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

Ž .Chemical Physics 244 1999 387–403www.elsevier.nlrlocaterchemphysStructure and dynamics of the symmetric hydrogen bond inpotassium hydrogen maleate: a neutron scattering studyF. Fillaux a,) , N. Leygue a , J. Tomkinson b , A. Cousson c , W. Paulus caLab. de Dynamique, Interactions et ReactiÕite, ´ ´ Centre Nat. de la Rech. Scientifique ( LADIR-CNRS ), 2 rue Henry Dunant, 94320 Thiais,Franceb ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX, UKcLaboratoire Leon ´ Brillouin ( CEA-CNRS ), CE Saclay, 91191 Gif-sur-YÕette Cedex, FranceReceived 4 February 1999AbstractThe crystal structure of potassium hydrogen maleate KHŽ OOC–CH5CH–COO.has been studied at 300, 14 and 5 Kusing three-dimensional single-crystal neutron diffraction data. There is no evidence for any phase transition. The crystalŽllstructure is orthorhombic, P D ., with four entities in the unit cell Ž Zs4 .bcm 2h, in accord with previous X-ray diffractionwork. The ion is nearly planar and deviation from C2vsymmetry is negligible. The short internal hydrogen bond parallel tothe c axis, R s2.427Ž.1 A˚O PPP Oat 5 K, is symmetrical with the proton located at the center. Inelastic neutron scatteringŽ .y1INS spectra, from 16 to 4000 cm , of the fully hydrogenated sample and partially deuterated analogues, KHŽOOC–CD5CD–COO. and KDŽ OOC–CH5CH–COO ., have been recorded for powdered samples and aligned single crystals at 20K. Complex spectral profiles are observed for the stretching mode of the hydrogen bond, naOHO, and for the totallysymmetric out-of-plane deformation of the maleate ion. An isotopic mixture of KHŽ OOC–CD5CD–COO ., 20%, andKDŽ OOC–CD5CD–COO ., 80%, reveals that intermolecular coupling is negligible. Frequencies and intensities areamenable to symmetrical potential functions with a central minimum between secondary minima at higher energy. The INSand infrared band profiles suggest that the planar conformation with C2vsymmetry of the maleate ring is unstable in excitedvibrational states. The quantum nature of the hydrogen bond is emphasised with the concept of ‘hydrogen bondingrantibonding’states. q 1999 Elsevier Science B.V. All rights reserved.Keywords: Symmetric hydrogen bond; Potassium hydrogen maleate; Neutron scattering1. IntroductionIn hydrogen bonds AH PPP B, it is widely acceptedthat the potential energy for the motion of thehydrogen atom has two minima w1–10 x. For symmetricsystems AH PPP A, the two wells can be equivalent.There are then two tautomeric forms and proton) Corresponding author. Tel.: q33-1-49-78-12-83; Fax: q33-1-49-78-13-23; E-mail: fillaux@glvt-cnrs.frtunnelling may occur. For shorter hydrogen bonds,the distance between the two minima decreases andthe potential barrier between them may disappear.There remains only a single well and the symmetricstructure can be regarded as the ‘intermediate-state’for proton transfer in chemical reactions or biologiw11–13x.The mono-anion of maleic acid in potassium hy-cal processesdrogen maleate, KHŽ OOC–CH5CH–COO .,ŽFig.1a.is a classic example of a symmetric intramolec-0301-0104r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0301-0104 99 00153-6

388( )F. Fillaux et al.rChemical Physics 244 1999 387–403Fig. 1. Schematic representation of the hydrogen maleate anion Ž. aand of the crystal structure of potassium hydrogen maleate at 14 KŽ. b . The dot dash line is going through the centre of gravity ofeach HCCOO entity.ular hydrogen bond. An extremely short O PPP HPPP O bond with length R s2.437 A˚O PPP Oand theproton located at the center has been shown bydiffraction studies w14,15 x. Infrared and Raman w16–21 x, inelastic neutron scattering Ž INS. w22–24xandother techniques w25–27xare in general agreementthat this strong hydrogen bond is, at least statistiw28–30xconverge to the conclusion that in solution hydrogencally, symmetrical. However, NMR studiesmaleate and many other monoanions of diacids existas pairs of asymmetric equilibrating tautomers withina double-well potential. This was claimed as ‘aremarkably simple counterexample to the prevailinghope that a crystal structure describes the solutionstructure’ w28 x.Vibrational spectroscopy provides information onthe proton dynamics on a much shorter time scalethan that accessible with NMR or diffraction. However,the broad infrared bands below 1800 cm y1typical of short hydrogen bonds are not fully underw16x. Unfortunately, it is difficult to establishstoodany assignment scheme on the basis of force-fieldcalculation w17 x, isotopic substitution or polarisationeffects w18,19,21 x. The most straightforward informationwas obtained with the INS technique: intensebands at ;1250 and 1650 cm y1 are clearly the gOHO and d OHO modes, respectively. The assignmentof the naOHO mode, on the other hand, is noteasy, partially because of technical limitations regardingbackground definition, accessible frequencyrange, resolution and intensity definition. Five bandsbetween 400 and 1000 cm y1 , with rather modestintensities, were tentatively regarded as combinationsof n OHO, n OHO and ring modes w22 xas. It wasconcluded that the naOHO mode most likely splitsinto several components. Thorough investigations ofthe infrared and Raman spectra were in generalagreement with this assignment scheme w19 x. However,in more recent studies, the naOHO mode wasreassigned to a very broad band centred at ;800cm y1 with two wide transmission windows at ;800and 600 cm y1 due to strong anharmonic interactionwith ring deformations and d COO w21 x. The resultingoptical profile is composed of three broad bandsat 545, 700 and 990 cm y1 . However, the small shiftof the n OHO upon deuteration Ža na OHOrnaODO;1.09.could not be explained. A frequency ratioclose to unity is normally regarded as the signatureof a possible double-well potential w31 x, but this is inconflict with the structure of the hydrogenate maleateat room temperature w14 x.The TFXA spectrometer at the ISIS pulsed neutronsource Ž Rutherford Appleton Laboratory, UK.covers a larger frequency range with better resolutionand intensity measurements than used for previw22x. We have recorded the INSous experimentsspectra from 16 to 4000 cm y1 of the totally hydrogenatedsample, KHMH 2, and isotopic analoguesKHMD and KDMH . Furthermore, the excellent2 2

