An extended Jahn-Teller Hamiltonian is presented for the case where the (slow) nuclear motion extends far from the symmetry point and may be described approximately as motion on a sphere. Rather than the traditional power series expansion in the displacement from the C3v symmetry point, an expansion in the spherical harmonics is employed. Application is made to the vibrational Jahn-Teller effect in CH3XH, with X = S, O, where the equilibrium CXH angles are 83° and 72°, respectively. In addition to the symmetry-required conical intersection (CI) at the C3v symmetry point, ab initio calculations reveal sets of six symmetry-allowed vibrational CIs in each molecule. The CIs for each molecule are arranged differently in the large-amplitude space, and that difference is reflected in the infrared spectra. The CIs in CH3SH are found in both eclipsed and staggered geometries, whereas those for CH3OH are found only in the eclipsed geometry near the torsional saddle point. This difference between the two molecules is reflected in the respective high-resolution spectra in the CH stretch fundamental region.
Dawadi, M. B., Thapaliya, B. P., & Perry, D. S. (2017). An extended E⊗e Jahn-Teller Hamiltonian for large-amplitude motion: Application to vibrational conical intersections in CH3SH and CH3OH. The Journal of Chemical Physics, 147(4), 044306. https://doi.org/10.1063/1.4994699
Journal of Chemical Physics