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A study of hydrogen-bond dynamics in carboxylic acids by NMR T1 measurements: isotope effects and hydrogen-bond length dependence
CHEMICAL PHYSICS LETTERS
Volume 139, number 3,4
28 August 1987
A STUDY OF HYDROGEN-BOND DYNAMICS IN CARBOXYLIC ACIDS BY NMR T, ME~U~ME~~ ISOTOPE EFFECTS AND H~ROGEN-BOND LENGTH DEPENDENCE * T. AGAKI ‘, F. IMASHIRO, T. TERAO, N. HIROTA Department of Chemistry, Faculty ofscience, Kyoto Vniversrty, Kyoto 606, Japan
and S. HAYASHI Institutefor Chemical Research, Kyoto University, Uji 611, Japan
Received 8 June 1987
Proton (deuteron) transfer ofhydrogen bonds in benzoic, glutark and pformylbenzoic acids was studied by proton (deuteron) T, measurements. Deuteration of carboxylic protons was found to increase the barriers to classical proton jumping as well as quantum-mechanical tunneling. The former barriers increase as the hydrogen-bond distance increases.
NMR spectroscopy has shown that the two carboxylic protons in some carboxylic acid dimers undergo a simultaneous classical proton jump and quantum-mechanical tunneling along the hydrogen bonds [l-6]. The simultaneous proton transfer interconverts two different configurations A and B. Qo--HO, R-C ~O”__O~
,OH--0% C-R
=
R-C *0_+0
A B Whereas the two configurations are energetically degenerate in the free dimers, the degeneracy is generally removed in the solid state by distortion of the double-minimum intermolecular potential due to intermolecular interactions, producing a small enthalpy difference ALI between con~gurations A and B, as shown in fig. 1. The dynamics in this interesting system are studied mainly by proton T, meas-
* A part of this work was presented in the 22nd Ampere Congress, Zurich (1984). ’ Present address: Central Research Laboratory, Ishiham Sangyo Kaisha Ltd., Kusatsu, Shiga 525, Japan.
A
C-R
B
Fig. 1. Potential curve for proton (deuteron) transfer in hydrogen-bonded carboxytic acids.
urements and the results have stimulated theoretical attempts to reproduce the unusually low potential wells obtained [ 7-101 and the quantum-mechanical behaviour [ lo]. In this work, we investigate proton (deuteron) transfer in carboxylic acids and their deuterated compounds by proton (deuteron) T, measurements. Deuteration changes the O...O hydrogen-bond distance Ro. .. and hence the potential curve, particularly in the Ro...o range from 2.44 to 2.63 A [ 111, This is related to the difference in the proton and deuteron motions in this range [ 121. Accordingly,
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we selected three different carboxylic acids with different Ro...o values: benzoic acid (1) ( Ro.,.o = 2.63 A [ 13]), glutaric acid (2) (2.69 A [ 141) and p-formylbenzoic acid (3) (2.57 8, [ IS]). (Hereafter, if necessary, we add “‘D” or “H” to the compound numbers and parameters to represent the deuterated or non-deuterated carboxylic acid, respectively.)
28 August 1987
protons on the hydrogen bonds in a dimer govern the relaxation, the equation for polycrystalline samples can be rewritten as 1 -=
-5$y4fr’r-” sin28 -(1 +aa)2 B(r)*
TF
(1)
with a=exp(AH/RT),
2. Experimental
B(7)= Commercially available 2H was recrystallized from ethanol. Form-I crystals of 3H were obtained according to the method described in ref. [ 151, and the content confirmed to be more than 80% by IR spectroscopy. Compounds 1D and 3D were prepared by hydrolysis of the corresponding acid anhydrides with equimolar D20 in sealed glass tubes. Form-I crystals of 3D were obtained in the same manner as those of 3H. In order to obtain 2D, 2H was dissolved in D20-EtOD under NZ, and then the solvent was evaporated under reduced pressure; this procedure was repeated three times. Proton and deuteron T, values were measured on a home-built spectrometer operating at 90.0 MHz for ‘H and at 13.8 MHz for ‘H. Sample temperatures were controlled by the N2 gas flow method above 77 K and by the reduced-pressure He gas flow method below 77 K [ 161. Deuteron T, values were determined by plotting the average heights of multiple solid echoes [ 171 against repetition times. IR spectra were taken with a Nicolet 6000 FT IR spectrometer in order to obtain the enthalpy difference AH. For lD, AH could be determined by the same procedure as was used for 1H [ 31. However, bsI for 2 and 3 could not be determined because the absorption bands attributed to different configurations were not well resolved.
