A NEW PROGRAM FOR NON-EQUIVALENT TWO-TOP INTERNAL ROTORS WITH A C_{s} FRAME

\underline{I. KLEINER}, Laboratoire Interuniversitaire des Systèmes Atmosphériques, CNRS et Universités Paris 7 et Paris 12, 61 av. Général de Gaulle, 94010, Créteil, France; J. T. HOUGEN, Optical Technology Division, National Institute for Standards and Technology, Gaithersburg, MD 20899-8441, USA.

We have written a new program to calculate and fit torsion-rotation transitions in molecules containing two inequivalent methyl tops (C_{3}_{v}) and having the rest of the atoms lying in a plane of symmetry. We based our work on the theoretical model and Hamiltonian described by Ohashi et al for the N-methylacetamide molecule^{a}. In the absence of top-top interactions, each asymmetric top energy levels splits into AA, AE, EA and EE components where the individual letters A and E indicate the symmetry species of the wave function with respect to internal rotation of one of the methyl tops. The pair of letters taken together indicates the species in the G_{1}_{8} permutation-inversion group appropriate for the molecule, so AA, AE, EA, and EE correspond to A_{1} (or A_{2}), E_{2}, E_{1} and E_{3} ⊕ E_{4}, respectively. In the previous study, the torsion-rotation Hamiltonian was diagonalized directly in a one-step process using torsion-rotation functions |J, K > |m_{1} > |m_{2} > where m_{1} and m_{2} represent the free-rotor basis functions for top 1 and top 2. The one-step diagonalization made however the least-squares fitting of moderate J values very slow, even for rather small values of m_{1} and m_{2}. Our goal is to write a code which will be faster and which allows us to reach higher J values. We follow a two-step procedure to diagonalize the Hamiltonian and implemented a banded-matrix diagonalization routine in order to speed up the code. We tested the code with the published N-methylacetamide Fourier-transform microwave data. The principles of the method, as well as the limitations will be discussed^{b} .

aN. Ohashi, J. T. Hougen, R. D. Suenram, F.J. Lovas, Y. Kawashima, M. Fujitake and J. Pyka, J. Mol. Spectrosc., 227, 28-42 (2004)

bIK thanks the ANR-08-BLAN-0054 for financial support