Knowledge Bank

A new analytic approach to the torsional-rotational Hamiltonian for an asymmetric top molecule containing a methyl group internal rotor is proposed and a formal theory of centrifugal distortion is then formulated. A detailed discussion is presented of the relationships between the distortion constants and the vibrational potential constants. The reduced Hamiltonian for a molecule containing a plane of symmetry is given and formulas are obtained that relate the empirical constants appearing in the reduced Hamiltonian to the basic molecular parameters of the original Hamiltonian. As a check, we have fitted to within experimental accuracy a global data set for methanol containing 850 microwave lines involving transitions with $J\le 12,K\le 8$ and $\nu t$ (torsional quantum number) $\le 2$. The root-mean-square (RMS) deviation of 0.082 MHz for the MW fitting has been achieved. We also carried out a global fit of $\nu t=0,1$ and $J\le 12$ methanol data set obtained by combining 670 microwave lines with 2370 far infrared lines. The MW and FIR lines were fit to the RMS deviation of 0.096 MHz and $0.0003cm-1$, respectively.