3510
J. Phys. Chem. 1983,87,3510-3514
Carbon-13 Spin-Lattice Relaxation and Methyl Rotation Barrier in Sodium Acetate Masato Kaklhana, Masahlro Kotaka, and Makoto Okamoto' Research laboratory for Nuclear Reactors, Tokyo Institute of Technology, 2- 12- 1 ookayama, Meguro-ku, Tokyo 162, Japan (Received:July 27, 1982; I n Final Form: March 23, 1983)
The carbon-13 spin-lattice relaxation times were measured by use of the inversion-recovery pulse sequence [180°-t-900] for the methyl and carboxylate carbons of 1-,2-, and 1,2-13C-labeledsodium acetates in deuterium oxide at several temperatures. The relaxation of the two carboxylate carbons was found to follow single-exponential behavior with different recovery rates. The more rapid ~arboxylate-'~C relaxation in the doubly labeled species was attributed to the simple additional 13C-13C dipolar interaction, on the basis of which the effective correlation time for the rotation about the C-C axis, Teff(CC), was calculated. In the case of the methyl group, the pure 13C-lH dipolar relaxation rate was determined with a combination of the observated relaxation rate and the proton nuclear Overhauser enhancement factor for the methyl carbon, and the effective correlation time for the rotation about the C-H axis, Teff(CH), was evaluated. The overall and methyl internal rotational diffusion constants, D and Dht,were deduced from the values of T ~ ~ ( ( c cand ) T e f f ( c ~ on ) the basis of the stochastic diffusion model. The temperature dependence of D and Dht was found to follow Arrhenius-type behavior with mean activation energies of 24 and 9.8 kJ mol-', respectively. The latter one can be related to the threefold V3 barrier for the methyl internal rotation, and finally the torsional vibrational frequency for the methyl group was estimated to be 204 cm-'.
Introduction Hindered internal rotation of methyl groups has been widely investigated by a variety of techniques. The measurements of 13Cspin-lattice relaxation times (TI)give a convenient means of studying such internal motion. A mathematical model for internal rotation imposed on overall molecular motion was given by Woessner and coworker~.'-~According to Woessner's theory, separation of the two types of motions (the internal rotation of methyl group and the overall molecular tumbling) from 13C-relaxation data has been performed and internal rotational barriers for methyl groups have been estimated for several molecular system^.^-'^ In order to extract pure information about the internal rotation from relaxation data of methyl-13C,it is necessary to measure relaxation times for appropriate nuclei in a moiety without internal rotation, which provide information about the overall molecular motion. For this purpose, T1 of 13C in a rigid 13CHzor 13CH moiety is preferably measured, because the relaxation rate (Trl)of protonated carbon is often dominated by the intramolecular dipoledipole (l3C-IH) interaction whose magnitude is easily estimated; thus the relaxation rate due to the dipolar interaction is directly related to the motion of the internuclear vector, i.e., the carbon-hydrogen bond. Even in a case where other mechanisms contribute to the relaxation rate, the dipolar contribution can be determined by measuring the proton nuclear Overhauser enhancement (NOE) for the carbon.'l (1) Woessner, D. E. J. Chem. Phys. 1962,36,1. (2) Woessner, D. E. J. Chem. Phys. 1962,37,647. (3)Woessner, D. E.;Snowden, B. S.,Jr.; Meyer, G. H. J. Chem. Phys. 1969,50,719. (4)Kuhlmann, K. F.;Grant, D. M. J. Chem. Phys. 1971,55, 2998. (5)Lyerla, J. R.,Jr.; Grant, D. M. J. Phys. Chem. 1972, 76, 3213. (6)Collins, S.W.; Alger, T. D.; Grant, D. M.; KuhImann, K. F.; Smith, J. C. J.Phys. Chem. 1975, 79,2031. (7)Ladner, K. H.; Dalling, D. K.; Grant, D. M. J.Phys. Chem. 1976, 80, 1783. (8)Axelson, D. E.;Holloway, C. E. Can. J. Chem. 1976, 54, 2820. (9)Platzer, N.Org. Magn. Reson. 1978,11, 350. (10)Ericsson, A.; Kowalewski, J.; Liljefors, T.; Stilbs, P. J. Magn. Reson. 1980,38,9.
