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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
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