( )F. Fillaux et al.rChemical Physics 244 1999 387–403 389definition of the momentum transfer direction for aTFXA-like spectrometer was exploited to study orientedsingle crystals for momentum transfer alongthe OHO stretching mode parallel to the c crystalaxis Ž Fig. 1b .. Unfortunately, the maleate rings formlayers almost perpendicular to each other’s and it isnot possible to observe extinction for in-plane bendingmodes.The band assignment scheme presented below isin general agreement with previous INS work w22 x,but quite at variance with assignments based oninfrared spectra w21 x. Complex spectral patterns areassigned to the naOHO, on the one hand, and to anout-of-plane deformation of the maleate ring, on theother. They confirm spectacular anharmonicity forthese vibrations. The energy level schemes are notamenable to the usual single or double minimumpotential functions and it is necessary to considermore complex potential functions. Since the potentialfunction may not be unique, it is of primary importanceto determine the mean positions and temperaturefactors of the protons in the crystal at lowtemperature. The fully hydrogenated potassium hydrogenmaleate has been studied at 300, 14 and 5 K,using three-dimensional single-crystal neutrondiffraction data. In all cases, the hydrogen maleatering remains planar and the proton is at the center ofthe hydrogen bond. It is then possible to determineprecisely the potential functions governing the dynamics.2. ExperimentalThe samples were obtained by crystallisation fromaqueous solutions Ž H O or D O.2 2 of maleic anhydrideand K 2CO 3. KHMD2was obtained from partiallydeuterated dimethyl fumarate, C6H 6D2O 4,prepared according to Ref. w32 x. This ester was hydrolysedand the acid was heated at 1608C withphosphoric anhydride, P2O 5, to obtain the maleicanhydride. Single crystals were obtained by slowevaporation of aqueous solutions.For neutron diffraction measurements, an approximatelycubic sample was cut Ž3=3=3 mm 3. froma large crystal Ž3=3=2 cm 3., and tested at roomtemperature. It was then enclosed in an aluminiumcontainer and mounted in a helium vapour streamcryostat. Measurements at room temperature, 14 and5 K Ž see Table 1.were carried out on a Stoefour-circle diffractometer on the 5C2 channel Žls0.8302Ž. 2 A˚. at the hot source of the Orphee ´ reactorŽ Laboratoire Leon ´ Brillouin, Saclay, France ..For INS measurements, platelets parallel to theŽ .3a,b plane ;20=20=2 mm grow naturally. Theorientation was confirmed with a polarising microscope.The TFXA spectrometer at the ISIS pulsed neutronsource ŽRutherford Appleton Laboratory,Chilton, UK.is an inverted time-of-flight spectromew33x. The detectedter with resolution Dvrv;3%spectra, normalised to the incident monitor, wereconverted by standard programs from counts perchannel to the conventional scattering functionSŽ Q,v .. The momentum transfer Q is the vectordifference between the incident and scattered wavevectors < k < s2prl and < k

