Neutron scattering study of dynamically disordered hydrogen bonds: Terephthalic acid

CHEMICAL

YoIume 103. number 3

NEUTRON

SCATTERING

TEREPHTHALIC

30 December

PHYSICS LCTTCRS

STUDY OF DYNAMiCALLY

DISORDERED

HYDROGEN

1963

BONDS:

ACID

B.H. MEIER, R. MEYER, R.R. ERNST Luboratorium ji& Physiknlische C%emie. Eidgeniissische Technische Hochschule. 8092 Zurich, Switzerland

and P. ZOLLIKER,

A. FURRER

and W. HIiLG

Institut f& Reaktortecbnik, Eidgeniissische Tecbnische Hochschule, 5303 Wiirenlingen. Switzerland Received 8 September

1983; in final form 18 October

1983

Incoherent neutron scattering experiments have been performed on the disordered hydrogen-bonded dimers of terephthalic acid. An abnormally high Debye-Wailer factor is found in contradiction to a simple t\\o-site jump model. The inelastic incoherent neutron spectrum is analyzed by using different isoropicdly substituted molecules. The resulrs are cornpared with the Arrhenius parameters of the exchange process obtained by solid-state NMR experiments.

1. Introduction

in one of the tautomeric v&de at high temperature

Recently it has been shown by nuclear magnetic resonance measurements [ 1,2], that the previously observed disorder in many solid carboxylic acid dimers * is due to a dynamic process between the two tautomeric forms:

forms occurs. A similar behaviour has also been found for terephthalic acid by a determination of the structure at high and low temperatures by neutron diffraction [4] and by NMR lineshape studies [_‘I. The details of the proton transfer mechanism have so far not been determined, although it is known that at high temperature the dynamic behaviour is in agreement with a simple classical two-site exchange process. NMR relaxation measurements on solid terephthalic acid suggest that at temperatures higher than 100 K the dynamics are governed by an exchange process with an activation energy of 27 meV (2.6 kJ/mol) while at temperatures lower than 80 K a second process wirh an ap‘parent activation energy of only S5 meV (0.8 kJ/mol) seems to become dominant [2] _Both activation energies are much lower than the barrier calculated ab initio for related systems [6-l I] _ In order to obtain further experimental insight into the dynamic behaviour, we investigated neutron scattering of terephthalic acid. In section 3 we report and dis-

,0-H...\ R-C C-R ‘O., *H-O’

kl

-t

2

)

O...H-0, R-C’ C-R ‘O-H.. .O’

While the two forms are isoenergetic in the gas and in the liquid phases, the degeneracy is normally removed by lattice interactions in the solid phase. For p-toluic acid we determined the energy difference between the two forms to be 1.0 5 02 kJ/mol [2] _A somewhat smaller value (0.4 kJ/mol) has been found by Nagaoka et al. for benzoic acid [ 11. As a consequence of the asymmetric potential, the carboxylic protons localize * For a review on X-ray results of carboxylic state, see ref. [ 3]_

acids in the solid

0 009-2614/83/S 03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

positions at low temperature. eschange between the two

169

Volume 103. number 3

cuss the temperature dependence- of elastic scattering while section 4 deals with the inelastic scattering spectra in the range below 60 meV.

2. Experimental The following polycrystalline samples of isotopically substituted terephtbalic acid have been investigated: HOOC-CgH4--COOH [TA], HOOC-CgD4-_COOH [Ta+], DOOC-CsH,-COOD [TA-(O&7 , DOOCC,D,-COOD [TA-d, ] _The samples were sealed in ahrminium cylinders or flat cells and the penetration width was chosen according to optimum neutron transmission properties_ The neutron scattering experiments were performed on a triple axis spectrometer at the Saphir reactor of the Eidgenijssisches lnstitut fiir Reaktorforschung Wiirenlingen (EIR). The measurements were carried out in the constant Q mode of operation in the neutron energy-loss configuration with the analyzer energy kept fxed at 15 meV_ A pyrolitbic graphite filter was used to reduce contamination by higher-order scattering_ The resolution was 1 meV for the elastic line and decreased to ==Z5 meV for trw = 25 meV and to 5 meV for fiw = 50 meY.