3. Results and discussion 3. I. Temperature dependence of T The general equation for the proton relaxation time Tr by a classical jumping process between unequally populated configurations A and B has been derived previously [ 3,181. If only the two carboxylic 332
(2)
4? l+;272+ 1+4w272'
(3)
where N is the number of protons in a dimer, r is the distance between the two carboxylic protons, 8 is the flip ar@e of the proton-pair orientation following a proton jump and o is the Larmor frequency. The correlation time 7 can be expressed as exp( K,/RT)I(l+a),
7=t0
(4)
where r. is a constant. If or < 1 (at high temperatures) or wr * 1 (at low temperatures), eq. ( 1) may be reduced to
TY
mm=-
(vo+M)
RT
+const.
(w7c
1)
(5) or
Tz: = (Kl-Aff> ln(l+a) RT
+const.
(wz~l).
(6)
Hence the T, curve due to the classical jumping process is steeper in the low-temperature branch unless LW=O. The deuteron relaxation is caused mainly by the jump-induced fluctuation of the electric field gradient (EFG) at the deuteron site. In order to obtain an equation for T’p #I we use a similar procedure to that for Tj” [ 31, and assume that the quadrupole coupling constant e2qQlh and the asymmetry parameter r are invariant to the deuteron jump. In this event TP for polycrystalline samples is given by (7) #’ An equation for TP has already been obtained by two groups [ 5,101,Our result is consistent with that of Benz et al. [ 51. The equation obtained by Meyer and Ernst [ IO] differs from ours by a factor of 8121.
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CHEMICAL PHYSICS LETTERS
Volume 139, number 3,4
with _f=sin20,+
~~(cos~~~,-cos~~,,)
+4q2(sin20,+sin20
yy+cos2e~~+cos2~y~), (8)
where ocup (ar, /3=X, Y, Z) is the angle between the Q and B principal axes in conf’lgurations A and B, respectively. The asymmetry parameter 21is generally very small in hydrogen-bonded crystals. Moreover, the magnitudes of the three angular parts in eq. (8) are comparable to each other, because the Y axis is almost normal to the molecular plane. These facts lead to a simpler equation: zz (1 +naJ2 B(T).
(9)
kK/T
0.1 -
10
20
30
40
50
60
i
D
Fig. 2. Temperature dependence of proton and deuteron T, values for solid benzoic acid 1H (open circles) at 59.5 MHz [ 31 and 1D (filled circles) at 13.8 MHz.
at low temperatures.
differences between the zero-point energies in the transition and ground states have been estimated to be 5.2 kcal mol- ’ for the formic acid (4H) dimer [ 81 and 3.5 kcal mol- ’ for the deuterated formic acid (4D) dimer [ 23 1. If we assume that the potential curve is invariant to deuteration, these values result in an increase of the potential barrier following deuteron substitution by 1.7 kcal mol-‘. This value is in good agreement with the observed increase ( V,” V,“) of 2.1 kcal mol-‘.
3.2. Benzoic acid (I)
3.3. Glutaric acid (a)
The temperature dependence of T? for 1D is shown in fig. 2 together with that of T y for 1H [ 3 J. As is the case for T y, the T f curve shows a gentler slope below the Ty minimum. This means that tunneling still takes place in the deuterated compound. The potential barrier VF was determined from the slope above the Tp minimum using the AL! value obtained from IR studies, and the activation energy E, for the tunneling motion from that below 100 K. These activation parameters for 1D are listed in table 1 together with those for 1H [ 31. From the minimum value of Tf and the quadrupole coupling constant (estimated to be 174 kHz by its dependence on Ro..o for OH...0 hydrogen bonds [ 19]), we obtain ezz= 7.1’. This value seems reasonable by comparison with the values of 12.5 and 14.3” for malonic acid on the basis of single-crystal deuteron NMR [ 20,2 I] and X-ray [22] studies. From ab initio molecular orbital calculations, the
Both T, curves for 2H and 2D shown in fig. 3 are nearly symmetric around the respective T, minima. Hence one might hastily conclude that the spin-lattice relaxation is caused by the classical jumping process with m= 0. With this assumption,
If wz << 1 or OT >> 1, eq. (9) reduces to eq. (5) or ( 6)) respectively. As a parameter representing the degree of tunneling motion, we employ the activation energy E, defined by E,=tl In T,IaP
(j?= 1IRT)
(10)
Table 1 Thermodynamic and activation parameters (in kcal mol- ’ ) for benzoic acid ( I), glutaric acid (2) and pformylbenzoic acid (3)
1H a’ 1D 2H 2D 3H 3D
AH
VO
-%
0.10 * 0.02 b, 0.3140.02 b, 0.80 ” I .40 c’ 0.34 c’ 0.66 c’
1.17+0.02 3.27kO.31 2.33 4.70 0.84 3.61
0.18+0.03 0.66+0.01 0.99kO.13 3.OOkO.37 0.23 f 0.02 0.67kO.06
a) Fromref. [3]. b’ Determined by IR measurements. ‘) Determined from T, minima.