390( )F. Fillaux et al.rChemical Physics 244 1999 387–403Table 2Atom coordinates for potassium hydrogen maleateAtom xra yr b zrcKŽ. 1 0.2628Ž.3 0.7500 0.00000.2610Ž.2 0.7500 0.00000.2610Ž.3 0.7500 0.0000OŽ. 1 0.4842Ž. 2 0.2965Ž. 1 0.17391Ž.50.4895Ž. 1 0.29438Ž. 5 0.17376Ž.20.4894Ž. 2 0.2942Ž. 1 0.17376Ž.4OŽ. 2 0.2368Ž. 2 0.4195Ž. 1 0.07191Ž.60.23586Ž. 9 0.41932Ž. 6 0.07109Ž.20.2359Ž. 2 0.4194Ž. 1 0.07104Ž.4CŽ. 1 0.2824Ž. 1 0.3968Ž. 1 0.14745Ž.40.28292Ž. 8 0.39632Ž. 5 0.14694Ž.20.2828Ž. 1 0.39637Ž. 9 0.14691Ž.4CŽ. 2 0.0904Ž. 2 0.48852Ž. 9 0.20790Ž.50.08707Ž. 8 0.48966Ž. 5 0.20783Ž.20.0871Ž. 1 0.48989Ž. 9 0.20785Ž.4H21 Ž . y0.0744Ž. 4 0.5650Ž. 2 0.1767Ž.1y0.0813Ž. 2 0.5675Ž. 1 0.17664Ž.6y0.0809Ž. 4 0.5673Ž. 3 0.1767Ž.1HŽ. 1 0.4942Ž. 5 0.2939Ž.3 0.25000.4985Ž. 3 0.2919Ž.2 0.25000.4987Ž. 5 0.2921Ž.3 0.2500For each atom, the three rows are, from the top, the coordinates at300, 14 and 5 K.sample. There is a small component Ž Q .H and theneutron momentum polarisation is:< Q < 25 E0Rs ( Ž 12.< Q < EHfŽy1E and E 32 cm .0 f are the energies of the incidentand scattered neutrons, respectively. At low energyŽy1transfer, R is only moderate ;3 at 100 cm ..However, the polarisation improves rapidly, suchthat R;25 at 800 cm y1 . For large energy transfer,any influence of Q H can be ignored.The crystals wrapped in aluminium foil weremounted in a closed cycle refrigerator such that themomentum transfer component Q 5 was parallel tothe c crystal axis. For powders, about 3 g of sampleswere wrapped in aluminium foil and loaded into aclosed cycle refrigerator. For all samples, the temperaturewas Ž 20"2.K.Potential functions were calculated using basissets of 40 harmonic oscillator wave functions w34,35 x.INS intensities were calculated by numerical integraw36x:SŽ Q ,v . s