3. Debye-WaUer factor and m-square of nuclei

= Cd;

9

exp[-2

where C is a constant, &‘c

(2)

k and k’ being the wave vectors of the incoming and

outgoing neutrons, respectively. The sum in eq. (1) is restricted to protons of the unit cell, neglecting the small contributions of other nuclear species in the sample. To describe scattering in the presence of a dynamic interconversion, expected at higher temperatures, eq. (1) has to be modified. The simplest description of the dynamic process is a two-site jump model with negligibly short jump time. The thermal motion is assumed to be equal in both tautomeric structures. For this model, the elastic part of the differential cross section, eq. (l), is replaced by the sum of purely elastic line and of a lorentzian-shaped quasi-elastic line reflecting the motional process with correlation time 7C. For non-equal populations PA and pB of the two tautomeric forms and for a polycrystailine sample we can generalize the expression given in refs. [ 13,141: d2&fdfi

dw = C I+H exp [--2ryH

x [Co6(w)+ C1?+@(l

(Q)l

+ J+)],

(3)

with

Tc = (k, +7c,y’,

W,(Q)],

the incoherent

Q=k-k’,

displacement

It is well known that the elastic -mcoherent differential cross section provides information on the thermal motion of the nuclei through the dependence of the Debye-Wailer factor on the mean-square nuclear displacement;This dependence is utilized to test the mechanism of the hydrogen transfer. In the case of localized hydrogen-bond protons, the elastic incoherent differential cross section is given by the well-known expression f 12]

do$C/da

30 December 1983

CHEMICAL PHYSICS LETTERS

(1) scattering

cross section of protons, and exp 1-2 W,(Q)]

where .$ is the jump distance between the two hydrogen sitesA and B, andjo is a spherical Bessel function. We note that the integral of eq. (3) over the frequency variable is equal to eq. (1). As long as the instrumental linewidth

is much broader

than the width of the

eq. (3), it is not possible to distinguish elastic and quasielastic contributions and the measured intensities can be explained by eq. (1) even in the presence of a dynamic interconversion. This was the case in the present measurements. In the harmonic approximation of the vibrational motion, there is a simple relation between the DebyeN’aller factor and mean-square displacement of the nuclei. For a powder sample, lorentzian

in

the Debye -Wailer factor which depends on the scattering vector

~W=((Q-U)~)=$Q~(U*)

Q,

where u is the displacement of the hydrogen atom from its equilibrium position.

170

(4)

CHEhilCAt

Volume 103, number 3

PHYSICS

We determined the intensity of the elastic peak for terephthalic acid in the temperature range 10 < T < 4OOKasafunctionofQfor 1.57 60 K, (u ‘>* increases linearly. The increase is unusually large: at room temperature, the mean-square displacement is already 0.11 A2 _It is much too large to be explained by thermal vibrations in one potential minimum. Similar observations have been made in hydrosulfides [ 14, 15 ] and for hydrogen diffusion in metals [ 13,141. The apparent mean displacement could be caused by a very fast exchange process with 7 2 IO-13 s for temperatures above 100 K leading to a lorentzian line whose width exceeds the instrumental linewidth of 1 meV. In this

30 December

LETTERS

1983

case the measured intensity would no longer be equal to the total quasi-elastic scattering. The assumption of a fast process is however in contradiction with the Arrhenius parameters determined from NMR relaxation measurements [Z] . The abnormally high Debye-Waller factor seems to indicate that the description of the dynamics by a simple iump model is not appropriate. The following underlying assumptions may be inadequate - For the derivation of eq. (3) we had to assume that the jump time is negligible compared to the time spent in one of the two potential minima and that vibrational and jump processes can be separated in the sense that the intermediate scattering functions are factorized according to

F&Q, 1) = F,u(Q. tf CCQ, ~1, where F,U(Q, t) represents the vibrational contribution and Ff(Q, t) the contribution by the jump process ]I61 - The ~brationally excited levels (including the lowest state in the energetically higher well) may be delocalized over both wells and the harmonic approximation of the potential used in the derisarion of eq. (4) may no longer be justified.

