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Universität zu Köln
Mathematisch-Naturwissenschaftliche Fakultät
Fachgruppe Physik

I. Physikalisches Institut

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Reconstruction of the Energy Levels of CH5+


  • asvany
  • brackertz
  • schlemmer


In the Cologne-Laboratories high-resolution rovibrational spectra of CH5+ 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 CH5+ without relying on any model. In parallel a superrotor theory of CH5+ is in developement in our group and has been verified based on the reconstructed energy term scheme. ...more


Reconstruction of Molecular Energy Levels Using Combination Differences: From Lines to states without a Model
For molecules which lack an appropriate model (as CH5+) 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 CH5+.
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{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 ofCH5+. 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 1: CD spectra of CH5+. (A) at a nominal temperature of 10K, (B) at a nominal temperature of 4K
Figure 2: Reconstruction of the energy levels of CH5+, set 1



  • This work has been financially supported by the Deutsche Forschungsgemeinschaft (DFG) via grant AS 319/2-2.