( )F. Fillaux et al.rChemical Physics 244 1999 387–403 391Table 4Thermal parameters Ž in A˚2units.for potassium hydrogen maleateŽ . Ž . Ž . Ž . Ž . Ž . Ž .Atom U 11 U 22 U 33 U 23 U 13 U 12 U isoKŽ. 1 0.0352Ž. 9 0.0350Ž. 9 0.0303Ž. 9 0.0011Ž.8 0.0000 0.0000 0.03340.0046Ž. 3 0.0054Ž. 3 0.0041Ž. 3 0.0001Ž.2 0.0000 0.0000 0.00470.0055Ž. 6 0.0051Ž. 7 0.0050Ž. 6 0.0004Ž.5 0.0000 0.0000 0.0052OŽ. 1 0.0433Ž. 5 0.0507Ž. 6 0.0261Ž. 7 y0.0023Ž. 4 0.0011Ž. 3 0.0150Ž.4 0.03710.0070Ž. 2 0.0079Ž. 2 0.0044Ž. 2 y0.0001Ž. 1 0.0001Ž. 1 0.0027Ž.1 0.00600.0081Ž. 3 0.0086Ž. 4 0.0040Ž. 3 y0.0002Ž. 2 y0.0002Ž. 2 0.0026Ž.3 0.0063OŽ. 2 0.0526Ž. 6 0.0481Ž. 6 0.0254Ž. 5 0.0020Ž. 5 y0.0050Ž. 3 0.0011Ž.4 0.03970.0082Ž. 2 0.0079Ž. 2 0.0037Ž. 2 0.0001Ž. 1 y0.0005Ž. 1 0.0008Ž.1 0.00610.0089Ž. 3 0.0081Ž. 3 0.0035Ž. 3 0.0002Ž. 2 y0.0005Ž. 2 0.0013Ž.2 0.0062CŽ. 1 0.0329Ž. 5 0.0308Ž. 5 0.0248Ž. 4 y0.0002Ž. 3 y0.0016Ž. 3 y0.0024Ž.3 0.02920.0055Ž. 1 0.0053Ž. 1 0.0037Ž. 1 y0.00018Ž. 9 y0.00005Ž. 8 0.00021Ž.9 0.00480.0062Ž. 3 0.0059Ž. 3 0.0032Ž. 3 y0.0004Ž. 2 y0.0001Ž. 2 0.0002Ž.2 0.0048CŽ. 2 0.0341Ž. 5 0.0333Ž. 5 0.0298Ž. 4 0.0011Ž. 3 y0.0022Ž. 3 0.0043Ž.3 0.03210.0061Ž. 1 0.0064Ž. 1 0.0042Ž. 1 0.00005Ž. 8 y0.00025Ž. 9 0.0014Ž.1 0.00540.0065Ž. 3 0.0073Ž. 3 0.0039Ž. 3 0.0001Ž. 2 y0.0002Ž. 2 0.0013Ž.2 0.0056HŽ 21. 0.066Ž. 1 0.068Ž. 1 0.051Ž. 1 0.0074Ž. 8 y0.0079Ž. 9 0.0264Ž.9 0.04800.0207Ž. 4 0.0254Ž. 4 0.0167Ž. 4 0.0025Ž. 3 y0.0031Ž. 3 0.0111Ž.3 0.01840.0214Ž. 7 0.0268Ž. 8 0.0170Ž. 7 0.0031Ž. 5 y0.0033Ž. 5 0.0119Ž.7 0.0187HŽ. 1 0.048Ž. 1 0.056Ž. 1 0.044Ž. 1 0.0000 0.0000 0.0139Ž.9 0.05640.0163Ž. 4 0.0183Ž. 5 0.0225Ž. 5 0.0000 0.0000 0.0030Ž.4 0.01870.0159Ž. 9 0.020Ž. 1 0.023Ž. 1 0.0000 0.0000 0.0034Ž.8 0.0193For each atom the three rows are, from the top, the thermal parameters at 300, 14 and 5 K.Temperature factors of all atoms decrease substantiallyŽ Table 4.and the decrease is larger for heavieratoms than for protons. Considering the maleateanion as a rigid body, excluding the hydrogen atoms,a thermal libration analysis w37xshows a large decreaseof libration, from "88 at room temperature to"38 at 5 and 14 K. The principal axis of libration isperpendicular to the maleate anion. Librational correctionsto heavy atom bond lengths are negligibleŽ no more than 0.001 A˚at low temperature .. Themaleate ion is virtually planar, with maximum deviationfrom the mean plane less than 0.01 A. ˚ Thethermal parameters for hydrogen bonding protonsHŽ. 1 and for protons bound to carbon atoms HŽ 21.are similar.of much better quality. These sharp bands are incontrast to infrared spectra. Above 2000 cm y1 , onlythe CH stretching modes are observed at ;3080cm y1 for the KHMH 2 and KDMH 2 derivatives. Theassignment scheme proposed in Table 5 is straightforward.Bands due to the three modes of the hydrogenbond dominate the spectra of the KHMD2sampleŽ Fig. 4 .. The oriented single crystal confirms that4. INS spectra and band assignmentThe INS spectra of powdered samples and alignedsingle crystals of KHMH Ž Figs. 2 and 3 .2 , KHMD2Ž Figs. 4 and 5. and KDMH Ž powder only, Fig. 6.2reveal well-resolved bands below 2000 cm y1 , ingeneral agreement with previous works w22,24 x, butFig. 2. INS spectrum of totally hydrogenated potassium hydrogenmaleate. Powdered sample at 20 K.

392( )F. Fillaux et al.rChemical Physics 244 1999 387–403Fig. 3. INS spectrum of totally hydrogenated potassium hydrogenmaleate. Single crystal at 20 K with Q parallel to the c crystalaxis.Fig. 5. INS spectrum of partially deuterated potassium hydrogenmaleate KHŽ OOC–CD5CD–COO .. Single crystal at 20 K withQ parallel to the c crystal axis.many bands must be attributed to the n OHO mode.aMost of the intensity appears as a doublet at 500–530cm y1 and a third band at 660 cm y1 . Weaker bandsbetween 800 and 1100 cm y1 also have a pronouncedn OHO character. They may be transitions to higherastates or combinations, or even mixing with ringvibrations. The two weak doublets between 250 and450 cm y1 are certainly due to mixing with ringcoordinates, presumably with antisymmetric in-planedeformations. Finally, the sharp band at 1210 cm y1and two partially resolved broader bands at 1625 and1710 cm y1 correspond to the OHO bending modes.The main n OHO components are virtually idenatical for KHMH 2 and KHMD2and frequency differencesdo not exceed 10 cm y1 . Consequently, thedynamics of naOHO and maleate ring are wellseparated and can be discussed separately. Beforefurther analysis of the naOHO dynamics, it is neces-sary to consider possible collective dynamics andband splitting due to intermolecular interaction. Protonsare largely isolated in an isotopic mixture containing20% of KHMD2 and 80% of KDMD 2. Theprobability for two nearest neighbour sites to beoccupied by protons is ;4%. The spectrum Ž Fig. 7.is almost identical to that of pure KHMD Ž Fig. 4 .2 .Therefore, intermolecular and intramolecular couplingare negligible and the many naOHO bands arerelated to the local proton dynamics.For the modes involving Ž C.H displacements, twoquite different dynamics can be distinguished. On theone hand, the CH in-plane bending modes givey1intense bands at 1210 and 1360 cm Žsee Figs. 2Fig. 4. INS spectrum of partially deuterated potassium hydrogenŽ .maleate KH OOC–CD5CD–COO . Powdered sample at 20 K.Fig. 6. INS spectrum of partially deuterated potassium hydrogenŽ .maleate KD OOC–CH5CH–COO . Powdered sample at 20 K.

