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D-transfer dynamics in the hydrogen bonds in partially deuterated benzoic acid crystals
Volume 198, number $4
CHEMICAL PHYSICS LETTERS
9 October 1992
Evidence of quantum correlations in the H/D-transfer dynamics in the hydrogen bonds in partially deuterated benzoic acid crystals Sadamu Takeda, Akihiko Tsuzumitani ’ Department of Chemistry, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan
and C.A. Chatzidimitriou-Dreismann Iwan N. Stranski Institute for Physical and Theoretical Chemistry Technical University of Berlin, Street 17. Juni 112, W-1000 Berlin 12, Germany
Received 30 June 1992
A precise investigation of spin-lattice relaxation rates for protons and deuterons of partially deuterated benzoic acid crystals showed a remarkable quenching of the transfer rate of an HD pair in hydrogen-bonded dimeric units of carboxyl groups with increasing concentration of D in the surrounding hydrogen bonds. A similar effect was also observed for partially deuterated crystals of acetylenedicarboxylic acid. This finding supports recent theoretical predictions of thermally activated protonic quantum correlation in condensed matter and proposes a new mechanism for the proton transfer in hydrogen bonds in condensed matter.
1. Introduction Knowledge of proton-transfer quantum dynamics in hydrogen bonds is necessary for understanding many important chemical and biological processes. An example of the extensive investigations of this topic is “double proton transfer” in hydrogen-bonded dimers of carboxyl groups in carboxylic acid crystals [l-7]. In these systems, the quantum tunneling effect is believed to play a dominant role in the transfer of two protons (HH pair) and also two deuterons (DD pair) in dimeric units of carboxyl groups at sufficiently low temperatures. At higher temperatures additional thermally activated processes become important [ 5-71, for which an effect of coupling between hydrogen motion and another oscillator has been discussed as a key mechanism to Correspondence to: S. Takeda, Department of Chemistry, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan. ’ Present address: LSI Research Center High-Technology Research Laboratories, Kawasaki Steel Corporation, Technical Research Division, Kawasaki-cho 1, Chiba 260, Japan.
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determine the temperature dependence of the transfer rate of hydrogens in the hydrogen bonds [ 5,7]. In addition to the conventional knowledge, we present in this Letter novel results showing a remarkable quenching of the transfer rate of an HD pair in a dimeric unit at relatively high temperatures with increasing mole fraction of D in the hydrogen bonds in the H/D mixed crystals of benzoic acid. Our experiment consists of measuring the transfer rate of an HD pair in the hydrogen-bonded dimeric unit of carboxyl groups in benzoic acid crystals as a function of the H/D fraction of acid protons. The phenyl group of the molecule is protonated. The transfer rate was determined by measuring the spin-lattice relaxation rate T r’ of H and D nuclear magnetic resonances. The present experimental results, which seem beyond conventional theoretical treatment, are discussed along with a recent theoretical prediction of thermally activated protonic quantum correlations in condensed matter [ 8,9].
05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.
Volume198,number 3,4
9 October 1992
CHEMICALPHYSICSLETTERS
2. Experimental
enriched and the 90% for (sample
Four specimens with various X ( = D/ (H + D) ) of the acid proton, i.e. X=0.13 (sample I), 0.70 (II),
0.80 (III), 0.96 (IV), were prepared by recrystallization at 290 k 10 K from mixed solvents of H,O, DzO and ( CH3)&0 in various ratios. The samples
by “0 up to 14% for the carboxyl group other (sample VI) is deuterated more than acid hydrogen. T i ’ of normal benzoic acid VII) and of sample VIII (X=0.85, normal
“0 ) for which the phenyl group was deuterated were also measured. The concentrations of the isotopes were determined by the method described above. The samples we measured are summarized in table 1. T I ’ of H and of D were measured by a conventional 90” train-z-90” method at 37 MHz and by a 90; train-T-90;~t-90; method at 30.8 MHz, respectively. The magnetization recovery curves of H and D were respectively described by a single exponential function. The temperature of the specimen was measured by chromel-P-constantan and Au(Fe)-chrome1 thermocouples. The uncertainty of the temperature was between -0.1 and 50.2 K.