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28 August 1987
It should be noted that hydrogen-bond dynamics also takes place in 2 despite the presence of chains with long hydrogen bonds. It has recently been reported [ 61 that a similar compound, malonic acid (5) (Ro,.,o=2.68 and 2.71 A [22]), exhibits only the classical proton jump between inequivalent potential wells; AH (0.81 f0.13 kcal mol-I) for 5 is very close to that for 2H and V, (1.74 kcal mol-‘) is slightly smaller. Fig. 3. Temperature dependence of proton r, at 90.0 MHz for solid glutaric acid (2H, open circles) and pformylbenzoic acid (3H, open triangles), and of deuteron T, at 13.8 MHz for solid 2D (filled circles) and 3D (tilled triangles).
however, the calculated coefficient of B( z) in eq. (1) is about four times larger than the experimental value. Moreover, the lengths of the CO single and double bonds in 2H are significantly different [ 141, while they should be equal if AH=O. Although the IR experiments could not determine AH values for 2H and 2D, they do suggest notably large values. The finite, rather large, AH value implied by these results yields a theoretical T, curve with a steeper slope in the low-temperature branch as far as the classical jumping process is assumed. The fact that the observed slope in the low-temperature branch is gentler than that predicted by the classical model suggests that the proton (deuteron) spin-lattice relaxation for 2H (2D) on the low-temperature side is affected by tunneling. Using the geometrical parameters (Ro.,,o=2.678 A, r= 2.38 8, and 8 = 38’ ) reported for succinic acid from a neutron diffraction study at 300 K [ 241 and the minimum value of Ty , we obtain a AH’ of 0.80 kcal mol- ’ for 2H. The potential barrier Vf is determined to be 2.33 kcal mol-’ from the slope of the T F curve at high temperatures. Similarly, we can also obtain AH and V, for 2D employing a 8, of 9.9” estimated from the same geometrical parameters the quadrupole coupling constant of 192 kHz obtained from the Ro ..o dependence [ 191 and the minimum value of T 7. The activation parameters obtained are collected in table 1. The increase in V, (2.4 kcal mol-‘) due to deuteron substitution is similar to that for 1 (2.1 kcal mol-‘) and the calculated value for 4 (1.7 kcal mol- ’ ). The activation energies E,H and E,D are considerably larger than for 1. 334
3.4. p-formylbenzoic acid (3) As seen from fig. 3, the slopes of the low-temperature branches of the T, curves for both 3H and 3D are less than those for the corresponding high-temperature branches, indicating the presence of tunneling in both 3H and 3D. AH, V, and E. for 3H and 3D were obtained as for 2H and 2D, and are listed in table 1. The notably small V, value for 3H is considered to be due to the short Ro..o of 2.57 A. The increase in V. (2.8 kcal mol- ’ ) following deuteron substitution is the largest among the three compounds studied, and somewhat larger than the value calculated for 4 (1.7 kcal mol-‘). Both of the activation energies E,H and E,D for tunneling in 3 are similar to the corresponding values for 1.