4_ Inelastic scattering

spectra

The incoherent inelastic neutron scattering spectra are particularly sensitive to proton motions and may therefore contain important information on the energy levels associated with vibrations and tunneling of the hydrogen bond system. The frequency-dependent inelastic incoherent differential cross section which describes the inelastic part of the single-crystal spectrum is given by 1131 -=C_-.-. as2aw

x E G+zrl + 100

200

T

300

400

K

Fig. 1. Temperature dependence of the mean-square displacement of the carI~oxyIic protons in TA-de.

r;,c,) +lF(y

IQ -e,,jm2 fJ+J)"(~

- ~jW)f

‘

+ c$Q)) (51

MH is the mass of the hydrogen atom. The first summation extends over all protons in the unit cell neglecting the small contributions from other nucdei in the sample. The second summation extends over the wave 171

30 December 1983

CHEMICAL PHYSICS LElTERS

Volume 103, number 3

vectors 4 in the first Brillouin zone and over the polarization branchesi. ~~(4) and ed &g) are the eigenvalue and the corresponding eigenveitor of the lattice mode with vector 4 and polarization j, and n&q) is the respective Bose occupation number. The first term in the square brackets corresponds to absorption and the second to emission of vibrational quanta. According to eq. (5) the cross section at frequency o depends on the number of transitions with gain or loss of the energy ~IW, weighted by a factor involving the quantity 1Q -e,_~j(q) I* which in the powedr average is a measure of the mean-square hydrogen displacement in the respective mode. If a given scattering peak is largely due

higher-order Bragg scattering and should be disregarded. To facilitate a direct comparison, the data for the partially deuterated species were normalized on the basis of expected integrated intensities. The effects of deuteration can readily be seen. Qualitatively, the spectrum of the fully protonated TA can be considered as a superposition of the spectra of the species TA-(Od)2 exclusively with ring protons and of TA-d4 with carboxylic protons only. A comparison of the spectra obtained for the two partially deuterated species allows one to estimate the relative contributions of ring protons and carboxylic protons in different viirational modes. The intense

to the motion of a particular hydroegn atom Hd, deuteration at this site will reduce the intensity of the peak by an order of magnitude, thus providing a powerful tool for assignment.

peaks of TA near 16 and 53, meV and the features be-

4.1. Deuteration

TA-(C?@2. In the frequency region below 10 meV both partially deuterated species give rise to scattering, indicating involvement of both ring and carboxylic protons at these frequencies.

effects

The energy loss spectra of fully protonated terephthalic acid (TA) and of the two partially deuterated species TA
0

100

200

300

400

500

5

0

cm’ 1

0

10

20

30 ENERGY

40

50

60

TRANSFER

Fig. 2. Inelastic neutron scattering spectra of polycrystaliine terephthalic acid and of two partially deuterated species at T = 10 K and Q = 4.4 X1 _The peak at 45 meV is due to contamination by higher-orderBragg scattering.Upper solid line:

TA, broken line: TA-(Od)z, lower solid liner TA-d.+

172

tween 30 and 40 meV are related to scattering by the ring protons. Similarly, carboxylic protons appear to give rise to the peak near 28 meV present in the spectra of TA and TA-d4 but missing in the spectrum of

4.2. Comparison

with optical spectra

When comparing the inelastic neutron scattering data with optical spectra we have to note that in neutron spectroscopy the measured powder spectrum contains the entire dispersion of all modes, whereas in infrared or Raman spectroscopy only the frequencies near the center of the Brillouin zone are relevant. Generally, the energetically higher modes, which can be assigned to intramolecular vibrations, are expected to have relatively small dispersion (of the order of 10%) but the low-lying lattice modes are likely to exhibit strong dispersion. In particular, the phonon modes involving the motion of rigid molecules may cover the entire Iow-energy range up to =20 meV. The matching of inelastic neutron scattering peaks with infrared and Raman bands is therefore not expected to be quantitative. In table 1 the optical dhld published by Tripathi and Sheng [ 171 for TA and TA-d4 are listed, for frequencies up to 480 cm-l (60 mev), along with the present neutron scattering data. Arenas and Marcos [ 183 reported similar results exclusively for protonated TA, differing in some observed frequencies and in assignments proposed.

