Research Projects
Reconstruction of the Energy Levels of CH_{5}^{+}
Investigators
 asvany
 brackertz
 schlemmer
Description
In the CologneLaboratories highresolution rovibrational spectra of CH_{5}^{+} are measured. But so far there is no analytical description of this prototype of a floppy molecule. This is why we use the properties of kernel density estimators in combination with a new combinatorial approach to reconstruct the energy levels of CH_{5}^{+} without relying on any model. In parallel a superrotor theory of CH_{5}^{+} is in developement in our group and has been verified based on the reconstructed energy term scheme. ...moreMethods
Reconstruction of Molecular Energy Levels Using Combination Differences: From Lines to states without a Model
For molecules which lack an appropriate model (as CH_{5}^{+}) common data evaluation methods which are based on the assignments of the measured lines to those of the model cannot be applied. Instead pattern recognition methods have to be applied to the measured data to reconstruct at least the energy levels of the molecule (without quantum numbers).
Such a pattern recognition method is the Ritz combination principle which is more than 100 years old. It is based on calculating all possible CDs from the measured lines and searching for cumulationg values. This method has been enhanced a lot to be reliably applicable even to very dense spectra as that of CH_{5}^{+}.
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Instruments
{Mathematical Statistics}
Recent Results
The results obtained so far math very well with the results of the molecular superrotor theory developed by Schmiedt et al.
Figure 2 shows the reconstructed ground states (lower part) and ex cited states (upper part) for of the of a set ofCH_{5}^{+}. For the reconstruction of the excited states, for every CD (red vertical lines) the candidate excited states are listed (short blue horizontal lines in upper part). Only those excited states which appear often enough are considered reliable (red horizontal line).
Figure 2 shows the reconstructed ground states (lower part) and ex cited states (upper part) for of the of a set ofCH_{5}^{+}. For the reconstruction of the excited states, for every CD (red vertical lines) the candidate excited states are listed (short blue horizontal lines in upper part). Only those excited states which appear often enough are considered reliable (red horizontal line).
Publications

Experimental groundstate combination differences of CH5+
Oskar Asvany, Koichi M. T. Yamada, Sandra Brünken1, Alexey Potapov1, Stephan Schlemmer
Science 347 1346  1349 (2015) 
Analyse komplexer Molekülspektren (diploma thesis: http://kups.ub.unikoeln.de/6954/)
Stefan Brackertz
(2016) 
Collective Molecular Superrotation: A Model for Extremely Flexible Molecules Applied to Protonated Methane
Schmiedt, H. and Jensen, P. and Schlemmer, S.
Physical Review Letters 117 223002 (2016) 
Searching for new symmetry species of CH5+ – From lines to states without a model
Stefan Brackertz, Stephan Schlemmer, Oskar Asvany
Journal of Molecular Spectroscopy 342 73  82 (2017)
Acknowledgments
 This work has been financially supported by the Deutsche Forschungsgemeinschaft (DFG) via grant AS 319/22.