Molecular torsion: Comparison of harmonic oscillator and free rotor bases

In this work we describe a method of solving the eigenvalue problem of torsional motion in polyatomic molecules by expanding the eigenfunctions in a harmonic oscillator basis. By comparing the eigenvalues obtained with a harmonic oscillator basis and those calculated with a free rotor basis, it is found that a basis with only 5–7 oscillator functions will reproduce the low-lying energy levels for large torsional barriers with the same accuracy as a basis with about 10 free rotor functions. The method has been applied to a calculation of the barriers to internal rotation for methyl ammonium chloride. The barriers were obtained from a least squares fit of the torsional frequencies of methyl ammonium chloride and seven of its deuterated derivatives, treating the molecule as a double rotor. The method is recommended for the calculation of large rotational barriers from spectroscopic data on systems in any state of aggregation, and may therefore be useful in the testing of theoretical models.