Structure and dynamics of the symmetric hydrogen ... - ResearchGate

400( )F. Fillaux et al.rChemical Physics 244 1999 387–403tively ‘broken’. The potential energy function in Fig.8 gives a rather modest dissociation energy of ;500y1Žy1cm 1.5 kcal mol .. This is a clear example of avery strong hydrogen bond that is nonetheless easilydissociated by thermal activation and probably solventeffects.The dissociation energy can be regarded in twodifferent ways. In the most superficial view, this iscrudely the excess energy gain upon formation of theŽy1 y1hydrogen bond ;3000 cm or 9 kcal mol . afteraccounting for the strain energy, which is needed toflatten the ring. This illustrates how ambiguous theconcept of binding energy can be for the case ofhydrogen bonds. For the hydrogen maleate ion, 1.5and 9 kcal mol y1 are equally acceptable values,depending on which initial and final states are considered.Moreover, there is no straightforward reasonto consider that the bond energies should be correlatedto the strain energy. In this view, the dissociationenergy should be specific to a given system andquite different from any other symmetric hydrogenbond. This is largely in conflict with the well-establishedcorrelation between the OH stretching frequenciesand the O PPP O distances in hydrogenbonded systems w31 x. Furthermore, energy gains uponformation of hydrogen or deuterium bonds should bedifferent and yield different dissociation energies.Instead of that, the very small frequency shifts obw21xshow that the dissociation energies are virtually iden-served in the infrared for the deuterium maleatetical for the two analogues.Alternatively, in a broader view, the dissociationenergy can be seen a consequence of the quantumnature of the hydrogen bond because the totallysymmetric structure Ž. I only exists in the vibrationalground state. The probability distribution for the2proton C is well localized at the center Ž Fig. 8 .0.The probability distributions of vibrational excitedstates, Cn2 , show that the proton is largely localizedaway from the central position. Then, structure Ž II.is the dominant one and the hydrogen bond is broken.In other words, the proton ground state is‘hydrogen bonding’ whilst excited states are ‘hydrogenanti-bonding’. If this mechanism is correct, thevibrational spectra are not simply related to theenergy gain upon the hydrogen bond formation andsystems containing formally symmetric hydrogenbonds should have similar dissociation thresholds,and overall potential functions, almost independentlyof their chemical nature. The correlation betweenfrequencies and distances is thus recovered, as wellas the very small frequency shifts upon deuteration.It might be argued that proton dynamics in intermolecularsystems with short symmetric hydrogenbonds have been interpreted differently w38,39 x.However, we suspect they are amenable to potentialfunctions similar to that for potassium hydrogenmaleate.7.3. Infrared spectraInfrared spectra reported for an electrical fieldparallel to the hydrogen bond Ž E in Ref. w21x.5 candthe potential presented in Fig. 8 can be rationalisedon the basis of symmetry related selection rulesŽ Table 6 .. For a symmetrical hydrogen bond, infraredintensities are determined by the leading termsof the dipole moment derivatives E 2 j MrEr 52 j . Consequently,transitions from the ground state to antisymmetricstates are inactive. The rather broad bandsobserved at 545, 700 and 990 cm y1 may thus corre-Žy1. Žy1spond to the 02 530 cm , 04 744 cm .Žy1and 06 958 cm . transitions. Conversely, transmissionwindows reported at 605 and 795 cm y1 areŽy1attributed to the 03 665 cm . and 05 Ž856y1cm . inactive transitions. The additional transmissionwindow visible at ;1050 cm y1 in the infraredspectrum ŽFig. 2 in Ref. w21x.may correspond to they107 transition calculated at 1065 cm Ž Table 6 ..This assignment scheme suggests that the hydrogenbond is effectively symmetrical even on the shortŽy13time-scale of vibrational spectroscopy ;10 –y1410 s .. The alternative assignment scheme prow21x, based on a very broad n aposed previouslyOHO band with transmission windows due to stronganharmonic coupling with other internal vibrations,is clearly in disagreement with the INS spectra.7.4. Band shapesThe rather sharp bands observed for the protonstretching-mode suggest well-defined excited stateswith rather long lifetimes. There is no evidence forthe relaxation of the maleate ring to the twist configurationby rotation of a carboxylic group in theproton excited states. Therefore, excited states corre-