were purified by sublimation and powdered specimens were sealed off into glass ampoules with lo-20 Torr of He gas. To measure clearly the dynamics of H in the HD pair in the samples III and IV, the “0 isotope, which has a magnetic dipole moment and strongly enhances the T r ’ of H related to the transfer motion of H in an HD pair, was enriched up to 14% for the carboxyl group before deuteration of the acid proton. The deuteron fraction X and the concentration of I70 were determined by comparing the
intensity of ‘H and I70 NMR spectra of the isotopic derivatives in (CD,)&0 solutions with those of normal benzoic acid. The estimated errors in X and in the concentration of I70 were kO.02 and f lo/o, respectively. For the comparison of the transfer rates between an HH pair, and HD pair and a DD pair, two other isotopic derivatives of benzoic acid were prepared. One (sample V) is fully protonated and
3. Results and discussion When the acid proton was exchanged by a small amount of D (sample I; X=0.13), most of the D (86%; random combination of H and D in a dimeric unit of carboxyl groups was assumed to be estab-
Table 1 Isotopicderivatives of benzoicacid and parametersfor calculationof 7’;’ for H and D Sample D/(H+D) of acid D
“0
C8
c&I
CA”
(%)
(Io*s-2)
(108s-2)
(10’ sm2)
TkJ/mo*)
(k.J/mol)
0.4 c’ [0.25] lO.21
2.5 2.5 IO.751 [0.75] 2.5
10.0 10.5 ~4.21 14.21 10.5
13.0 5.0 L1.71 11.71 3.3
12.0 14.21 14.21 (13.0) 14.21
2.0 L1.71 il.71 (5.0)
II
0.13 0.70
III
0.80
14
IV
0.96
14
I
V
VI VII VIII *’
0.00
20.9 0.00 0.85
0.037b’ 0.037b,
14 0.037b, 0.037b) 0.037b)
170 -
0.075 [0.003] 11.51 (120) -
0.4(Cd,,)
[i.OOS] i2.51 e,
~2.51 -
L2.51
V
&] [0.75] (3.0) (0.751 I&]
r,’ (10” s-1)
10.5
Il.71 1.3
14.21
il.71
ko
(108 s-1) 1.0
$1 $1 I:::] t2.51 (0.4) i2.51 ,:I,
n) The values in brackets are related to transfer motion of an HH pair. The values in parentheses are related to transfer motion of a DD pair. b, The value is the natural abundance of “0. ‘) DipolecouplingbetweenH in an HD pair and H of the phenyigroup,whereasother valuesfor Cin in this column are dipole couplings between protons within an HH pair. d, The phenyl group of sample VIII is deuterated while the phenyl groups of other samples are al1protonated. ClDipole coupling between H and D within an HD pair, which is negligibly small for other samples.
317
Volume 198, number 3,4
lished) form HD pairs in dimeric units of carboxyl groups in the crystal, for which T I’ of D was measured at 30.XMHz between 64 and 220 K, T ;’ maximum was observed at 1IO K (fig. 1; closed circles). The observed T r ’ curve shifted to lower temperature compared with the T ;’ curve of D in a DD pair of sample VI (fig. 1; curve ( 1) measured at 30.8 MHz). In reverse, when the acid proton was almost completely deuterated (sample IV; X= 0.96 and “0 enriched to 14%), most (96%) of the remaining H forms HD pairs in the crystal, for which Ti’ of H was measured at 37.0 MHz between 31 and 300 K and a maximum of T i ’ was observed near 140 K (fig. 1; open circles). The T i ’ maximum shifted to higher temperature compared with the T r’ curve of H in an HH pair in sample V (fig. 1; curve (2) measured at 37.0 MHz). The following analysis of the T; ’ curves of H and D indicates that both the transfer rate of D in an HD pair in sample I (X=0.1 3) and the transfer rate of H in an HD pair in sample IV (X=0.96) are in between the transfer rates of H T/K
in an HH pair (curve (2) ) and of D in a DD pair (curve (1)). The temperature dependence of the transfer rate of D in an HD pair in sample I and that of a DD pair in sample VI were determined by calculating T ;’ using a well-known formula of T 1’ related to deuteron dynamics in unequal potential wells [ 571, T;‘(D)=C$[2cosh(A/2RT)]-‘B(r,w&,
J(T,w)=T/(lt7’w2),
Fig. 1. T;’ of H and D of benzoic acid crystals. (0) Ty’ of D ofsamplel (D/(H+D)=O.l3foracidproton) measuredat30.8 MHz, (0) T;’ of H of sample IV (D/(HtD) =0.96, “O-enriched to 14%) measured at 37.0 MHz. Solid curve (1) is a smoothed curve of measured Ti’ of D (30.8 MHz) of sample VI for which the acid proton was deuterated by more than 90% and this curve is consistent with T,’ of D in a DD pair reported in ref. [ 5] when the different Larmor frequencies employed in the two experiments are taken into consideration. The broken curve (2) is a smoothed curve of T;- ’ of H (37 MHz) of sample V (fully protonated and I70 enriched to 14%). Typical scattering of the observed values from the curves ( 1) and (2) is f 10%.
