  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.
