Correlation problems and a correlation-free torsion-rotation Hamiltonian for a molecule with an internal rotor

To develop a correlation-free reduced form of torsion-rotation Hamiltonian that is suitable for analyzing observed spectra for methanol and its isotop ic species, the origin of various classes of correlation problems often enc ountered in fitting the molecular constants to experimental data are analyz ed for a molecule with an internal rotation. It is shown that the correlati on problems can be completely eliminated by considering either the data set or the reduction of the Hamiltonian together with practical considerations , where an appropriate definition of order of magnitude plays an important role. For a molecule with C-3v(M) symmetry such as methanol and its isotopi c species, it is found that some terms which are included in the traditiona l or a reduced Hamiltonian given so far should not be used simultaneously. For example, the traditional terms k(5)P(a)(2)(1-cos 3 gamma) and k(6)P(a){ P-gamma,1-cos 3 gamma} should not be used simultaneously as adjustable ones and one of three traditional terms k(6)P(a){P-gamma,1-cos 3 gamma}, k(7)(P -gamma(2),1-cos 3 gamma}, and (V-6/2)(1-cos 6 gamma) must be constrained. A proposed correlation-free Hamiltonian is tested fbr its usefulness by anal yzing observed data for O-18 methanol. Total 424 microwave lines with v(t)l ess than or equal to 2, J less than or equal to 20, and K less than or equa l to 9 are globally fitted to an root-mean square (RMS) deviation of 0.234 MHz including the Q-branch transitions for A species with v(t) = 1 and K = 9 <-- 8 which are successfully fitted to the experimental accuracy. (C) 199 9 American Institute of Physics. [S0021-9606(99)03301-2].