(1)
where A is the energy difference between the tautomerit states, OD is the Larmor frequency of D and 5 is the correlation time (inverse of the transfer rate). While there are some critical discussions about the slope of z-’ versus temperature [ $71, we used a simple formula of 5-l proposed by Skinner and Trommsdorff (eqs. (70) and (7 1) of ref. [ 6 ] ). This procedure does not spoil the conclusion of this paper. The dipole interaction between H and D in a dimeric unit of sample I was estimated to be negligibly small compared with quadrupole coupling and was ignored. The transfer rate of H in an HH pair in sample V (14% “0) was determined by a calculation of T; ’ of H which is a sum of two kinds of relaxation rates. One is due to dipole interaction between protons, which is described by a formula similar to eq. ( 1) with dipole coupling (C& ) instead of quadrupole coupling (Cs ) and the other is due to dipole interaction between H and “0 (14%), which is comparable to the former and is described by [ IO,1 1 ] Ti’(H)=C&[
318
9 October 1992
CHEMICAL PHYSICS LETTERS
(2cosh(A/2RT)]-2B’(r,
+6J(7, wN+oo) .
W) ,
(2)
I& and w, are Larmor frequencies of H and “0, re-
spectively. Here the quadrupole splitting of “0 might be negligibly small [ 12,131 compared with the proton frequency of 37 MHz and was ignored, which was justified by comparing the observed Ti’ of sample V (14% I’O) with that of sample VII (0.037% 170). The difference between the Ti’ curves of samples V and VII was reproduced well by eq. (2).
Volume198,number 3,4
CHEMICALPHYSICSLETTERS
The transfer rate of H in an HD pair in sample IV was derived from a calculation of T I I using eq. ( 2 ) . Here the small contribution of the HH pair (broken curve (3) in fig. 2) does not disturb the estimate of T--I of an HD pair above 64 K. The curve (3) was estimated from the broken curve (2) in fig. 1 by assuming spin temperatures among protons present in the sample IV and randomly distributed different pairs, HH:HD:DD=(l-X)‘:2X(I-X):X* (X= D/ (H+ D) ), which were safely established by our experiments for different X (table 1). The value of C&, in eq. (2 ) for H in sample IV was consistent with that in sample V when the spin temperature among protons was taken into consideration. Both the relaxation rate related to dipole interaction between H and D in an HD pair and that between H in an HD pair and H of a phenyl group were estimated to be less than 1OoYa of the relaxation rate controlled by dipole interaction between acid H and “0 ( 14%) as described below and were ignored. The dipole interaction between H and D in HD pair unit was determined by a measurement of T r ’ of H in sample VIII (X=0.85, 0.073OA~ “O), in which the phenyl group was deuterated and T ; ’ of H was controlled by dipole interaction between H and D. The dipole interaction between H in an HD pair and H
lo3
T-l / K-l
Fig. 2. (0) and (0 ) are the same plots as in fig. 1. The broken curve (3) was estimated as the contribution of an HH pair to the observed T;-’ (0 ) from curve (2) in fig. 1 (see text). The solid curves for ( l ) and ( 0 ] are the calculations of T: ’ , from which the transfer rate, t - ’ ( T), of an HD pair was obtained from sample I and for sample IV, respectively.
9 October 1992
of the phenyl group was estimated separately from the observed T r ’ of H in sample II (X= 0.7,0.037% “0) using the dipole interaction between H and D estimated above. The values for C$, C&,, C&,, I’, A, 7; ’ and k,, used in calculations for the different specimens, I through VIII, are listed in table 1. Our measurements suggest that the transfer of H and D, in an HD pair in a dimeric unit is not independent but concerted within an NMR time scale ( 10-6-1010 s), because the transfer rate of D in an HD pair is more similar to the transfer rate of H in an HD pair than to the transfer rate of D in a DD pair, and because the transfer rate of H in an HD pair is more similar to the transfer rate of D in an HD pair than to the transfer rate of H in an HH pair. The order of the transfer rates of different pairs was found as HH pair>HD pair >DD pair, which is consistent with the result of St&Ah et al. [ 51. They, however, did not measure the transfer rate of H in an HD pair but measured only the transfer rate of D in an HD pair for benzoic acid with X=0.5. Thus it became clear in our present experiment that the transfer rates of H and D in an HD pair are similar. In addition to this fact we have found the novel phenomenon that the transfer rate of an HD pair in a dimeric unit was remarkably quenched by an increase in the mole fraction X of deuterons in hydrogen bonds, as we demonstrate below. The temperature