CHEMICAL

Volume 103, number 3 Table 1 Comparison

of optical spectra with inelastic neutron scattering spectra for terephthJlic

TA-d4

TA

Raman

IF

TA

assignment

113

I07

229 242

-C6H4-

260

torsion

130(16-l)

-C,sHa-

mode ZOb

230(28.5)

combin.

108+

121

combin.

llO+

132

353 400

-CgHs-

126(15.6) 225(27_9)

-COOH

mode 17b

-COOH

270(33.5)

rocking

-C6H4-

mode 9b

-C6H4-

mode 16a

270(33-S)

3X(40.3)

-COOH rocking + -CeHqmode I5

308

and -COOH

SO(9.9)

I

-CgH4-

-CsH4-

240

353 410

major displacement of protons m

70f8.7)

O.-H stretching

223

266

70(8.7)

90( 11.2)

I

111 223

132

Ta-d4

lattice modes

108

320

Ta-(Od)z

SO(6.Z) II

84

245

and partially deuterdred species al

Raman

14

110

acid (TA)

1983

Neutron scattering spectra cl

Optical spectra b,

IR

30 December

PHYSICS LETTERS

420(52-l)

-&He-

420(5X1) J

a) in cm-’ ; values in parentheses in meV.

4.3. Modes iwolvi,tg

displacemew

b, Ref. [ 171.

c) This work.

of rijrg protom

Several of the observed modes are typical for -C6H4ring vibrations and are characterized, approximately, by Wilson modes [ 19]_ Among the peaks attributed to vibration of ring protons, the most intense ones (see fig. 2 and table 1) near 130 (16 mev) and 420 cm-1 (52 mev) are in good agreement with the vibrational frequencies assigned to ring torsions and to the ring twisting Wilson mode 16a, respectively. The scattering peak near 270 cm-l (33 meV) corresponds to a Raman band assigned to anorher out-ofplane ring deformation, mode 5 [ 181, or to a rocking mode of the csrboxyl groups [ 17]_ The latter assignment should imply substantial displacement of carboxylic protons which, however, is not observed throughout the range 245-480 cm-l (SO-60 meV). For the same reason the peak at 325 cm-l (40 meV), which is close to an infrared absorption at 320 cm-1 assigned [ 17 ] to the in-plane mode 15, is not likely to involve carboxyl rocking to any great extent. The assignment of further ring modes to the infrared frequen-

cy 245 cm-l (30 meV) and the Raman frequency 353 cm-l (44 meV) is compatible with neutron scattering intensity due to ring protons. Motion of ring protons is also found to contribute to the scattering intensity of the lattice modes below 90 cm-l (11 meV). 1.4. Modes involvirrg displacemet prorom

t o-f carbox$ic

In the frequency range considered we expect proton involvement in carboxyl torsion, wa:Ging and rocking modes coupled with other molecular distortions, and in the displacement of the carbosyl groups along the molecular axis. Furthermore, there should be scattering contributions from the simultaneous proton eschange within a hydrogen-bonded pair of carbosyi groups. Owing to its double-minimum potential, this motion is associated with low-lying energy levels and large proton displacements_ As the two possible tautomers are not equivalent but separated by an energy of the order of 10 meV, the neutron scattering spectra could also contain contributions from transitions be173

