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arXiv · 0805.4526

A Mathematical Theory for Vibrational Levels Associated with Hydrogen Bonds II: The Non--Symmetric Case

George A. Hagedorn·Alain Joye
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Abstract

We propose an alternative to the usual time--independent Born--Oppenheimer approximation that is specifically designed to describe molecules with non--symmetrical hydrogen bonds. In our approach, the masses of the hydrogen nuclei are scaled differently from those of the heavier nuclei, and we employ a specialized form for the electron energy level surface. As a result, the different vibrational modes appear at different orders of approximation. Although we develop a general theory, our analysis is motivated by an examination of the F H Cl- ion. We describe our results for it in detail. We prove the existence of quasimodes and quasienergies for the nuclear vibrational and rotational motion to arbitrary order in the Born--Oppenheimer parameter epsilon. When the electronic motion is also included, we provide simple formulas for the quasienergies up to order epsilon cubed that compare well with experiment and numerical results.

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George A. Hagedorn, Alain Joye. 2008-05-29. A Mathematical Theory for Vibrational Levels Associated with Hydrogen Bonds II: The Non--Symmetric Case. https://doi.org/10.1142/s0129055x09003621

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