dependence of the transfer rate, r-l(T), of HD pairs in sample IV was obtained by using eq. (2) as described above (fig. 2). The energy difference, A, between two tautomeric states was estimated to be 2.5 k.T/mol. The broken curve (4) in fig. 2 is a prediction of the T I’ of D in an HD pair, which was calculated using 5-l (T) and A obtained above for H in an HD pair in sample IV, using the quadrupole relaxation formula of D (eq. ( 1) ). In this calculation the dipole coupling between D and H was estimated to be negligiblysmall compared with quadrnpole coupling and was ignored. It is evident that curve (4) does not coincide with the observed T I’ of D in an HD pair in sample I (closed circles) and shifts remarkably to higher temperature. This result clearly indicates that the transfer of an HD pair in sample IV is slower than that in sample I in spite of the same HD pair unit in the two crystals. It should be noted that the present result does not depend on the formula of r-‘(T) employed, be319
Volume 198, number 3,4
CHEMICAL PHYSICS LETTERS
cause we used the common z-’ (T) and A for the comparison between the measured T; ’ of D in an HD pair of sample I and that of H in an HD pair of sample IV. The key point related to the different transfer rates of an HD pair between samples I and IV is the mole fraction X ( =D/(H+D)) of deuterons in hydrogen bonds. Fig. 3 shows the X dependence of the transfer rate, r-‘, at constant temperatures near the Tr’ maximum at which the obtained T- ’ is most reliable and it demonstrates the remarkable quenching of the transfer rate of an HD pair as the concentration of D in the surrounding hydrogen bonds increases. A similar effect was also observed for partially deuterated crystals of acetylenedicarboxylic acid [ 141. We are not aware of any conventional theoretical treatment of this effect. An observation with a certain resemblance to the present effect was recently reported [ 81, i.e. an “anomalous” decrease of H+/D+ mobility in H20/ D20 mixtures in the liquid state. The underlying the-
[ I] S. Nagaoka, T. Terao, E Imashiro, A. Saika, N. Hirota and
200 K
I
;i
ly---yO l0l0 !;: 1080
0.5
1
D/ (H+D) Fig. 3. Transfer rate 5-i of an HD pair as a function of the mole fraction of D of acid hydrogen of benzoic acid at constant temperatures. Solid curves are guides to the eyes. T-’ for D/ (H t D) = 0.70 and 0.80 was obtained from T; I for H of sample II (0.037% “0) and of sample III (14% “0) by a similar method to the sample IV, where in both cases the shoulder of T I’ related to transfer motion of an HH pair was clearly separated from the T r’ maximum related to the transfer motion of an HD pair. r -’ of an HD pair for D/( H t D)=0.5 was calculated from the T;‘dataofDinanHDpairinref. [5].
320
ory of thermally activated quantum correlations between fermions in condensed matter [ 91, which motivated the above experiments, may apply in both cases to the protons constituting hydrogen bonds. As a consequence, protons may now exhibit the typical quanta1 delocalization features; thus time-dependent quantum interference between adjacent protons becomes feasible [S,9]. In the case of H/D mixtures, as in the present experiment, protonic correlations become disrupted by deuterons being “near” or “between” the protons; this follows from the so-called spin superselection rule. This effect furthermore causes a localization of protons (and deuterons), which is tantamount to a decrease of the transfer rate (or mobility) [ 8,9], in agreement with the characteristic curves in fig. 3 of the present experimental results. This effect proposes a new mechanism of proton transfer in the hydrogen bonds in condensed matter. Further work is underway.
References
loI1 l-----l F-4
9 October 1992
S. Hayashi, J. Chem. Phys. 79 (1983) 4694. [2] T. Agaki, F. Imashiro, T. Terao, N. Hirota and S. Hayashi, Chem. Phys. Letters I39 (1987) 331. [ 31 N. Imaoka, S. Takeda and H. Chihara, Bull. Chem. Sot. .Iapan61(1988)1865. [4] A.J. Horsewill and A. Aibout, J. Phys. Condens. Matter 1 ( 1989) 9609. [ 51A. Stlckli, B.H. Meier, R. Kreis, R. Meyer and R.R. Ernst, J. Chem. Phys. 93 ( 1990) 1502. [6] J.L. Skinner and H.P. Trommsdorlf, J. Chem. Phys. 89 (1988) 897. [7] A. Heuer and U.J. Haeberlen, J. Chem. Phys. 95 ( 1991) 4201. [ 81 H. Weingiirtner and C.A. Chatzidimitriou-Dreismann, Nature 346 (1990) 548. 19] CA. Chatzidimitriou-Dreismann, Advan. Chem. Phys. 80 (1991) 201. [ lo] A. Abragam, Principles of nuclear magnetism (Oxford Univ. Press, Oxford, 1961) ch. 8. [ 1 I] S. Takeda, H. Chihara, T. Inabe, T. Mitani and Y. Maruyama, Chem. Phys. Letters 189 (1992) 13. [ 121 C.P. Cheng and T.L. Brown, J. Am. Chem. Sot. 101 (1979) 2321.
