Study of the torsion-rotation Hamiltonian for symmetric tops using the millimeter wave spectrum of methyl silane

Abstract

The torsion-rotation Hamiltonian for symmetric tops has been tested in methyl silane by combining recent anticrossing molecular beam measurements in the ground torsional state ( v = 0) with pure rotational spectra taken for v as high as 4. The earlier microwave data set which consisted of J = 1 ← 0 and 2 ← 1 has been greatly extended by studying millimeter transitions for J = 4 ← 3, 5 ← 4, and 13 ← 12. An analysis of the 72 rotational frequencies for v ≤ 2 and the 15 anticrossing data for v = 0 yielded an excellent fit using 14 rotational, torsional, and distortion constants including the effective values for the A rotational constant and the barrier height V 3. No satisfactory fit could be obtained when the data set was extended to include measurements for ( v = 3) or ( v = 4). For each of these higher torsional levels, the difference between the observed frequencies and the predictions based on the best ( v ≤ 2) constants can be expressed in terms of a shift δB v in the B rotational constant, where δB v is a smooth function of the torsional energy. This disagreement is of particular interest because it may result from the fact that the molecule passes from hindered to free rotation as v is increased from 2 to 4. The possibility of perturbation by a low-lying vibrational level is considered briefly. The information contained in the different types of spectra is discussed; the redundancy relations are treated and a Fourier expansion of the diagonal torsional matrix elements is introduced. For 12CH 3 29SiH 3, 12CH 3 30SiH 3, and 13CH 3 28SiH 3 pure rotational spectra for v = 0 were studied briefly in natural abundance. The results were combined with existing data for two deuterated symmetric rotors to obtain a structure based only on symmetric top rotational constants.