4. Conclusion
From T, measurements simultaneous proton (deuteron) transfer along the hydrogen (deuterium) bonds was found for the three hydrogen- and deuterium-bonded carboxylic acids: benzoic acid ( 1) , glutaric acid (2) and p-formylbenzoic acid (3). Moreover, preliminary studies in hydrogen-bonded p-toluic, terephthalic and n-capric acids showed that proton or deuteron transfer also takes place in these compounds. Dicarboxylic acids generally have a long R. .o, in which proton disorder in the hydrogen bonds has not been found by X-ray and neutron diffraction. However, we have obtained proof of proton transfer in glutaric, suberic and succinic acids; proton transfer may therefore be a general phenomenon in dicarboxylic acids. The activation parameters for the deuterated compounds are considerably larger than those for the
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corresponding non-deuterated analogues. These results strongly suggest that the T, minima observed in the present carboxylic acids may be ascribed to proton transfer along the hydrogen bonds. Differences in the dynamics and activation parameters among the carboxylic acids with different R. o values can be qualitatively discussed in terms of the geometric isotope effect [ 111 on hydrogen bonding and its theoretical explanation [ 121: When &... >2.64 A, deuteration does not change R o. .o, because tunneling may be neglected in hydrogen bonds at such large distances 1121. Althou~ malonic acid with Ro..,o of 2.68 and 2.7 1 w has indeed been reported to show only classical motion [ 61, we did observe a small tunneling effect in 2 with an R. ..* of 2.69 A. However, the activation energies for tunneling are noticeably larger than those for 1 and 3 so that the tunneling motion in 2 is considered to have no effect on the hydrogen-bond length. When 2.44 < Ro. o ~2.64 A, the difference in quantummechanical behaviour between hydrogen and deuterium causes the isotope effect on bond lengths and therefore on the activation parameters. The differences AI’, (= I’:- I$) in the potential wells between deuterated and non-deuterated compounds are found to be 2.4, 2.1 and 2.8 kcal mol-’ for 2, 1 and 3, respectively. The fact that the AVOvalue for 3 with the short Ro...-, of 2.57 8, is the largest is consistent with the explanation [ 121 for the geometric isotope effect: In such short hydrogen bonds, the two oxygen atoms involved in the hydrogen bond are drawn towards each other by the tunneling motion of the proton; this effect is smaller in deuterated compounds. As a result, RE. .. becomes shorter than Rg,.o, increasing the value of AI’,. In 1 with an intermediate Ro.. o, the activation parameters obtained are like those of 2 at high temperatures and those of 3 at low temperatures. This result may be attributed to changes in the potential curve caused by the temperature dependence of the bond length. In this Letter we have reported a study on the isotope effect and hydrogen-bond length dependence of hydrogen-bond dynamics in some carboxylic acids. Further studies in hydrogen-bonded compounds with a wider range of bond distances, involving the determination of AH, need to be carried out to elucidate the nature of hydrogen-bond dynamics in more detail.
28 August 1987
We thank Mr. T. Ohno of Mitsui Petrochemical Industries Ltd for advice on the preparation of formI crystals of 2. Efficient service by the Data Processing Center at Kyoto University is also acknowledged.
References
[ 1] S. Nagaoka, T. Terao, E Imashiro, A. Saika, N. Hirota and S. Hayashi, Chem. Phys. Letters 80 ( 198 1) 580.
[ 21 B.H. Meier, F. Graf and R.R. Ernst, J. Chem. Phys. 76 (1982) 767.