[ 131 L.G. Butler, C.P. Cheng and T.L. Brown, J. Phys. Chem. 85 (1981) 2738. [ 14] S. Takeda and A. Tsuzumitani, to be published.
CHEMICAL PHYSICS LETTERS
9 October 1992
Evidence of quantum correlations in the H/D-transfer dynamics in the hydrogen bonds in partially deuterated benzoic acid crystals Sadamu Takeda, Akihiko Tsuzumitani ’ Department of Chemistry, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan
and C.A. Chatzidimitriou-Dreismann Iwan N. Stranski Institute for Physical and Theoretical Chemistry Technical University of Berlin, Street 17. Juni 112, W-1000 Berlin 12, Germany
Received 30 June 1992
A precise investigation of spin-lattice relaxation rates for protons and deuterons of partially deuterated benzoic acid crystals showed a remarkable quenching of the transfer rate of an HD pair in hydrogen-bonded dimeric units of carboxyl groups with increasing concentration of D in the surrounding hydrogen bonds. A similar effect was also observed for partially deuterated crystals of acetylenedicarboxylic acid. This finding supports recent theoretical predictions of thermally activated protonic quantum correlation in condensed matter and proposes a new mechanism for the proton transfer in hydrogen bonds in condensed matter.
1. Introduction Knowledge of proton-transfer quantum dynamics in hydrogen bonds is necessary for understanding many important chemical and biological processes. An example of the extensive investigations of this topic is “double proton transfer” in hydrogen-bonded dimers of carboxyl groups in carboxylic acid crystals [l-7]. In these systems, the quantum tunneling effect is believed to play a dominant role in the transfer of two protons (HH pair) and also two deuterons (DD pair) in dimeric units of carboxyl groups at sufficiently low temperatures. At higher temperatures additional thermally activated processes become important [ 5-71, for which an effect of coupling between hydrogen motion and another oscillator has been discussed as a key mechanism to Correspondence to: S. Takeda, Department of Chemistry, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan. ’ Present address: LSI Research Center High-Technology Research Laboratories, Kawasaki Steel Corporation, Technical Research Division, Kawasaki-cho 1, Chiba 260, Japan.
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0009-2614/92/$
determine the temperature dependence of the transfer rate of hydrogens in the hydrogen bonds [ 5,7]. In addition to the conventional knowledge, we present in this Letter novel results showing a remarkable quenching of the transfer rate of an HD pair in a dimeric unit at relatively high temperatures with increasing mole fraction of D in the hydrogen bonds in the H/D mixed crystals of benzoic acid. Our experiment consists of measuring the transfer rate of an HD pair in the hydrogen-bonded dimeric unit of carboxyl groups in benzoic acid crystals as a function of the H/D fraction of acid protons. The phenyl group of the molecule is protonated. The transfer rate was determined by measuring the spin-lattice relaxation rate T r’ of H and D nuclear magnetic resonances. The present experimental results, which seem beyond conventional theoretical treatment, are discussed along with a recent theoretical prediction of thermally activated protonic quantum correlations in condensed matter [ 8,9].
05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.
Volume198,number 3,4
9 October 1992
CHEMICALPHYSICSLETTERS
2. Experimental
enriched and the 90% for (sample
Four specimens with various X ( = D/ (H + D) ) of the acid proton, i.e. X=0.13 (sample I), 0.70 (II),
0.80 (III), 0.96 (IV), were prepared by recrystallization at 290 k 10 K from mixed solvents of H,O, DzO and ( CH3)&0 in various ratios. The samples
by “0 up to 14% for the carboxyl group other (sample VI) is deuterated more than acid hydrogen. T i ’ of normal benzoic acid VII) and of sample VIII (X=0.85, normal
“0 ) for which the phenyl group was deuterated were also measured. The concentrations of the isotopes were determined by the method described above. The samples we measured are summarized in table 1. T I ’ of H and of D were measured by a conventional 90” train-z-90” method at 37 MHz and by a 90; train-T-90;~t-90; method at 30.8 MHz, respectively. The magnetization recovery curves of H and D were respectively described by a single exponential function. The temperature of the specimen was measured by chromel-P-constantan and Au(Fe)-chrome1 thermocouples. The uncertainty of the temperature was between -0.1 and 50.2 K.