( )F. Fillaux et al.rChemical Physics 244 1999 387–403 393Fig. 7. INS spectrum of an isotopic mixture of partially deuteratedpotassium hydrogen maleate KHŽ OOC–CD5CD–COO ., 20%,and KDŽ OOC–CD5CD–COO ., 80%. Powdered sample at 20 K.and 6 ., still observed in the single-crystal spectrumŽ Fig. 3 .. The CH out-of-plane bending at 875 and1010 cm y1 is totally extinguished for the singlecrystal Ž compare Figs. 2 and 3 .. On the other hand,the sharp bands at 155, 305 and 605 cm y1 for thepowdered KHMH Ž Fig. 2.2 which disappear for thesingle crystal Ž Fig. 3. and for KHMD Ž2 Figs. 4 and5.correspond to out-of-plane deformations of themaleate ring. The observed intensities are due tocontributions of the Ž C.H protons.The lattice density of states below 150 cm y1comprises many sharp components compatible withrather weak intermolecular coupling. The rathermodest intensities confirm that the proton dynamicsare largely decoupled from the lattice. However, thesharp band at 80 cm y1 observed for the singlecrystal of KHMH Ž Fig. 3. suggests that the Ž C.2Hprotons may ride some lattice modes. The very weaklattice mode intensity for the KHMD2single crystalshows that the naOHO mode is largely decoupledfrom the lattice, in agreement with the spectrum ofthe isotopic mixture Ž Fig. 7 .. The anomalous largelattice mode intensity for the KHMD2powder islikely due to the presence of some N2ice in thecryostat.5. Proton dynamics in the hydrogen bondAccording to the spectra presented above, intraand intermolecular coupling are of minor importancefor the n OHO mode and we assume that theamultiple components arise from a very anharmonicpotential function. According to the crystal structure,the potential function is symmetrical with a well-definedcentral minimum. Any double minimum potentialfunction similar to those proposed for strongsymmetric hydrogen bonds w1–10,31,38,39xcan beeliminated. For the KHMD single crystal Ž Fig. 5 .2,the energy level scheme of naOHO should accountfor the main components at 500, 530 and 655 cm y1y1and higher transitions above 800 cm Ž Table 5 ..The three components can be regarded as an almosttriply degenerate level and the rule of thumb is tosuppose a symmetric potential function with threeminima. To be consistent with the structure, thecentral minimum should be at a lower energy thanthe other two. The dynamics are rather well representedwith the potential presented in Fig. 8 andTable 6. However, this potential is not totally free ofsome arbitrariness because, unfortunately, it is notpossible to precisely identify the naOHO bandsamongst the features observed between 800 and 1500cm y1 , in the range of the ring deformations. Theseundesignated naOHO levels leave some flexibility tothe shape of the upper part of the potential. Therefore,potential functions with different power termsŽ2namely x or x 4. give broadly the same reasonableagreement with observations Ž see Table 6 .. Nevertheless,these potentials are very similar in shape andcorrespond to the same dynamics.INS intensities provide further support for thesepotential functions. In the harmonic case, intensitiesdecrease rapidly Ž exponentially.as the quantumnumber of the final state increases w36 x. In contrast tothis, calculated intensities remain quite high in thetriple minimum potential Žat least for n-8, see. Žy1Table 6 and the 03 transition 665 cm . is themost intense, as is observed. Intensities calculatedy1between 700 and 1100 cm Ž ns4–7.confirm thatbands in this region can be attributed to naOHO.Some support to the x 2 potential function, over thatwith x 4 , comes from a consideration of the relativeintensities for the doublet at 500–530 cm y1 in Table6. Beyond 1100 cm y1 , the spectra provide littlediscriminatory information by which the potentialscould be further restricted.Supposing the potential of Fig. 8 also applies tothe deuterated analogue, the calculated frequencyratios naOHOrnaODO, range from 0.9 to 1.1

394( )F. Fillaux et al.rChemical Physics 244 1999 387–403Table 5Žy1Inelastic neutron scattering: band frequencies cm ., relative intensities Ž s: strong; m: medium; w: weak; v: very; sh: shoulder.andassignments Ž o.: overtone; c.: combination.

