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Issue 3, 2017
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A semi-classical approach to the calculation of highly excited rotational energies for asymmetric-top molecules

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Abstract

We report a new semi-classical method to compute highly excited rotational energy levels of an asymmetric-top molecule. The method forgoes the idea of a full quantum mechanical treatment of the ro-vibrational motion of the molecule. Instead, it employs a semi-classical Green's function approach to describe the rotational motion, while retaining a quantum mechanical description of the vibrations. Similar approaches have existed for some time, but the method proposed here has two novel features. First, inspired by the path integral method, periodic orbits in the phase space and tunneling paths are naturally obtained by means of molecular symmetry analysis. Second, the rigorous variational method is employed for the first time to describe the molecular vibrations. In addition, we present a new robust approach to generating rotational energy surfaces for vibrationally excited states; this is done in a fully quantum-mechanical, variational manner. The semi-classical approach of the present work is applied to calculating the energies of very highly excited rotational states and it reduces dramatically the computing time as well as the storage and memory requirements when compared to the fullly quantum-mechanical variational approach. Test calculations for excited states of SO2 yield semi-classical energies in very good agreement with the available experimental data and the results of fully quantum-mechanical calculations.

Graphical abstract: A semi-classical approach to the calculation of highly excited rotational energies for asymmetric-top molecules

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Publication details

The article was received on 12 Aug 2016, accepted on 08 Dec 2016 and first published on 09 Dec 2016


Article type: Paper
DOI: 10.1039/C6CP05589C
Citation: Phys. Chem. Chem. Phys., 2017,19, 1847-1856
  • Open access: Creative Commons BY license
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    A semi-classical approach to the calculation of highly excited rotational energies for asymmetric-top molecules

    H. Schmiedt, S. Schlemmer, S. N. Yurchenko, A. Yachmenev and P. Jensen, Phys. Chem. Chem. Phys., 2017, 19, 1847
    DOI: 10.1039/C6CP05589C

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