An Analysis of Higher Order Vibration–Torsion–Rotation Interactions and Spectra for a Molecule with an Internal Rotor

Abstract

Motivated by attempts to answer the questions (i) if the same order of magnitude is really appropriate for the torsional angular momentum termsP2γand the rotational angular momentum termP2(orP2a), (ii) how to systematically analyze various higher order interaction effects, especially the torsional effects, and (iii) if a reduced Hamiltonian can be used to fit observed spectroscopic data to an accuracy approaching experimental uncertainties over a significant range of quantum states, a detailed discussion is presented on the order of magnitude of a Hamiltonian termHmlnfor molecules with an internal rotation. A new scheme of the ordering by magnitude is proposed to analyze the vibration–torsion–rotation (VTR) interactions, in which the importance of the torsional problem is emphasized. The contact transformation technique is applied to the VTR Hamiltonian, which makes it possible to analyze clearly various higher order VTR interactions and their effects in the VTR spectra of the molecule. The resulting formulas are applicable to analyze observed spectra. A reduced torsion–rotation Hamiltonian for the molecule withC3v(M) symmetry is given in the new ordering scheme. As an application, a total of 568 microwave lines withvt≤ 3,J≤ 42 andK≤ 8 for CH318OH have been fitted to 64 molecular constants by using the reduced Hamiltonian with a root mean square (rms) of 0.262 MHz, where theAandEsubstates are treated simultaneously. About 35 newly assigned lines are added to our former fitting data (M. Ikeda, Y. B. Duan, S. Tsunekawa, and K. Takagi,ApJS,117, 249 (1998)).