Ž .Table 5 continued( )F. Fillaux et al.rChemical Physics 244 1999 387–403 395

396( )F. Fillaux et al.rChemical Physics 244 1999 387–403Ž . Ž . Ž Ž ..Fig. 8. Potential function left and wave functions right for the n OHO mode see Table 6, Eq. 1 .aŽ Table 6 ., in agreement with previous observationsin the infrared w19,21 x. This is an example wherefrequency ratios close to unity are not due to adouble-well potential.Intuitively, the naOHO spectrum can be picturedas a single transition at 665 cm y1 , due to the centralminimum, and a doublet at 500–530 cm y1 , due tothe double minimum. This view is in qualitativeagreement with the shapes of the wave functionsŽ Fig. 8 .: C1 and C2are similar to wave functionsfor a double-well potential with minima located at;"0.8 A, ˚ except that the antisymmetric state isnow below the symmetric state. C3is largely delocalizedover all three wells. However, in the rangespanned by C0it is similar to the ns1 state in aharmonic potential.In the ground state, the proton is fairly welllocalised at the center of the hydrogen bond, inagreement with diffraction data. The shape of thewave function resembles that of a harmonic oscillatorat frequency ;670 cm y1 , close to the 03transition. It is almost impossible to determine theanharmonicity of the potential function from measurementsof the probability distribution of protonsat low temperature Žfor example, neutron diffraction,neutron Compton scattering, etc. . The calculatedmean-square amplitude Ž 0.025 A˚2. compares wellwith the temperature factor determined by neutrondiffraction at low temperature Ž 0.016 A˚2in Table 4 ..A major consequence of the potential shape is theŽy1large zero-point energy ;600 cm .. In the harmonicapproximation, the mean square amplitudeshould be ;0.016 A ˚2. However, the very largeanharmonicity spreads the wave function across theregion normally forbidden within classical mechanics.6. Maleate-ring dynamicsThe out-of-plane bending of the maleate ring canbe represented as an anti-rotation of the CHCOOentities around an axis parallel to the C5C bond andgoing through the center of gravity of each residueŽ see Fig. 1a .. This axis is very close to the OŽ . 2˚2atoms and the moment of inertia is about 44 amu Afor each entity. The most intense bands at 153, 303,605 cm y1 and some weaker bands above 800 cm y1Ž Table 5.are not amenable to either harmonic orvery flat Ž square-like.potentials. A symmetric doubleminimum potential is also unlikely and should beincompatible with the crystal structure. Followingthe same line of reasoning as for the naOHO bands,the energy level scheme can be fitted with a tripleminimum potential function Ž Fig. 9 and Table 7 ..INS relative intensities calculated assuming the Ž C.Hprotons ride the HCOO entities are in agreementwith the observations Ž see Table 7 ..

( )F. Fillaux et al.rChemical Physics 244 1999 387–403 397Table 6Žy1Calculated frequencies in cm units.and relative intensities for the yaOHO mode. The potential functions are:Vs183 x 2 q359 expŽ y2.84 x 2 . y1163 expŽ y31.2 x 2 .. Ž 1a.Vs232 x 4 q1080 expŽ y1.7x 2 . y1427expŽ y12 x 2 .. Ž 2a.y1 ˚UV and x are in cm and A units, respectively. The oscillator mass is 1 amu Transmission window.The ground state is largely delocalized over thethree wells and the shape of the wave function iscomplex Ž see Fig. 9 .. The mean square amplitude ofthe heavy atoms Ž0.0024 rad 2. corresponds to amean deviation of "38 with respect to the mid-plane,but this value depends on the choice of the coordinateand requires some caution. At room temperature,excited vibrational states are highly populated.In these states, the mean square amplitude is ;0.01rad 2 and the deviation from planarity is about 5times larger. These dynamics are quite consistentwith the thermal parameters for out of plane displacementsof the O and C atoms Ž Table 4 .. Incontrast to the naOHO, it is not possible to distin-guish between states localised in the central well andthose associated with the double well.

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.