[ 3 ] S. Nagaoka, T. Terao, F. Imashiro, A. Saika, N. Hirota and S. Hayashi, J. Chem. Phys. 79 (1983) 4694. [4] A. Gough, M.M.I. Haq and J.A.S. Smith, Chem. Phys. Letters 117 (1985) 389. [ 51 S. Benz, U. Haeberlen and J. Tegenfeldt, J. Magn. Reson. 66 (1986) 125. [6] S. Idziak and N. PiSlewski, Chem. Phys. 111 (1987) 439. [ 71 F. Graf, R. Meyer, T.-K. Ha and R.R. Ernst, J. Chem. Phys. 75 (1981) 2914. [ 81 S. Hayashi, J. Umemu~, S. Kate and K. Moro~rn~ J. Phys. Chem. 88 (1984) 1330. [9] S. Nagaoka, N. Hirota, T. Matsushita and K. Nishimoto, Chem. Phys. Letters 92 (1982) 498. [ lo] R. Meyer and R.R. Ernst, J. Chem. Phys. 86 (1987) 784. [ 1 I ] M. Ichikawa, Acta Cryst. I334 (1978) 2074. [ 121 E. Matsushita and T. Matsubara, Progr. Theoret. Phys. 6 (1982) I. [ 131 R. Feld, MS. Lehmann, K.W. Muir and J.C. Speakman, 2. Krist. 157 (1981) 215. [ 141 J.D. Morrison and J.M. Robertson, J. Chem. Sot. (1949) 1001. [ 151 M. Haisa, S. Kashino, F. Ikejiri, T. Ohno and K. Teranishi, Acta Cryst. B32 (1976) 857. [ 161 S. Matsui, T. Terao and A. Saika, J. Chem. Phys. 77 (1982) 1788. [ 171 J.H. Davis, K.R. Jeffrey, M. Bloom, MI. Valic and T.P. Higgs, Chem. Phys. Letters 42 (1976) 390. [ 181 E.R. Andrew and L. Latanowicz, J. Magn. Reson. 68 (1986) 232. f 191 L.G. But1erandT.L. Brown, J. Am. Chem. Sot. 103 (1981) 6541. [ 20) W. Derbyshire, T.C. Gorvin and D. Warner, Mol. Phys. 17 (1969) 401. [ 211 C. Milller, S. Idziak, N. Pislewski and U. Haeberlen, J. Maen. Reson. 47 (1982) 227. [ 221 J.A. Goedkoop and C.H. MacGillavry, Acta Cryst. 10 (1957) 125. [ 231 S. Hayashi, unpublished results. [ 241 J.-L. Leviel, G. Auvert and J.-M. Savariault, Acta Cryst. B37 (1981) 2185.
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Volume 139, number 3,4
28 August 1987
A STUDY OF HYDROGEN-BOND DYNAMICS IN CARBOXYLIC ACIDS BY NMR T, ME~U~ME~~ ISOTOPE EFFECTS AND H~ROGEN-BOND LENGTH DEPENDENCE * T. AGAKI ‘, F. IMASHIRO, T. TERAO, N. HIROTA Department of Chemistry, Faculty ofscience, Kyoto Vniversrty, Kyoto 606, Japan
and S. HAYASHI Institutefor Chemical Research, Kyoto University, Uji 611, Japan
Received 8 June 1987
Proton (deuteron) transfer ofhydrogen bonds in benzoic, glutark and pformylbenzoic acids was studied by proton (deuteron) T, measurements. Deuteration of carboxylic protons was found to increase the barriers to classical proton jumping as well as quantum-mechanical tunneling. The former barriers increase as the hydrogen-bond distance increases.
NMR spectroscopy has shown that the two carboxylic protons in some carboxylic acid dimers undergo a simultaneous classical proton jump and quantum-mechanical tunneling along the hydrogen bonds [l-6]. The simultaneous proton transfer interconverts two different configurations A and B. Qo--HO, R-C ~O”__O~
,OH--0% C-R
=
R-C *0_+0
A B Whereas the two configurations are energetically degenerate in the free dimers, the degeneracy is generally removed in the solid state by distortion of the double-minimum intermolecular potential due to intermolecular interactions, producing a small enthalpy difference ALI between con~gurations A and B, as shown in fig. 1. The dynamics in this interesting system are studied mainly by proton T, meas-
* A part of this work was presented in the 22nd Ampere Congress, Zurich (1984). ’ Present address: Central Research Laboratory, Ishiham Sangyo Kaisha Ltd., Kusatsu, Shiga 525, Japan.
A
C-R
B
Fig. 1. Potential curve for proton (deuteron) transfer in hydrogen-bonded carboxytic acids.
urements and the results have stimulated theoretical attempts to reproduce the unusually low potential wells obtained [ 7-101 and the quantum-mechanical behaviour [ lo]. In this work, we investigate proton (deuteron) transfer in carboxylic acids and their deuterated compounds by proton (deuteron) T, measurements. Deuteration changes the O...O hydrogen-bond distance Ro. .. and hence the potential curve, particularly in the Ro...o range from 2.44 to 2.63 A [ 111, This is related to the difference in the proton and deuteron motions in this range [ 121. Accordingly,
0 009-2614/87/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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we selected three different carboxylic acids with different Ro...o values: benzoic acid (1) ( Ro.,.o = 2.63 A [ 13]), glutaric acid (2) (2.69 A [ 141) and p-formylbenzoic acid (3) (2.57 8, [ IS]). (Hereafter, if necessary, we add “‘D” or “H” to the compound numbers and parameters to represent the deuterated or non-deuterated carboxylic acid, respectively.)
