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Universität zu Köln
Mathematisch-Naturwissenschaftliche Fakultät
Fachgruppe Physik

I. Physikalisches Institut


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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+. ...more


Illustration of different types of combination differences. The energy scale on the left is typical of the underlying experiment.
Principle of kernel density estimation. The vertical lines are the positions of CDs. The density estimation (blue) results by summing up kernel functions (red) at the CD positions. (Source: Wikipedia)
Peaks in the CD spectrum carry information on the topology of the spectroscopic network: Every gsCD consists of 2 'legs'. If two legs of different CD peaks share measured lines (red) these legs join a common energy level.
Reconstruction of the vibrational ground states: From left to right, the energy scheme is successively built up by considering the topological information of the found CD peaks shown in the table.


{Mathematical Statistics}

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