules And C <sub> 6 </ Sub> D <sub> 6 </ Sub> Molecular Spectrum Algebraic Calculations

With the rapid development of science and experimental technology, especially the use of laser ,the high overtones of some molecules can be assessed. On the other hand, with the appearance of highly symmetrical molecules, such as CM, plenty of research have been done about the big complicated molecules. It challenges many theoretical physicists, that how to construct a new theory to explain the data rising continuously from the corresponding experiments. Because of the slow convergence and large numbers of parameters, the traditional force field expansion method became inappropriate. Nowadays, what is needed for modern spectroscopy is the formalism able to discuss both level structure beyond the harmonic limit and the corresponding dynamics.To describe the experiments and to study the intensities of all kinds of transitions, from 1980s, Wulfman, Levine, lachello and Oss tried a new method and proposed the algebraic model of molecules, i.e., to calculate the spectroscopy of molecules by algebraic method. By making use of the algebraic model, we got precise results with less parameters. But it became very difficult to calculate anything as the overtone v increased, for they were done in a non-symmetry adapted bases.In 1990s based on the eigenfunction method of representation theory of groups, a new method, the symmetrized boson representation (SBR) method, was brought forward. It's a general method to construct the symmetry adapted bases of point groups. It has the advantage that the algebraic solutions of point groups can be obtained and the solutions are independent of representation space. So it is very suitable to construct the symmetry bases of point groups of molecules.In this paper we studied the spectra of G6H6 and C6D6 and the intensities of infrared and Raman transitions, by combining the algebraic model with the SBR technique. A great agreement between observations and calculations was obtained. The brief introduction of the algebraic model of molecules was present and the irreducible bases of the point group D6h of the molecule benzene were obtained by using SBR method. Then the hamiltonian of the IO algebraic model was diagonalized on the symmetrical bases, and the energy spectra of benzene and the corresponding wave function are obtained. The infrared and Raman transitions are also calculated by using the wave function.The results show us that the algebraic model method has the advantages: quick convergence, high precision, small number of parameters. The SBR method to construct the symmetric bases of point groups is efficient and concise. The combination of this two make the high overtones be accessible with high precision. So the combination of the algebraic model and the SBR technique provides a powerful fool for the solutions of molecular vibration problems.