28 August 1987
protons on the hydrogen bonds in a dimer govern the relaxation, the equation for polycrystalline samples can be rewritten as 1 -=
-5$y4fr’r-” sin28 -(1 +aa)2 B(r)*
TF
(1)
with a=exp(AH/RT),
2. Experimental
B(7)= Commercially available 2H was recrystallized from ethanol. Form-I crystals of 3H were obtained according to the method described in ref. [ 151, and the content confirmed to be more than 80% by IR spectroscopy. Compounds 1D and 3D were prepared by hydrolysis of the corresponding acid anhydrides with equimolar D20 in sealed glass tubes. Form-I crystals of 3D were obtained in the same manner as those of 3H. In order to obtain 2D, 2H was dissolved in D20-EtOD under NZ, and then the solvent was evaporated under reduced pressure; this procedure was repeated three times. Proton and deuteron T, values were measured on a home-built spectrometer operating at 90.0 MHz for ‘H and at 13.8 MHz for ‘H. Sample temperatures were controlled by the N2 gas flow method above 77 K and by the reduced-pressure He gas flow method below 77 K [ 161. Deuteron T, values were determined by plotting the average heights of multiple solid echoes [ 171 against repetition times. IR spectra were taken with a Nicolet 6000 FT IR spectrometer in order to obtain the enthalpy difference AH. For lD, AH could be determined by the same procedure as was used for 1H [ 31. However, bsI for 2 and 3 could not be determined because the absorption bands attributed to different configurations were not well resolved.
3. Results and discussion 3. I. Temperature dependence of T The general equation for the proton relaxation time Tr by a classical jumping process between unequally populated configurations A and B has been derived previously [ 3,181. If only the two carboxylic 332
(2)
4? l+;272+ 1+4w272'
(3)
where N is the number of protons in a dimer, r is the distance between the two carboxylic protons, 8 is the flip ar@e of the proton-pair orientation following a proton jump and o is the Larmor frequency. The correlation time 7 can be expressed as exp( K,/RT)I(l+a),
7=t0
(4)
where r. is a constant. If or < 1 (at high temperatures) or wr * 1 (at low temperatures), eq. ( 1) may be reduced to
TY
mm=-
(vo+M)
RT
+const.
(w7c
1)
(5) or
Tz: = (Kl-Aff> ln(l+a) RT
+const.
(wz~l).
(6)
Hence the T, curve due to the classical jumping process is steeper in the low-temperature branch unless LW=O. The deuteron relaxation is caused mainly by the jump-induced fluctuation of the electric field gradient (EFG) at the deuteron site. In order to obtain an equation for T’p #I we use a similar procedure to that for Tj” [ 31, and assume that the quadrupole coupling constant e2qQlh and the asymmetry parameter r are invariant to the deuteron jump. In this event TP for polycrystalline samples is given by (7) #’ An equation for TP has already been obtained by two groups [ 5,101,Our result is consistent with that of Benz et al. [ 51. The equation obtained by Meyer and Ernst [ IO] differs from ours by a factor of 8121.
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Volume 139, number 3,4
with _f=sin20,+
~~(cos~~~,-cos~~,,)
+4q2(sin20,+sin20
yy+cos2e~~+cos2~y~), (8)
where ocup (ar, /3=X, Y, Z) is the angle between the Q and B principal axes in conf’lgurations A and B, respectively. The asymmetry parameter 21is generally very small in hydrogen-bonded crystals. Moreover, the magnitudes of the three angular parts in eq. (8) are comparable to each other, because the Y axis is almost normal to the molecular plane. These facts lead to a simpler equation: zz (1 +naJ2 B(T).
(9)
kK/T
0.1 -
10
20
30
40
50
60
i
D
Fig. 2. Temperature dependence of proton and deuteron T, values for solid benzoic acid 1H (open circles) at 59.5 MHz [ 31 and 1D (filled circles) at 13.8 MHz.
at low temperatures.
differences between the zero-point energies in the transition and ground states have been estimated to be 5.2 kcal mol- ’ for the formic acid (4H) dimer [ 81 and 3.5 kcal mol- ’ for the deuterated formic acid (4D) dimer [ 23 1. If we assume that the potential curve is invariant to deuteration, these values result in an increase of the potential barrier following deuteron substitution by 1.7 kcal mol-‘. This value is in good agreement with the observed increase ( V,” V,“) of 2.1 kcal mol-‘.
