CORRELATION PROBLEMS AND CORRELATION-FREE TORSION ROTATION HAMILTONIAN FOR A MOLECULAR WITH AN INTERNAL ROTOR

\underline{YUN-BO DUAN}, LI WANG, AND KOJIRO TAKAGI, Department of Physics, Toyama University, Toyama 930-8555, Japan.

Motivated by investigating how to develop a correlation-free reduced form of torsion-rotation Hamiltonian that is rapid convergent and suitiable for analyzing observed spectra for methanol and its isotopic species, the origin of various classes of correlation problems often encountered in fitting the molecular constants to experimental data is analyzed for a molecule with an internal rotation. This analysis will help spectroscopists to overcome certain difficulties in the process of fitting observed spectra. It is showed that the correlation problems can be completely eliminated by considering either the data set or the reduction of Hamiltonian together with practical considerations, where an appropriate definition of order of magnitude is very important. For a molecule with C_{3v}(M) symmetry such as methanol and its isotopic species, it is found that some terms which are included in the traditional or a reduced Hamiltonian given so far shou1d not be used simultaneously. For example, the traditional terms k_{5}P_{a}^{2}(1 − cos 3γ) and k_{6}P_{a}{P_{γ}, 1 − cos 3γ} should not be used simultaneously, one of three traditional terms k_{6}P_{a}\{P_{γ}, 1−cos 3γ\}, k_{7}\{P_{γ}^{2}, 1−cos 3γ\}, and \frac{V_{6}}{2} (1−cos 6γ) must be removed, and the term DD_{ab}P^{4}{P_{a}, P_{b}} should be removed. In addition, some terms with ΔK = ±3 and ΔK = ±4 matrix elements should be included in a reduced Hamiltonian. A proposed correlation-free Hamiltonian is tested on analyzing observed data for methanol and its isotopic species.