- 08-94 George A. Hagedorn, Alain Joye
- A Mathematical Theory for Vibrational Levels Associated with Hydrogen Bonds II: The Non-Symmetrical Case
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.