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-

( )F. Fillaux et al.rChemical Physics 244 1999 387–403 401spond to maxima of the effective potentials along therotational coordinate.Within the adiabatic approximation, the relevantcoordinate Rtin the naOHO excited states includesrotation of the carboxylic group. The adiabatic potentialV Ž R .n t in the nth state has two minima wellseparated from the equilibrium position in the groundstate, supposedly located at ;"0.8 radian ŽFig.11 .. The barrier height should be on the order of thestrain energy. However, it may be partially counterbalancedby an increase of the OH vibrational energydue to the weakening of the hydrogen bond. In the n aOHO ground state, the planar structure is stable andwe assume that the potential function V Ž R .0 t isqualitatively similar to that presented in Fig. 9 forthe ring deformation. Regarding the shape of V Ž R .n tand the rather large effective masse for the rotationof the carboxylic group, the rotational states shouldbe comparable to a continuum of quasi-free states.Unfortunately, this continuum is not observed, presumablybecause the INS cross-section of O atoms isnegligible and the Rtcoordinate does not involveany significant proton displacement.This result illustrates the important role of themomentum transfer in the interconversion process.With INS, only transitions via energy and momentumtransfer to protons are observed. Momentumtransfer parallel to the hydrogen bond ŽQalong theH 5n OHO coordinate r .a 5 gives sharp bands corre-sponding to transitions to the top of the centralbarrier of V Ž R . Ž Fig. 11 .n t . Transitions to the contin-uum of states Ž along R .t occur only for momentumtransfer perpendicular to the maleate ring Ž Q .H .However, because the proton and ring dynamics arewell separated, transitions to this continuum occuronly for momentum transfer to the O atoms: Q O H .This continuum cannot be observed in the infrared orRaman because only ‘vertical’ transitions Ž Q;0.tothe top of the upper potential are possible. Unfortunately,the ring dynamics involved in the interconversionprocess cannot be fully observed with thevibrational spectroscopy techniques under considerationin this section.Band profiles in INS, with Q Hs0, and in theinfrared are both determined by the shape of V Ž R .n tin the range spanned by the ring wave function in theground state w41 x. They should be identical. Howw21xŽever, the infrared widths estimated from Ref.y150–100 cm . are greater than those measured withŽy1INS ;30 cm .. The broadening could be a consequenceof the sample preparation. The polishing ofvery thin platelets may introduce disorder. Reflectioncould also contribute to the broadening of infraredbands.7.5. ReactiÕityFig. 11. Schematic representation of the effective potentials forring deformation in the ground, V Ž R . Ž solid .0 H , and excited,V Ž R . Ž dash .n t , na OHO states. RHrepresents the symmetricout-of-plane deformation of the HCCO2 moieties. Rtis therotation of a carbonyl groups around the CC single bond. Thesetwo coordinates are represented in an arbitrary plane. V Ž R .n t wasestimated from Ref. w15 x. The minima are at ;"0.8 radian andthe barrier height is ;2500 cm y1 .Given the dissociation threshold of ;500 cm y1and the measured density of vibrational sates ŽFig. 8and Table 6 ., more than 10% of the ions should be inthe non-planar conformation at room temperatureand fast interconversion between the planar andnon-planar structures should occur. This is of littleconsequence for crystal diffraction data and Ramanspectra in solution w18xwhich are both in agreementwith a dominant symmetrical hydrogen bond and C 2vsymmetry. On the other hand, NMR experimentssuggesting pairs of asymmetric equilibrating tauw28–30xare presumably consistent with fasttomersinterconversion averaged on the NMR time-scale.Therefore, there is no longer conflict between NMRresults, vibrational results and crystal structure results.In solution, interconversion between the planarand non-planar structures and proton transfer are

402( )F. Fillaux et al.rChemical Physics 244 1999 387–403driven by collisions with the molecules of the solvent.Momentum transferred to the proton parallel tothe hydrogen bond Ž Q .H 5 is needed for the excitationof the stretching mode whilst the rotation of thecarboxylic groups requires momentum transfer to theoxygen atoms Ž Q , Fig. 10 .O H . Therefore, energyand momentum must be transferred to the H and Oatoms independently and simultaneously, within thevery short life time of vibrational excited statesŽy11-10 s .. The interconversion rate at a giventemperature depends on the distribution of kineticmomentum in the solution and thus on the mass andshape of the molecules in the solvent.8. ConclusionNeutron diffraction and INS confirm that the hydrogenbond in potassium hydrogen maleate at lowtemperature is symmetrical with the proton located atthe center. The maleate ring is planar with moderatemean-square amplitudes for the out-of-plane deformations.The naOHO dynamics and the totallysymmetric out-of-plane ring deformation are largelydecoupled from other modes and from each other.They are compatible with very anharmonic potentialfunctions composed of three non-equivalent minima.These potentials account for infrared band activitiesand frequency shifts upon deuteration. All the datasupport C 2v symmetry for the hydrogen maleate.The potential function for the proton stretchingmodeis quite different from single or double wellsaccounted for by theoretical models. The narrowcentral well shows that the hydrogen bond is stableonly if the proton is localised at the center of theO PPP O bond. This can be related to the distributionof electrical charges in the symmetric planar ion.Upon rather small proton displacements away fromthe central position, the distribution of electriccharges and the structure change. We conclude thatthe proton ground state is hydrogen bonding whilstexcited vibrational states are hydrogen anti-bonding.This is a spectacular manifestation of the quantumnature of the strong symmetric hydrogen bond. Consequently,the binding energy, which is essentiallyelectrostatic in nature, is not simply related to thedissociation energy determined by the quantum dynamicsof the proton.In the ground state, the hydrogen maleate ion canbe effectively regarded as an intermediate state forproton transfer from one carboxylic group to theother. In excited vibrational states of the protonstretching-mode, the hydrogen bond is broken, theproton is transferred to an oxygen atom and thecarboxylic group rotates by a large angle of ;"458.The energy dissociation of ;500 cm y1 is compatiblewith thermal activation at room temperature. Theconcept of hydrogen bondingranti-bonding statescould be thus a key issue in further studies andmodelling of the proton transfer mechanism.AcknowledgementsHere, we should thank S.W. Parker for the helpfulassistance on the TFXA spectrometer and stimulatingdiscussions.Referenceswx 1 A.N. Baker, J. Chem. Phys. 22 Ž 1954.1625.wx 2 G.C. Pimentel, A.L. McClellan, The Hydrogen Bond, Freeman,San Francisco, 1960.wx 3 S.N. Vinogradov, R.H. Linell, Hydrogen Bonding, Van Nostrand-Reinhold,New York, 1971.wx 4 M.D. Joesten, L.J. Schaad, Hydrogen Bonding, MarcelDekker, New York, 1974.wx 5 R. Janoschek, in: P. Schuster, G. Zundel, C. Sandorfy Ž Eds. .,The Hydrogen Bond, Recent Developments in Theory andExperiments, Vol. 1, North-Holland, 1976, p. 165 and referencescited therein.wx 6 E. Matsushita, T. Matsubara, Prog. Theor. Phys. 67 Ž 1982.1.wx 7 K. Shibata, S. Ikeda, J. Phys. Soc. Jpn. 61 Ž 1992.411.wx 8 S. Ikeda et al., J. Phys. Soc. Jpn. 61 Ž 1992.2619.wx 9 E. Matsushita, J. Phys. Soc. Jpn. 62 Ž 1993.2079.w10x S. Ikeda et al., J. Phys. Soc. Jpn. 63 Ž 1994.1001.w11x W.W. Cleland, Biochemistry 31 Ž 1992.317.w12x W.W. Cleland, M.M. Kreevoy, Science 264 Ž 1994.1887.w13x J.A. Gerlt, P.G. Gassman, Biochemistry 32 Ž 1993.11943.w14x S.F. Darlow, W. Cochran, Acta Crystallogr. 14 Ž 1961.1250.w15x S.F. Darlow, Acta Crystallogr. 14 Ž 1961.1257.w16xH.M.E. Cardwell, J.D. Dunitz, L.E. Orgel, J. Chem. Soc.,1953, p. 3740.w17xK. Nakamoto, Y.A. Sarma, G.T. Behnke, J. Chem. Phys. 42Ž 1965.1662.w18xJ. Maillols, L. Bardet, R. Marignan, J. Chim. Phys., 66,1969, pp. 522 and 529.w19xF. Avbelj, B. Orel, M. Klanjsek, D. Hadzi, Spectrochim.Acta 41A Ž 1985.75.

