The limitations associated with the common practice of fitting a quadratic Hamiltonian to vibronic levels of a Jahn-Teller system have been explored quantitatively. Satisfactory results for the prototypical X∼2E′ state of Li3 are obtained from fits to both experimental spectral data and to an “artificial” spectrum calculated by a quartic Hamiltonian which accurately reproduces the adiabatic potential obtained from state-of-the-art quantum chemistry calculations. However the values of the Jahn-Teller parameters, stabilization energy, and pseudo-rotation barrier obtained from the quadratic fit differ markedly from those associated with the ab initio potential. Nonetheless the RMS deviations of the fits are not strikingly different. Guidelines are suggested for comparing parameters obtained from fits to experiment to those obtained by direct calculation, but a principal conclusion of this work is that such comparisons must be done with a high degree of caution.
Tran, H. K., Stanton, J. F., & Miller, T. A. (2018). Quantifying the effects of higher order coupling terms on fits using a second order Jahn-Teller Hamiltonian. Journal of Molecular Spectroscopy, 343, 102–115. https://doi.org/10.1016/j.jms.2017.09.010