On the other hand, for a nonprotonated carbon, several nondipolar mechanisms (e.g., spin rotation, chemical shift anisotropy interactions, etc.) must also contribute simultaneously to the relaxation rate, the separation of these mechanisms being quite difficult. The present molecule is just the case and Tl of I3C in the carboxylate group (-COO-) might give less information about the molecular motion. However, this difficulty in the present molecular system may be overcome by considering the relaxation due to the 13C-13C dipolar interaction. Moreland and CarrolllZhave measured 13Cspin-lattice relaxation times for diethyl malonate-l-13C and -1,2-13C2 and found that the dipole-dipole (13C-13C)mechanism contributed significantly to the relaxation rate of the carbonyl carbon in the doubly labeled compound. Similar relaxation measurements were made on acetate -1,2J3C2 by Suzuki et al.13 London et al.14first pointed out that the carbon-13 relaxation in multiple l3C-1abeledspecies containing nonprotonated carbons served as an excellent probe of studying internal motion and/or anisotropic rotation of the molecule; they have treated the AM(X,J spin system in which A represents the nonprotonated carbon, M the adjacent protonated carbon, and X the decoupled protons. Recently, separation of the pure dipole-dipole (13C-13C) interaction part from the overall relaxation rate was successfully made on several molecules involving carbonyl carbons by comparing the relaxation behavior of the I3C13Cmultiplet lines with that of the 12C-13Csinglet line in the same molecule.15J6 Useful dynamic information can be provided from the 13C-13C dipolar interactions, the rotational correlation time of the carbon-carbon bond, T ~ being estimated if the bond length between the two carbons is known. In all of the multiple 13C-labelingstudies (11)Kuhlmann, K. F.;Grant, D. M.; Harris, R. K. J. Chem. Phys. 1970,52, 3439.
(12) Moreland, C. G.; Carroll, F. I. J. Magn. Reson. 1974, 15, 596. (13)Suzuki, K. T.;Cary, L.W.; Kuhlmann, K. F. J. Magn. Reson.
1975,18, 390. (14)London, R. E.;Matwiyoff, A. J. Chem. Phys. 1975, 63,4442. (15)Nery, H.; Canet, D. J. Magn. Reson. 1981,42, 370. (16)London, R. E.;Phillipi, M.; Stewart, J. Biochemistry 1982,21, 470.
0022-365418312087-351 OQQl.50I0 0 1983 American Chemical Society
~
,
The Journal of Physical Chemistry, Vol. 87, No. 18, 1983 3511
Methyl Rotation Barrier in Sodium Acetate
published to date, the rotational correlation times (TCC) were found to be significantly longer than the rotational correlation times (7CH) estimated in the usual method on the basis of the protonated carbons' relaxation data analysis. The discrepancy between the 7cc and 7CH values may be understood by considering the internal motion and/or anisotropic rotation of the molecule as pointed out by London et al.16 A variable-temperature relaxation measurement provides a useful means of studying such motions because of their different sensitivity to the temperature. Furthermore, the anisotropic motion of the molecule affects both 7cc and 7CH values, whereas the internal rotation around the C-C bond does not affect the 13C-13C dipolar interaction. Consequently, information about the overall molecular tumbling can be obtained from the rotational correlation time (7cc) deduced on the basis of the 13C-13C dipolar interaction, and additional information about the anisotropic rotation of the molecule may be obtained if the temperature dependence of 7cc is examined. In the present study, first we have measured spin-lattice relaxation times of 13C in the carboxylate groups for sodium acetate-l-13C and -12J3C2 in deuterium oxide over the temperature range between 273.7 and 303.0 K in order to obtain the pure dipole-dipole (13C-13C) interaction parts of the relaxation rates. The effective correlation time, 7eff(cc),which characterizes the overall molecular motion, is deduced on the basis of the 13C-13C interaction, and the temperature dependence of is reported. Second, spin-lattice relaxation times and proton NOE factors for the carbon in the methyl moiety have been measured in order to extract the pure dipolar interaction ('V-lH) parts from the relaxation rates. We analyzed the two sets of dipolar relaxation data (regarding 13C-13C and 13C-lH interactions) on the basis of the stochastic diffusion model" in which the overall and internal molecular motions are characterized by the rotational diffusion constant, D, and the internal rotational diffusion constant, Dht, respectively. Finally, the activation energy for the methyl internal rotation in sodium acetate is given based on the temperature dependence of Dint.
Experimental Section Carbon-13-enriched modifications of sodium acetates (12CH313COONa(lJ3C), 13CH312COONa(2-13C), and 13CH313COONa(l,2-13C))were purchased from the Prochem Co. Ltd. in London with 90% 13C-isotopicpurity. Deuterium oxide (2HzO)with enrichment of 99.7% in deuterium was obtained from Merck Sharp and Dohme Canada Ltd. and was twice distilled from an all-glass apparatus before use. The solution of the 2J3C-labeled species was prepared to 0.5 mol dm-3 in 2Hz0. Equimolar amounts of the 1-and 1,2-13C-labeledmodifications were mixed and then the solution of 0.5 mol dm-3 was prepared in 2H20,this making it possible to determine the relaxation times of 13C in the carboxylate moieties simultaneously. This becomes particularly important in the case of a solution containing a small amount of paramagnetic impurities (such as heavy metal ions and oxygen, with unpaired electrons); the contribution of the electron-13Cnuclear interactions to the relaxation rates for the two carboxylate carbons should be of the same order. The solution was filled in a 10-mm (outer-diameter) sample tube with a false bottom (Shigemi Standard Joint Co. Ltd. MB-004B), the sample chamber being divided by an inner glass cap with a hole. The filling height of the sample solution was 10 mm. Argon gas was passed through the (17)Bloembergen, N. Phys. Reu. 1956,104, 1542.