CHEhllCAL

Volume 103, number 3

PHYSICS LETTERS

tween the two lowest levels in the asymmetric doubleminimum potential_ The deuteration effects on the scattering peak at 225 cm-r (28 mev) indicate motion of carboxylic protons, which could be due to carboxyl rocking at this frequency, as suggested by preliminary force-field calculations [20]_ On the other hand, the peak could also be attributed to vibrational excitation along the proton-transfer coordinate_ However, the previous assignment of the ring mode lob [ 173 to a Raman band near this frequency is not supported by the present neutron scattering data, since it does not involve substantial motion of carboxylic protons. In the lattice-mode region, large carboxylic proton displacements give rise to strong scattering with a peak at 80 cm-* (10 mev) and leveling off at 160 cm-* (20 mev). Possibly, the peak includes the proton exchange transition from the lowest level in the deeper potential well to the lowest level in the higher well. The energy 10 meV could then be an estimate for the energy difference between the vibrational ground states of the two wells. However, such an interpretation needs further testing on the basis of model calculations and singlecrystal polarization data. Nevertheless it is interesting to note that the two energies are close to the apparent low-temperature activation energy of 8.5 meV and to the high-temperature activation of 27 meV for the proton exchange measured by proton NMR relaxation f2].

Acknowledgement This research has been supported tional Science Foundation.

temperature

as shown

factor

by elastic

neu-

tron scattering on terephthalic acid indicates that the carboxylic protons undergo large-amplitude vibrational motions leading possibly to a delocalization over both potential wells. The measurements cannot be explained by classical jumps between localized structures. The inelastic scattering spectra measured for terephthalic acid and for three deuterated species allowed the assignment of modes due to the motion of carboxylic protons and of ring protons. The coincidence of scattering peak energies assigned to carboxylic protons with acti-

174

by the Swiss Na-

References [ 1] S. Nagaoka, T. Terao, F. Imashiro, A. Saika, N. Hirota and S. Hoyashi. Chem. Phys. Letters 80 (1981)

580.

[ 11 B.H. Meier, F. Graf and R.R. Ernst, J. Chem. Phys. 76 (1982) 767. [ 31 L. Leiserowitz, Acta Crist. B32 (1976) 775. [4] A-W. Hewat, J. Jorgensen, P. Fischer, P. Zolliker, A. Furrer, B.H. Meier and R.R. Ernst, to be published_ [S] BH. Meier and R.R. Ernst, to be published. [6] E. Ady and J. Brickmann, Chem. Phys. Letters ll(lV71) 302. [7] S. Iwata and K. hlorokuma,

[8] [ 91

[IO] [ 111

[ ;3]

The strong increase in the Debye-Wailer with increasing

1983

vation energies for the two-proton exchange process observed by NMR is a subject of further study.

[ 121

5. Conclusions

30 December

[ 141 [ 151 [ 161 [ 171 [ 181 [ 191 [ 201

Theoret. Chim. Acta 44 (1977) 323. S. Schrenier and C-W. Kern, J. Am. Chem. Sot. 101 (1979) 4081. A. Agresti and A. Ranfagni, Chem. Phys. Letters 79 (1981) 100. F. Graf, R. Meyer, T.-K. Ha and RR_ Ernst, J. Chem. Phys. 75 (1981) 2914. S. Nagaoka and N. Hirota. Chem. Phys. Letters 92 (1982) 498. W. Marshall and S.W. Lovesy, Theory of thermal neutron scattering (Clarendon Press, Oxford. 197 1). T. Springer, in: Dynamics of solids and liquids by neutron scattering, eds. SW. Lovesey and T. Springer (Springer, Berlin, 1977). JM. Rowe, R.G. Livingston and J.J. Rush. J. Chem. Phys. 59 (1973) 6652. JM. Rowe, R-G. Livingston and JJ. Rush, J. Chem. Phys. 58 (1973) 5469. LA. de Graaf. JJ. Rush, HE. Flotone and JM. Rowe, J. Chem. Phys. 56 (1972) 4574. GNR_ Tripathi and S J_ Shery, J. Mol. Structure 57 (1979) 21. J.F. Arenas and J.I. Marcos, Spectrochim. Acta 36A (1980) 107.5. G. Varsanyi, Assigmnentof vibrational spectra of benzene derivatives (Aca&miai Kiad& Budapest, 1974). P. Zolliker and A. Furrer, unpublished results.