Abstract
We propose an alternative to the usual time–independentBorn–Oppenheimer approximation that is specifically designed todescribe molecules with symmetrical Hydrogen bonds. In our approach,the masses of the Hydrogen nuclei are scaled differently from thoseof the heavier nuclei, and we employ a specialized form for theelectron energy level surface. Consequently, anharmonic effects playa role in the leading order calculations of vibrational levels.
Although we develop a general theory, our analysis is motivated byan examination of symmetric bihalide ions, such as FHF − orClHCl −. We describe our approach for the FHF − ion in detail.
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Communicated by H. Spohn
Partially Supported by National Science Foundation Grants DMS–0303586 andDMS–0600944.
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Hagedorn, G.A., Joye, A. A Mathematical Theory for Vibrational Levels Associated with Hydrogen Bonds I: The Symmetric Case. Commun. Math. Phys. 274, 691–715 (2007). https://doi.org/10.1007/s00220-007-0292-5
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DOI: https://doi.org/10.1007/s00220-007-0292-5