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 Title: FROM LINES TO STATES WITHOUT A MODEL Author(s): Brackertz, Stefan Contributor(s): Asvany, Oskar; Schlemmer, Stephan Subject(s): Mini-symposium: New Ways of Understanding Molecular Spectra Abstract: %\begin{wrapfigure}{l}{0pt} %\includegraphics[scale=0.3]{fred.eps} %\end{wrapfigure} The fundamental Ritz combination principle % \footnote{W. Ritz, On a new law of series spectra, Astrophys. J. 28 (1908) 237.} % originally found for atoms has also been applied to molecules as a method to reconstruct the energy states from measured lines without relying on any model Hamiltonian. In 2006 Nesbitt and coworkers % \footnote{C. Savage, F. Dong, D.J. Nesbitt, Toward a quantum-mechanical understanding of the high-resolution infrared spectrum of CH$_5^+$, in: Contribution TA05, 61st International Symposium on Molecular Spectroscopy, Columbus, OH, USA, 2006.} % proposed to apply it to protonated methane, CH$_5^+$. We used this idea to reconstruct a part of its ground state energies employing spectra of combination differences (CDs) determined from very high resolution ro-vibrational data % \footnote{Oskar Asvany, Koichi M. T. Yamada, Sandra Brünken, Alexey Potapov, Stephan Schlemmer. Experimental ground-state combination differences of CH$_5^+$. Science, 347(6228):1346–1349, 2015.}. % Since then the method has been significantly improved % \footnote{S. Brackertz, S. Schlemmer, O. Asvany, Searching for new symmetry species of CH$_5^+$ – From lines to states without a model, J. Mol. Spectrosc. 342 (2017) 73–82.} % as the CD lines essentially represent kernel density estimations, a well-known tool in mathematics. Furthermore, a combinatorial approach has been developed to reconstruct vibrational ground states as well as vibrationally excited states from the CD spectra without relying on measurements at different temperatures. As a result, 1063 of the 2897 measured lines of CH$_5^+$ being part of four different symmetry species could be assigned. This allowed for a comparison of the measurements with the analytical model of Schmiedt et al. % \footnote{H. Schmiedt, P. Jensen, S. Schlemmer, Rotation-vibration motion of extremely flexible molecules – the molecular superrotor, Chem. Phys. Lett. 672 (2017) 34–46.} % as well as with the {\it ab initio} calculations of Wang and Carrington % \footnote{X.-G. Wang, T. Carrington, Calculated rotation-bending energy levels of CH$_5^+$ and a comparison with experiment, J. Chem. Phys. 144 (2016) 204304.}. %In this talk we explain the improved method, discuss why we think it %is more reliable than earlier attempts and present some ideas for %further improvements as well as for applications in other contexts. Issue Date: 06/19/18 Publisher: International Symposium on Molecular Spectroscopy Citation Info: APS Genre: Conference Paper / Presentation Type: Text Language: English URI: http://hdl.handle.net/2142/100642 DOI: 10.15278/isms.2018.TH06 Other Identifier(s): TH06 Date Available in IDEALS: 2018-08-172018-12-12
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