Theoretical rovibronic energies of pathological molecules: Extreme floppiness and BornOppenheimer breakdown
This talk will discuss two cases of molecules for which the conventional, perturbed harmonicoscillator/rigid rotor description of the rotation and vibration breaks down severely.
The first case of that of extremely flexible (or extremely floppy) molecules [13], of which protonated methane CH_{5} is the prototypical example. CH5 lacks a welldefined 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 rotationvibration spectra of CH_{5} [4]. We have proposed an algebraicmethod description [13], considering the rotation in space together with two extremely soft internalrotation vibrational modes as a free rotation in fivedimensional 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, lowlying energies of CH_{5} [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 BornOppenheimer approximation. In simulations of rovibronic molecular spectra aimed at, for example, supporting remotesensing 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).
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