( )F. Fillaux et al.rChemical Physics 244 1999 387–403 403w20xH.R. Zelsmann, Z. Mielke, M.M. Ilczyszyn, Spectrochim.Acta 44A Ž 1988.705.w21xM.M. Ilczyszyn, J. Baran, H. Ratajczak, A.J. Barnes, J. Mol.Struct. 270 Ž 1992.499.w22xJ. Tomkinson, I.J. Braid, J. Howard, T.C. Waddington, Chem.Phys. 64 Ž 1982.151.w23xJ. Howard, J. Tomkinson, J. Eckert, J.A. Goldstone, A.D.Taylor, J. Chem. Phys. 78 Ž 1983.3150.w24xJ. Tomkinson, J. Penfold, J. Howard, J. Mol. Struct. 142Ž 1986.1.w25xM. Fukai, T. Matsuo, H. Suga, J. Chem. Thermodyn. 20Ž 1988.1337.w26xJ.E. Barry, M. Finkelstein, S.D. Ross, G.D. Mateescu, A.Valeriu, C. Svensson, J. Org. Chem. 53 Ž 1988.6058.w27x L.H. Mervin, S.D. Ross, Magn. Reson. Chem. 30 Ž 1992.440.w28x C.L. Perrin, J.D. Thoburn, J. Am. Chem. Soc. 114 Ž 1992.8559.w29x C.L. Perrin, J.B. Nielson, J. Am. Chem. Soc. 119 Ž 1994.12734.w30x C.L. Perrin, Y.-J. Kim, J. Am. Chem. Soc. 120 Ž 1998.12641.w31x A. Novak, Struct. Bonding 18 Ž 1974.177.w32xK.M. Lee, K. Ramalingam, J.K. Son, R.W. Woodward, J.Org. Chem. 54 Ž 1989.3195.w33xISIS users guide.w34xE. Heilbroner, H. Rutishauser, F. Gerson, Helv. Chim. Acta42 Ž 1959.2285.w35xE. Heilbroner, H. Rutishauser, F. Gerson, Helv. Chim. Acta42 Ž 1959.2304.w36xS.W. Lovesey, Theory of neutron scattered from condensedmatter, Nuclear Scattering, Vol. 1, Clarendon Press, Oxford,1984.w37x Shoemaker, Trueblood, Acta Crystallogr. B 24 Ž 1968.63.w38x F. Fillaux, J. Tomkinson, Chem. Phys. 158 Ž 1991.113.w39xF. Fillaux, A. Lautie, ´ J. Tomkinson, G.J. Kearley, Chem.Phys. 154 Ž 1991.135.w40xP. Gilli, V. Bertolasi, V. Ferretti, G. Gilli, J. Am. Chem. Soc.116 Ž 1994.909.w41x F. Fillaux, Chem. Phys. 74 Ž 1983.395.