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398( )F. Fillaux et al.rChemical Physics 244 1999 387–403Ž . Ž . Ž .Fig. 9. Potential function left and wave functions right for the out-of-plane bending of the maleate ring see Table 7 .The INS bands for the ring-deformation have nocounterparts in the infrared w21 x. Consequently, thedeformations are totally symmetric and produce nodisplacement of the hydrogen-bonding proton. Thepotential function is almost unaffected by ODO sub-Table 7Žy1Calculated frequencies in cm units.and relative intensities forthe out-of-plane deformation of the maleate ring. The potentialfunction is:V s51479u 2 q869expŽ y240u 2 . y600expŽ y2454u 2 .,with V and u in cm y1 and radian units, respectively. The momentof inertia is 44 amu A˚2stitution. These dynamics suggest a Cfor the hydrogen maleate.7. Discussion2vsymmetryThe potential functions presented in this work arerather unconventional and we are not aware of anyother reported example. However, these potentialsaccount very well for all the observations: frequencies,intensities and isotopic ratios. Furthermore, themodel is consistent with neutron diffraction data.These potentials are thus likely to be physicallyrelevant.7.1. Ring dynamicsThe strain energy of the maleate ion in the planarcis configuration was estimated to be ;2500 cm y1Žy1;7.5 kcal mol . w15 x. The strain would be totallyrelieved either by a collapse of the O PPP O distanceto that of a covalent-like bond, with an O PPP Odistance of ;1.47 A, ˚ or a rotation of ;"458 of acarboxylate group about the C–C bond. ŽThe Oatoms would be then located at "0.85 A˚off themid-plane. . This strained planar geometry is stabilisedby hydrogen bonding. Crystal stacking is oflittle importance since the maleate ring remains esw18x. The triple minimumsentially planar in solutionpotential for the out-of-plane bending of the ring
( )F. Fillaux et al.rChemical Physics 244 1999 387–403 399might be regarded as the superposition of a doubleminimum potential, due to internal strain, and acentral potential dip corresponding to the attractiveenergy of the hydrogen bond and partial covalentcharacter w40 x. Unfortunately, this naive decompositionis not unique and this view is certainly toosimplistic. The potential minima correspond to minordeviations from planarity, compared to the totallyrelaxed geometry, and INS intensities for the ringdeformation imply rather large Ž C.H displacements.This deformation is not amenable to the rotation ofcarboxylate groups around the CC bonds w15 x.The shape of the potential is certainly a delicatebalance of many contributions that cannot be rationalisedin simple terms. It must be regarded as aneffective potential averaged over the hydrogen bonddynamics. There is probably some connection betweenthe triple wells for the ring and proton modes.7.2. Hydrogen bond dynamicsThe potential function for the proton can be alsoregarded as the superposition of a double wellŽminima located at ;"0.8 A˚and barrier height ofy1150–200 cm . and a central rather narrow wellwith a dissociation threshold of 1200–1400 cm y1 .The energy gain upon hydrogen bond formation is amaximum when the proton is localised at the centerof the hydrogen bond in the totally symmetric structureŽ. I . Presumably, this structure is stabilised byelectrostatic interactions. This energy gain vanishesrapidly for even small displacements of the protonaway from the central position as a consequence ofthe rearrangement of the electrical charges picturedschematically in structure Ž II ..OH distances, each of ;0.4 A. ˚ However, thesesecondary minima are not due to any particularanalytical form chosen for the potential function.They are imposed by the naOHO splitting at 500–530y1cm Ž Table 6 .. It must, therefore, be concluded thatthese minima occur because the O atoms can moveaway from the mid-plane, by at least "0.8 A, ˚ so asto keep the OH distance within a reasonable rangeŽ Fig. 10 .. This twisting of the maleate ion relaxes thestrain energy. The triple well potential is thus relatedto the interconversion between a symmetric singlewell and an asymmetric double well. The effectivepotential along the stretching coordinate presented inFig. 8 is a snapshot of the proton dynamics beforethe rotation of the carboxylic group creates asymmetryin the potential surface.We conclude that the strained planar geometry isstabilized by hydrogen bonding only in the groundstate of the proton stretching-mode. The very shortand symmetrical intramolecular bond does not surviveif the proton is in an excited vibrational state.Then the ring twists, the O–H bond assumes atypical covalent length, the H PPP O distance in-˚creases to ;2 A and the hydrogen bond is effec-Surprisingly, whereas the covalent OH bond instructure Ž II.is anticipated to be ;1 A, ˚ the twoupper minima Ž Fig. 8.correspond to extremely shortFig. 10. Schematic representation of the opening of the maleatering. I planar conformation and symmetric hydrogen bond in theground state. II non-planar conformation in an excited naOHOvibrational state. "v and QH 5 are energy and momentum transfer,respectively, to the proton stretching mode. QO H is the momentumtransfer to oxygen atoms perpendicular to the hydrogenmaleate ring.
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