VIBRATIONAL DYNAMICS OF THE BIFLUORIDE ION .2. ADIABATIC SEPARATION AND PROTON DYNAMICS

Vibrational dynamics of the bifluoride ion FHF-, which exhibits strongly anharmonic and nonseparable vibrations, is studied using the extended ab initio model potential surface described in the first paper of this series. Adiabatic separation of the proton motion from the F-F (ν1) motion forms a zero-order basis for description, although strong coupling of adiabatic states by the ν1 motion is important in higher vibrational levels and must be considered to understand the spectrum. The adiabatic protonic eigenstates at F-F separations R from 3.75 to 6.40 a.u. have been determined using the self-consistent field approximation in prolate spheroidal coordinates to provide a basis set for configuration interaction expansion of the exact eigenstates. 78 SCF eigenstates (21 σg, 21 σu, 21 πu, and 15 πg) were computed by "exact" numerical solution of the SCF equations. The adiabatic CI eigenstates are shown to be converged in energy to better than 1.0 cm -1 for the ground state of each symmetry type and usually better than 10 cm-1 for the lowest three to five states, and pass critical tests of accuracy such as the Hellmann-Feynman theorem. The resulting CI potential energy curves closely resemble corresponding SCF energy curves and justify the concept of mode separation even in this very anharmonic system. The adiabatic CI potential energy curves explain most aspects of the dynamics relevant to the IR and Raman spectra of FHF- (e.g., in KHF2), and calculations of ν1 dynamics within the adiabatic approximation suffice to assign most of the observed IR spectrum of KHF2(s) (to about 6000 cm-1). States corresponding qualitatively to modal overtone and combination levels such as 3ν2 and (ν2 + 2ν3) however exhibit avoided crossings in the neighborhood of the equilibrium configuration and "Fermi resonance" involving interactions of two or more such adiabatic states via the ν1 motion must be treated by close-coupling to predict both frequencies and intensities in the relevant portions of the IR spectrum. From the viewpoint of current interest in classical studies of vibrational dynamics, this system provides an interesting model problem markedly different from the more nearly harmonic models mainly studied in the past. The multiplicity of narrow avoided crossings between protonic levels and persistent success of the SCF approximation as a zero-order description of the proton dynamics except at crossings suggest that comparisons of classical trajectory studies of the system with the quantum mechanical results obtained here may be fruitful. © 1990 American Institute of Physics.