were purified by sublimation and powdered specimens were sealed off into glass ampoules with lo-20 Torr of He gas. To measure clearly the dynamics of H in the HD pair in the samples III and IV, the “0 isotope, which has a magnetic dipole moment and strongly enhances the T r ’ of H related to the transfer motion of H in an HD pair, was enriched up to 14% for the carboxyl group before deuteration of the acid proton. The deuteron fraction X and the concentration of I70 were determined by comparing the
intensity of ‘H and I70 NMR spectra of the isotopic derivatives in (CD,)&0 solutions with those of normal benzoic acid. The estimated errors in X and in the concentration of I70 were kO.02 and f lo/o, respectively. For the comparison of the transfer rates between an HH pair, and HD pair and a DD pair, two other isotopic derivatives of benzoic acid were prepared. One (sample V) is fully protonated and
3. Results and discussion When the acid proton was exchanged by a small amount of D (sample I; X=0.13), most of the D (86%; random combination of H and D in a dimeric unit of carboxyl groups was assumed to be estab-
Table 1 Isotopicderivatives of benzoicacid and parametersfor calculationof 7’;’ for H and D Sample D/(H+D) of acid D
“0
C8
c&I
CA”
(%)
(Io*s-2)
(108s-2)
(10’ sm2)
TkJ/mo*)
(k.J/mol)
0.4 c’ [0.25] lO.21
2.5 2.5 IO.751 [0.75] 2.5
10.0 10.5 ~4.21 14.21 10.5
13.0 5.0 L1.71 11.71 3.3
12.0 14.21 14.21 (13.0) 14.21
2.0 L1.71 il.71 (5.0)
II
0.13 0.70
III
0.80
14
IV
0.96
14
I
V
VI VII VIII *’
0.00
20.9 0.00 0.85
0.037b’ 0.037b,
14 0.037b, 0.037b) 0.037b)
170 -
0.075 [0.003] 11.51 (120) -
0.4(Cd,,)
[i.OOS] i2.51 e,
~2.51 -
L2.51
V
&] [0.75] (3.0) (0.751 I&]
r,’ (10” s-1)
10.5
Il.71 1.3
14.21
il.71
ko
(108 s-1) 1.0
$1 $1 I:::] t2.51 (0.4) i2.51 ,:I,
n) The values in brackets are related to transfer motion of an HH pair. The values in parentheses are related to transfer motion of a DD pair. b, The value is the natural abundance of “0. ‘) DipolecouplingbetweenH in an HD pair and H of the phenyigroup,whereasother valuesfor Cin in this column are dipole couplings between protons within an HH pair. d, The phenyl group of sample VIII is deuterated while the phenyl groups of other samples are al1protonated. ClDipole coupling between H and D within an HD pair, which is negligibly small for other samples.
317
Volume 198, number 3,4
lished) form HD pairs in dimeric units of carboxyl groups in the crystal, for which T I’ of D was measured at 30.XMHz between 64 and 220 K, T ;’ maximum was observed at 1IO K (fig. 1; closed circles). The observed T r ’ curve shifted to lower temperature compared with the T ;’ curve of D in a DD pair of sample VI (fig. 1; curve ( 1) measured at 30.8 MHz). In reverse, when the acid proton was almost completely deuterated (sample IV; X= 0.96 and “0 enriched to 14%), most (96%) of the remaining H forms HD pairs in the crystal, for which Ti’ of H was measured at 37.0 MHz between 31 and 300 K and a maximum of T i ’ was observed near 140 K (fig. 1; open circles). The T i ’ maximum shifted to higher temperature compared with the T r’ curve of H in an HH pair in sample V (fig. 1; curve (2) measured at 37.0 MHz). The following analysis of the T; ’ curves of H and D indicates that both the transfer rate of D in an HD pair in sample I (X=0.1 3) and the transfer rate of H in an HD pair in sample IV (X=0.96) are in between the transfer rates of H T/K
in an HH pair (curve (2) ) and of D in a DD pair (curve (1)). The temperature dependence of the transfer rate of D in an HD pair in sample I and that of a DD pair in sample VI were determined by calculating T ;’ using a well-known formula of T 1’ related to deuteron dynamics in unequal potential wells [ 571, T;‘(D)=C$[2cosh(A/2RT)]-‘B(r,w&,
J(T,w)=T/(lt7’w2),
Fig. 1. T;’ of H and D of benzoic acid crystals. (0) Ty’ of D ofsamplel (D/(H+D)=O.l3foracidproton) measuredat30.8 MHz, (0) T;’ of H of sample IV (D/(HtD) =0.96, “O-enriched to 14%) measured at 37.0 MHz. Solid curve (1) is a smoothed curve of measured Ti’ of D (30.8 MHz) of sample VI for which the acid proton was deuterated by more than 90% and this curve is consistent with T,’ of D in a DD pair reported in ref. [ 5] when the different Larmor frequencies employed in the two experiments are taken into consideration. The broken curve (2) is a smoothed curve of T;- ’ of H (37 MHz) of sample V (fully protonated and I70 enriched to 14%). Typical scattering of the observed values from the curves ( 1) and (2) is f 10%.
