Theoretical rovibronic energies of pathological molecules: Extreme floppiness and Born-Oppenheimer breakdown

This talk will discuss two cases of molecules for which the conventional, perturbed harmonic-oscillator/rigid- rotor description of the rotation and vibration breaks down severely.

The first case of that of extremely flexible (or extremely floppy) molecules [1-3], of which protonated methane CH5 is the prototypical example. CH5 lacks a well-defined equilibrium structure. Adding a proton to methane changes completely the vibrational energetics, especially some of the bending motions become extremely "soft" - that is, almost free. This cannot be described by conventional molecular theory and in recent years there has been much discussion as to how to understand experimental rotation-vibration spectra of CH5 [4]. We have proposed an algebraic-method description [1-3], considering the rotation in space together with two extremely soft internal-rotation vibrational modes as a free rotation in five-dimensional space with the appropriate symmetry group SU(5). The mathematical theory for rotation in a 5D space is completely known. We used the rather simple, resulting energy expression (depending on one parameter only) for the experimentally known, low-lying energies of CH5  [5] and found that we could represent them rather well by fitting the one parameter to experiment.

The second case is that of the Renner effect. For a chain molecule, the electronic energy can be doubly degenerate at linear configurations but splits into two distinct electronic states as the molecule bends out of linearity. The two electronic states interact and must be treated together in calculations of rovibronic energies. This constitutes a breakdown of the Born-Oppenheimer approximation. In simulations of rovibronic molecular spectra aimed at, for example, supporting remote-sensing investigations of space, it seems likely that the next hurdle encountered will be the interaction of electronic states, of which the Renner effect is a relatively simple example. For about 20 years now, we have carried out calculations of rovibronic energies for triatomic Renner molecules and examples will be presented (see, for example, [6] and references therein).


  1. H. Schmiedt, P. Jensen, and S. Schlemmer, Phys. Rev. Lett. 117, 223002/1-5 (2016).

  1. H. Schmiedt, P. Jensen, and S. Schlemmer, Chem. Phys. Lett. 672, 34 (2017) 

  2. H. Schmiedt, P. Jensen, and S. Schlemmer,  J. Mol. Spectrosc.  342, 132–137 (2017).

  3. T. Oka, Science 347, 1313 (2015). 

  4. O. Asvany, K. M. T. Yamada, S. Brünken, A. Potapov, and S. Schlemmer, Science 347, 1346 (2015).

  5. B. Ostojić, P. Schwerdtfeger, P. R. Bunker, and P. Jensen, J. Mol. Spectrosc. 330, 130–141 (2016).