3.2. Benzoic acid (I)
3.3. Glutaric acid (a)
The temperature dependence of T? for 1D is shown in fig. 2 together with that of T y for 1H [ 3 J. As is the case for T y, the T f curve shows a gentler slope below the Ty minimum. This means that tunneling still takes place in the deuterated compound. The potential barrier VF was determined from the slope above the Tp minimum using the AL! value obtained from IR studies, and the activation energy E, for the tunneling motion from that below 100 K. These activation parameters for 1D are listed in table 1 together with those for 1H [ 31. From the minimum value of Tf and the quadrupole coupling constant (estimated to be 174 kHz by its dependence on Ro..o for OH...0 hydrogen bonds [ 19]), we obtain ezz= 7.1’. This value seems reasonable by comparison with the values of 12.5 and 14.3” for malonic acid on the basis of single-crystal deuteron NMR [ 20,2 I] and X-ray [22] studies. From ab initio molecular orbital calculations, the
Both T, curves for 2H and 2D shown in fig. 3 are nearly symmetric around the respective T, minima. Hence one might hastily conclude that the spin-lattice relaxation is caused by the classical jumping process with m= 0. With this assumption,
If wz << 1 or OT >> 1, eq. (9) reduces to eq. (5) or ( 6)) respectively. As a parameter representing the degree of tunneling motion, we employ the activation energy E, defined by E,=tl In T,IaP
(j?= 1IRT)
(10)
Table 1 Thermodynamic and activation parameters (in kcal mol- ’ ) for benzoic acid ( I), glutaric acid (2) and pformylbenzoic acid (3)
1H a’ 1D 2H 2D 3H 3D
AH
VO
-%
0.10 * 0.02 b, 0.3140.02 b, 0.80 ” I .40 c’ 0.34 c’ 0.66 c’
1.17+0.02 3.27kO.31 2.33 4.70 0.84 3.61
0.18+0.03 0.66+0.01 0.99kO.13 3.OOkO.37 0.23 f 0.02 0.67kO.06
a) Fromref. [3]. b’ Determined by IR measurements. ‘) Determined from T, minima.
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It should be noted that hydrogen-bond dynamics also takes place in 2 despite the presence of chains with long hydrogen bonds. It has recently been reported [ 61 that a similar compound, malonic acid (5) (Ro,.,o=2.68 and 2.71 A [22]), exhibits only the classical proton jump between inequivalent potential wells; AH (0.81 f0.13 kcal mol-I) for 5 is very close to that for 2H and V, (1.74 kcal mol-‘) is slightly smaller. Fig. 3. Temperature dependence of proton r, at 90.0 MHz for solid glutaric acid (2H, open circles) and pformylbenzoic acid (3H, open triangles), and of deuteron T, at 13.8 MHz for solid 2D (filled circles) and 3D (tilled triangles).
however, the calculated coefficient of B( z) in eq. (1) is about four times larger than the experimental value. Moreover, the lengths of the CO single and double bonds in 2H are significantly different [ 141, while they should be equal if AH=O. Although the IR experiments could not determine AH values for 2H and 2D, they do suggest notably large values. The finite, rather large, AH value implied by these results yields a theoretical T, curve with a steeper slope in the low-temperature branch as far as the classical jumping process is assumed. The fact that the observed slope in the low-temperature branch is gentler than that predicted by the classical model suggests that the proton (deuteron) spin-lattice relaxation for 2H (2D) on the low-temperature side is affected by tunneling. Using the geometrical parameters (Ro.,,o=2.678 A, r= 2.38 8, and 8 = 38’ ) reported for succinic acid from a neutron diffraction study at 300 K [ 241 and the minimum value of Ty , we obtain a AH’ of 0.80 kcal mol- ’ for 2H. The potential barrier Vf is determined to be 2.33 kcal mol-’ from the slope of the T F curve at high temperatures. Similarly, we can also obtain AH and V, for 2D employing a 8, of 9.9” estimated from the same geometrical parameters the quadrupole coupling constant of 192 kHz obtained from the Ro ..o dependence [ 191 and the minimum value of T 7. The activation parameters obtained are collected in table 1. The increase in V, (2.4 kcal mol-‘) due to deuteron substitution is similar to that for 1 (2.1 kcal mol-‘) and the calculated value for 4 (1.7 kcal mol- ’ ). The activation energies E,H and E,D are considerably larger than for 1. 334
3.4. p-formylbenzoic acid (3) As seen from fig. 3, the slopes of the low-temperature branches of the T, curves for both 3H and 3D are less than those for the corresponding high-temperature branches, indicating the presence of tunneling in both 3H and 3D. AH, V, and E. for 3H and 3D were obtained as for 2H and 2D, and are listed in table 1. The notably small V, value for 3H is considered to be due to the short Ro..o of 2.57 A. The increase in V. (2.8 kcal mol- ’ ) following deuteron substitution is the largest among the three compounds studied, and somewhat larger than the value calculated for 4 (1.7 kcal mol-‘). Both of the activation energies E,H and E,D for tunneling in 3 are similar to the corresponding values for 1.