(1)
where A is the energy difference between the tautomerit states, OD is the Larmor frequency of D and 5 is the correlation time (inverse of the transfer rate). While there are some critical discussions about the slope of z-’ versus temperature [ $71, we used a simple formula of 5-l proposed by Skinner and Trommsdorff (eqs. (70) and (7 1) of ref. [ 6 ] ). This procedure does not spoil the conclusion of this paper. The dipole interaction between H and D in a dimeric unit of sample I was estimated to be negligibly small compared with quadrupole coupling and was ignored. The transfer rate of H in an HH pair in sample V (14% “0) was determined by a calculation of T; ’ of H which is a sum of two kinds of relaxation rates. One is due to dipole interaction between protons, which is described by a formula similar to eq. ( 1) with dipole coupling (C& ) instead of quadrupole coupling (Cs ) and the other is due to dipole interaction between H and “0 (14%), which is comparable to the former and is described by [ IO,1 1 ] Ti’(H)=C&[
318
9 October 1992
CHEMICAL PHYSICS LETTERS
(2cosh(A/2RT)]-2B’(r,
+6J(7, wN+oo) .
W) ,
(2)
I& and w, are Larmor frequencies of H and “0, re-
spectively. Here the quadrupole splitting of “0 might be negligibly small [ 12,131 compared with the proton frequency of 37 MHz and was ignored, which was justified by comparing the observed Ti’ of sample V (14% I’O) with that of sample VII (0.037% 170). The difference between the Ti’ curves of samples V and VII was reproduced well by eq. (2).
Volume198,number 3,4
CHEMICALPHYSICSLETTERS
The transfer rate of H in an HD pair in sample IV was derived from a calculation of T I I using eq. ( 2 ) . Here the small contribution of the HH pair (broken curve (3) in fig. 2) does not disturb the estimate of T--I of an HD pair above 64 K. The curve (3) was estimated from the broken curve (2) in fig. 1 by assuming spin temperatures among protons present in the sample IV and randomly distributed different pairs, HH:HD:DD=(l-X)‘:2X(I-X):X* (X= D/ (H+ D) ), which were safely established by our experiments for different X (table 1). The value of C&, in eq. (2 ) for H in sample IV was consistent with that in sample V when the spin temperature among protons was taken into consideration. Both the relaxation rate related to dipole interaction between H and D in an HD pair and that between H in an HD pair and H of a phenyl group were estimated to be less than 1OoYa of the relaxation rate controlled by dipole interaction between acid H and “0 ( 14%) as described below and were ignored. The dipole interaction between H and D in HD pair unit was determined by a measurement of T r ’ of H in sample VIII (X=0.85, 0.073OA~ “O), in which the phenyl group was deuterated and T ; ’ of H was controlled by dipole interaction between H and D. The dipole interaction between H in an HD pair and H
lo3
T-l / K-l
Fig. 2. (0) and (0 ) are the same plots as in fig. 1. The broken curve (3) was estimated as the contribution of an HH pair to the observed T;-’ (0 ) from curve (2) in fig. 1 (see text). The solid curves for ( l ) and ( 0 ] are the calculations of T: ’ , from which the transfer rate, t - ’ ( T), of an HD pair was obtained from sample I and for sample IV, respectively.
9 October 1992
of the phenyl group was estimated separately from the observed T r ’ of H in sample II (X= 0.7,0.037% “0) using the dipole interaction between H and D estimated above. The values for C$, C&,, C&,, I’, A, 7; ’ and k,, used in calculations for the different specimens, I through VIII, are listed in table 1. Our measurements suggest that the transfer of H and D, in an HD pair in a dimeric unit is not independent but concerted within an NMR time scale ( 10-6-1010 s), because the transfer rate of D in an HD pair is more similar to the transfer rate of H in an HD pair than to the transfer rate of D in a DD pair, and because the transfer rate of H in an HD pair is more similar to the transfer rate of D in an HD pair than to the transfer rate of H in an HH pair. The order of the transfer rates of different pairs was found as HH pair>HD pair >DD pair, which is consistent with the result of St&Ah et al. [ 51. They, however, did not measure the transfer rate of H in an HD pair but measured only the transfer rate of D in an HD pair for benzoic acid with X=0.5. Thus it became clear in our present experiment that the transfer rates of H and D in an HD pair are similar. In addition to this fact we have found the novel phenomenon that the transfer rate of an HD pair in a dimeric unit was remarkably quenched by an increase in the mole fraction X of deuterons in hydrogen bonds, as we demonstrate below. The temperature dependence of the transfer