A new torsion–rotation fitting program for molecules with a sixfold barrier: Application to the microwave spectrum of toluene

Abstract

A new program is described for fitting rotation–torsion energy levels in molecules like toluene, in which the frame (C 6H 5) has C 2v symmetry and the methyl top has C 3v symmetry, i.e., for molecules where the internal rotation barrier is expanded in cos6 nα, where α is the internal rotation angle and n = 1,2,…. The program is based on the theoretical framework developed by Sørensen and Pedersen in their application of the Longuet-Higgins permutation-inversion group G 12 to the microwave spectrum of CH 3NO 2. It is specifically designed for sixfold barrier molecules, and allows the user to select almost any symmetry-allowed torsion–rotation term for inclusion in the fitting Hamiltonian. This program leads to a very successful fit of transitions in the microwave spectrum of toluene characterized by J ⩽ 30, K a ⩽ 12, and by the free-rotor quantum number ∣ m∣ ⩽ 3. In these fits we included both published and rather extensive unpublished new measurements, for which fits using other torsion–rotation programs have not been very successful. The fit presented here uses 28 parameters to give an overall standard deviation of 7.4 kHz for 372 line frequencies, and results in a much improved value for the sixfold barrier for toluene, V 6 = 13.832068(3) cal mol −1.