The Rotational Wave Equation of Tetramethylmethane for Zero Potential and a Generalization

An exact solution for the rotational wave equation of tetramethylmethane for constant potential has been found. The solution is very similar to that of the rigid spherical top, which is the other limiting case for the rotational motion of the molecule in question. The energy levels for free rotation of the methyl groups are spread out compared to those for fixed methyl groups. This might make possible an estimation of the potential function between the groups. The energy levels might be used to calculate the specific heat. Some selection rules are given for infrared and Raman spectra although the rotational spectra are just beyond the limit of resolution at present. A generalization has been made for a spherical top with attached gyroscopes whose axes are rigidly fixed on the top according to certain symmetry requirements.