ALBERT

Notes: Construction of an extended model potential surface for the bifluoride ion [FHF−] is described, based on ab initio calculations for the free ion at the CID (configuration interaction, double replacement) level with a Huzinaga–Dunning double-zeta basis set. 710 data points were generated, for displacements in the three noncyclic vibrational coordinates exploring the potential surface to a height at least 30 000 cm−1 above its minimum, and giving a realistic account of the dissociation into HF+F−. Analogous calculations were made for HF and F− using the same basis. The predicted hydrogen bond energy (De) is 48.13 kcal/mol, with equilibrium F–F separation Re =4.2905 a.u., in good agreement with other recent calculations. A model potential has been constructed, based on a superposition of Morse potentials associated with each H–F distance plus a fairly structureless correction function expressible as a 36-term least-squares polynomial in the prolate spheroidal coordinates used to describe vibrational displacements. The resulting model surface fits all 710 ab initio data points with an r.m.s. deviation of 65.6 cm−1, and points less than 15 000 cm−1 above the minimum with a deviation of 26.3 cm−1. This surface provides the basis for a series of vibrational dynamics studies on the FHF− system being done in this laboratory.

Notes: This paper concludes a theoretical study of vibrational dynamics in the bifluoride ion FHF−, which exhibits strongly anharmonic and coupled motions. Two previous papers have described an extended model potential surface for the system, developed a scheme for analysis based on a zero-order adiabatic separation of the proton bending and stretching motions (ν2,ν3) from the slower F–F symmetric-stretch motion (ν1), and presented results of accurate calculations of the adiabatic protonic eigenstates. Here the ν1 motion has been treated, in adiabatic approximation and also including nonadiabatic couplings in close-coupled calculations with up to three protonic states (channels). States of the system involving more than one quantum of protonic excitation (e.g., 2ν2, 2ν3 σg states; 3ν2, ν2+2ν3 πu states; ν3+2ν2, 3ν3 σu states) exhibit strong mixing at avoided crossings of protonic levels, and these effects are discussed in detail.Dipole matrix elements and relative intensities for vibrational transitions have been computed with an electronic dipole moment function based on ab initio calculations for an extended range of geometries. Frequencies, relative IR intensities and other properties of interest are compared with high resolution spectroscopic data for the gas-phase free ion and with the IR absorption spectra of KHF2(s) and NaHF2(s). Errors in the ab initio potential surface yield fundamental frequencies ν2 and ν3 100–250 cm−1 higher than those observed in either the free ion or the crystalline solids, but these differences are consistent and an unambiguous assignment of essentially all transitions in the IR spectrum of KHF2 is made. Calculated relative intensities for stretching mode (ν3, σu symmetry) transitions agree well with those observed in both KHF2 [e.g., bands (ν3+nν1), (ν3+2ν2), (3ν3), etc.] and the free ion (ν3,ν3+ν1). Calculated intensities for bending mode (ν2, πu symmetry) transitions agree well with experiment for the ν2 fundamental in the free ion and KHF2(s), and for a πu transition in KHF2 which we assign to ν2+2ν3, but are far too small to explain the prominence of progression bands (ν2+nν1) and especially the strong overtone 3ν2 in the spectrum of KHF2(s). Intensity of the progression bands (ν2+nν1) in KHF2 can be explained by hydrogen bonding between adjacent FHF− ions; in NaHF2(s) where such interaction is absent, the band (ν2+ν1) is 50–100 times weaker, in agreement with calculations.The relatively high intensity of the 3ν2 band, which also appears strongly in NaHF2(s), remains the major unexplained feature of the bifluoride spectrum in these solids. Suggestions are made for further experiments on the FHF− and FDF− systems which could test predictions of this dynamical analysis.

Notes: 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.

Notes: Classical and quantum descriptions of proton vibration are compared for a coupled nonharmonic model based on an ab initio potential for the bifluoride ion, [FHF]−. Accurate quantum calculations and exact classical dynamics are compared with quantum and classical versions of the self-consistent-field (SCF) approximation. Semiclassical and quantum SCF eigenvalues agree within JWKB-type errors. The SCF scheme closely approximates exact quantum states for the lowest 4–5 vibrational levels of each symmetry, except at avoided crossings where strong CI mixing of SCF levels occurs. True classical motion, however, is mainly irregular except at very low energies, and even where it remains regular it may be strongly reorganized by a 1:1 periodic resonance associated with major potential surface features. Strongly mixed CI states at systematic avoided crossings of SCF levels at higher energies do have classical analogs in the reorganized classical motions seen at low energies; stabilized CI components correspond to a stable periodic 1:1 orbit, destabilized components to an unstable periodic 1:1 elliptical orbit. Canonical perturbation theory is used to study further the sense in which the exactly separable classical SCF Hamiltonian is "close'' to the true Hamiltonian. Where true motion is modal or SCF-like, first-order perturbed trajectories and second-order perturbed energies describe it very accurately. However since the dynamics can be strongly disturbed even at very low energies, correlation effects are obviously not "small'' in the sense usually meant in classical dynamics, i.e., that regular trajectories mostly remain regular in the nonseparable perturbed system.