4. Conclusion
From T, measurements simultaneous proton (deuteron) transfer along the hydrogen (deuterium) bonds was found for the three hydrogen- and deuterium-bonded carboxylic acids: benzoic acid ( 1) , glutaric acid (2) and p-formylbenzoic acid (3). Moreover, preliminary studies in hydrogen-bonded p-toluic, terephthalic and n-capric acids showed that proton or deuteron transfer also takes place in these compounds. Dicarboxylic acids generally have a long R. .o, in which proton disorder in the hydrogen bonds has not been found by X-ray and neutron diffraction. However, we have obtained proof of proton transfer in glutaric, suberic and succinic acids; proton transfer may therefore be a general phenomenon in dicarboxylic acids. The activation parameters for the deuterated compounds are considerably larger than those for the
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CHEMICAL PHYSICS LETTERS
corresponding non-deuterated analogues. These results strongly suggest that the T, minima observed in the present carboxylic acids may be ascribed to proton transfer along the hydrogen bonds. Differences in the dynamics and activation parameters among the carboxylic acids with different R. o values can be qualitatively discussed in terms of the geometric isotope effect [ 111 on hydrogen bonding and its theoretical explanation [ 121: When &... >2.64 A, deuteration does not change R o. .o, because tunneling may be neglected in hydrogen bonds at such large distances 1121. Althou~ malonic acid with Ro..,o of 2.68 and 2.7 1 w has indeed been reported to show only classical motion [ 61, we did observe a small tunneling effect in 2 with an R. ..* of 2.69 A. However, the activation energies for tunneling are noticeably larger than those for 1 and 3 so that the tunneling motion in 2 is considered to have no effect on the hydrogen-bond length. When 2.44 < Ro. o ~2.64 A, the difference in quantummechanical behaviour between hydrogen and deuterium causes the isotope effect on bond lengths and therefore on the activation parameters. The differences AI’, (= I’:- I$) in the potential wells between deuterated and non-deuterated compounds are found to be 2.4, 2.1 and 2.8 kcal mol-’ for 2, 1 and 3, respectively. The fact that the AVOvalue for 3 with the short Ro...-, of 2.57 8, is the largest is consistent with the explanation [ 121 for the geometric isotope effect: In such short hydrogen bonds, the two oxygen atoms involved in the hydrogen bond are drawn towards each other by the tunneling motion of the proton; this effect is smaller in deuterated compounds. As a result, RE. .. becomes shorter than Rg,.o, increasing the value of AI’,. In 1 with an intermediate Ro.. o, the activation parameters obtained are like those of 2 at high temperatures and those of 3 at low temperatures. This result may be attributed to changes in the potential curve caused by the temperature dependence of the bond length. In this Letter we have reported a study on the isotope effect and hydrogen-bond length dependence of hydrogen-bond dynamics in some carboxylic acids. Further studies in hydrogen-bonded compounds with a wider range of bond distances, involving the determination of AH, need to be carried out to elucidate the nature of hydrogen-bond dynamics in more detail.
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We thank Mr. T. Ohno of Mitsui Petrochemical Industries Ltd for advice on the preparation of formI crystals of 2. Efficient service by the Data Processing Center at Kyoto University is also acknowledged.
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