rate, r-l(T), of HD pairs in sample IV was obtained by using eq. (2) as described above (fig. 2). The energy difference, A, between two tautomeric states was estimated to be 2.5 k.T/mol. The broken curve (4) in fig. 2 is a prediction of the T I’ of D in an HD pair, which was calculated using 5-l (T) and A obtained above for H in an HD pair in sample IV, using the quadrupole relaxation formula of D (eq. ( 1) ). In this calculation the dipole coupling between D and H was estimated to be negligiblysmall compared with quadrnpole coupling and was ignored. It is evident that curve (4) does not coincide with the observed T I’ of D in an HD pair in sample I (closed circles) and shifts remarkably to higher temperature. This result clearly indicates that the transfer of an HD pair in sample IV is slower than that in sample I in spite of the same HD pair unit in the two crystals. It should be noted that the present result does not depend on the formula of r-‘(T) employed, be319
Volume 198, number 3,4
CHEMICAL PHYSICS LETTERS
cause we used the common z-’ (T) and A for the comparison between the measured T; ’ of D in an HD pair of sample I and that of H in an HD pair of sample IV. The key point related to the different transfer rates of an HD pair between samples I and IV is the mole fraction X ( =D/(H+D)) of deuterons in hydrogen bonds. Fig. 3 shows the X dependence of the transfer rate, r-‘, at constant temperatures near the Tr’ maximum at which the obtained T- ’ is most reliable and it demonstrates the remarkable quenching of the transfer rate of an HD pair as the concentration of D in the surrounding hydrogen bonds increases. A similar effect was also observed for partially deuterated crystals of acetylenedicarboxylic acid [ 141. We are not aware of any conventional theoretical treatment of this effect. An observation with a certain resemblance to the present effect was recently reported [ 81, i.e. an “anomalous” decrease of H+/D+ mobility in H20/ D20 mixtures in the liquid state. The underlying the-
[ I] S. Nagaoka, T. Terao, E Imashiro, A. Saika, N. Hirota and
200 K
I
;i
ly---yO l0l0 !;: 1080
0.5
1
D/ (H+D) Fig. 3. Transfer rate 5-i of an HD pair as a function of the mole fraction of D of acid hydrogen of benzoic acid at constant temperatures. Solid curves are guides to the eyes. T-’ for D/ (H t D) = 0.70 and 0.80 was obtained from T; I for H of sample II (0.037% “0) and of sample III (14% “0) by a similar method to the sample IV, where in both cases the shoulder of T I’ related to transfer motion of an HH pair was clearly separated from the T r’ maximum related to the transfer motion of an HD pair. r -’ of an HD pair for D/( H t D)=0.5 was calculated from the T;‘dataofDinanHDpairinref. [5].
320
ory of thermally activated quantum correlations between fermions in condensed matter [ 91, which motivated the above experiments, may apply in both cases to the protons constituting hydrogen bonds. As a consequence, protons may now exhibit the typical quanta1 delocalization features; thus time-dependent quantum interference between adjacent protons becomes feasible [S,9]. In the case of H/D mixtures, as in the present experiment, protonic correlations become disrupted by deuterons being “near” or “between” the protons; this follows from the so-called spin superselection rule. This effect furthermore causes a localization of protons (and deuterons), which is tantamount to a decrease of the transfer rate (or mobility) [ 8,9], in agreement with the characteristic curves in fig. 3 of the present experimental results. This effect proposes a new mechanism of proton transfer in the hydrogen bonds in condensed matter. Further work is underway.
References
loI1 l-----l F-4
9 October 1992
S. Hayashi, J. Chem. Phys. 79 (1983) 4694. [2] T. Agaki, F. Imashiro, T. Terao, N. Hirota and S. Hayashi, Chem. Phys. Letters I39 (1987) 331. [ 31 N. Imaoka, S. Takeda and H. Chihara, Bull. Chem. Sot. .Iapan61(1988)1865. [4] A.J. Horsewill and A. Aibout, J. Phys. Condens. Matter 1 ( 1989) 9609. [ 51A. Stlckli, B.H. Meier, R. Kreis, R. Meyer and R.R. Ernst, J. Chem. Phys. 93 ( 1990) 1502. [6] J.L. Skinner and H.P. Trommsdorlf, J. Chem. Phys. 89 (1988) 897. [7] A. Heuer and U.J. Haeberlen, J. Chem. Phys. 95 ( 1991) 4201. [ 81 H. Weingiirtner and C.A. Chatzidimitriou-Dreismann, Nature 346 (1990) 548. 19] CA. Chatzidimitriou-Dreismann, Advan. Chem. Phys. 80 (1991) 201. [ lo] A. Abragam, Principles of nuclear magnetism (Oxford Univ. Press, Oxford, 1961) ch. 8. [ 1 I] S. Takeda, H. Chihara, T. Inabe, T. Mitani and Y. Maruyama, Chem. Phys. Letters 189 (1992) 13. [ 121 C.P. Cheng and T.L. Brown, J. Am. Chem. Sot. 101 (1979) 2321.
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