08-94 George A. Hagedorn, Alain Joye

A Mathematical Theory for Vibrational Levels Associated with Hydrogen Bonds II: The Non-Symmetrical Case (360K, pdf) May 21, 08

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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 $\eps$. When the electronic motion is also included, we provide simple formulas for the quasienergies up to order $\eps^3$ that compare well with experiment and numerical results.

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