Vibrational dynamics of hydrogen bonds. I. FHF− system

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Abstract
A general treatment of nonharmonic vibrational dynamics in an isolated hydrogen bond is presented, based on an adiabatic mode separation of hydrogenic motions from those of the heavier particles. The validity of the Stepanov (adiabatic) approximation is examined by including correct nonadiabatic couplings and solving the resultant coupled eigenvalue problem for a model system (FHF−) in which the couplings have maximal intrinsic strength. Convergence is demonstrated by including up to three coupled protonic states. Comparison with exact results thus obtained shows that the adiabatic approximation gives transition frequencies within 1%, and infrared relative intensities to about 10%—in cases where the coupled protonic levels are not degenerate. Cases of isolated strong coupling, arising from accidental or systematic degeneracies of proton levels, can be accommodated in the theory in a direct way, but do not arise for FHF−. The theory may similarly be extended as the basis for the dynamical analysis of systems involving two or more hydrogen bonds. Calculations on the FHF− system are based entirely on the ab initio potential energy surface of Almlo/f, but employ a model form with correct dissociation properties. The close agreement of computed and observed transition frequencies and IR relative intensities leads to a convincing assignment (in the adiabatic mode description) for nearly all transitions in the bifluoride spectrum (e.g., in KHF2(s)), on the basis of an isolated ion model.

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