Low-energy unphysical saddle in polynomial molecular potentials

Abstract

Vibrational spectra of polyatomic molecules are often obtained from a polynomial expansion of the adiabatic potential around a minimum. For several molecules, we show that such an approximation displays an unphysical saddle point of comparatively small energy, leading to a region where the potential is negative and unbounded. This poses an upper limit for a reliable evaluation of vibrational levels. We argue that the presence of such saddle points is general.

Acknowledgements

We thank J.H. van der Waals, G. Scoles, K. Lehmann, A. Callegari for useful discussions, and J.M.L. Martin and J.P. François for kindly providing us the PP parameters for ethylene.