li
, i n
Flgure 1. (a) Carboxylate carbon-13 spin-lattice relaxation spectra for a solution of 0.5 mol dm-3 containing equimolar amounts of 1(center line) and 1,2- (doublet lines) '3C-labeled sodium acetates at 282.6 K obtained by using the fast inversion-recovery pulse sequence [T-180°-t-900-S(t)], with m = 4 accumulationsand T = 90 s. The delay time tis indicated below each spectrum. The first free induction decay was excluded. (b) The corresponding line intensity S(t)-delay time t plots, the solid lines lndicatlng fitted single-exponential curves, S In arbltrary units.
sample solution under an atmosphere of argon in order to remove the dissolved oxygen. The NMR measurements were performed on a Varian XL-200 FT-NMR spectrometer operating at a 13C resonance frequency of 50.3 MHz using deuterium internal lock. Tl for the methyl carbon was measured by using the conventional inversion-recovery methodleJg (180°-t-900 pulse sequence) with a repetition time longer than 5T1 and the fast inversion-recovery methodz0 was used for the determination of T1 for the carboxylate carbons with a repetition time longer than l.OTl, the broad band decoupling being employed for both Tl measurements. The line intensities were fitted to a single-exponential curve through a three-parameter nonlinear least-squares procedurez1(the standard Varian disk system software). The proton NOE factor for the methyl carbon was determined by a comparison of the decoupled spectrum with the gated decoupled spectrum2zwith a pulse delay longer than 10T, in accordance with the suggestion of Opella et al.,23 and Harris et al.25
Results and Discussion Analysis of the Spin-Lattice Relaxation Times for the Carboxylate Carbons. Figure l a represents a typical example of carboxylate carbon-13 spin-lattice relaxation spectra measured at different delay times for an equimolar mixture of sodium acetate-I-l3C and -I,2J3C2in deuterium oxide at 282.6 K, where the center lines correspond to the resonances for the singly labeled one and the multiplet lines to those for the doubly labeled one. The corresponding line intensity (S)-delay time (t) plots are given in Figure Ib, where the experimental data were fitted to (18)Vold, R. L.; Waugh, J. S.; Klein, M. P.; Phelps, D. E. J. Chem. Phys. 1968,423,3831. (19)Freeman, R.;Hill, H. D. W.; Kaptein, R. J. Mugn. Reson. 1972, 7 .. , 82. (20)Canet, D.;Levy, G. C.; Peat, I. R. J. Mugn. Reson. 1975,18,199. (21)Kowalewaki, J.;Levy, G. C.; Johnson, L. F.; Palmer, L. J.Mugn. Reson. 1977,26,533. (22)Freeman, R.;Hill, H. D. W.; Kaptein, R. J. Mugn.Reson. 1972, I
nnn
I , JLI.
(23)Opella, S. J.; Nelson, D. J.; Jardetzky, 0. J. Chem. Phys. 1976, 64, 2533.
(24)Canet, D.J. Magn. Reson. 1976,23, 361. (25)Harris, R. K.; Newman, R. H. J. Mugn. Reson. 1976,24, 449.
3512
Kakihana et ai.
The Journal of Physical Chemistry, Vol. 87, No. 18, 1983
a three-parameter single-exponential equation indicated at the solid line; this fitting procedure was preferably used to e l i i a t e the systematic errors caused by inhomogeneity of the radio frequency field (H,) and imperfect choice of the parameters in measuremenkZ1 The single exponentiality of the recovery of the longitudinal magnetization was quite excellent over a wide range of delay times as shown in Figure lb. Such an excellent fit to a single-exponential curve strongly indicates that any cross-correlation terms can be neglected to a reasonable degree of accuracy. Cross-relaxations between the two 13C’s due to their dipolar interaction and between the 13C-13C dipolar and the chemical shift anisotropy interaction, which might render the recovery of the longitudinal magnetization after a perturbation no longer to follow a single-exponential curve, may contribute, in principle, to the relaxation rate of the carboxylate carbon in the doubly labeled compound. Theoretical aspects of intramolecular dipolar relaxation in coupled spin systems have been surveyed by Werbelow et al.= and Vold et al.,= and longitudinal nuclear magnetic relaxation for a 13C-13C-’H fragment (ABX spin system) including cross-correlation effects has been investigated theoretically by Canet et al.28 On the other hand, a chemical shift anisotropy mechanism, which becomes the more important relaxation mechanism at higher magnetic fields, may contribute to the relaxation rate of the carboxylate carbon. When the chemical shift anisotropy rate and the 13C-13C dipolar relaxation rate are comparable, the cross-correlation effects between the 13C-13C dipolar and the shift anisotropy terms may be observed.29 Such an effect has been found for the relaxation of the carboxyl carbon in doubly 13C-labeledglycine; l5the relaxation behavior of the doublet resonances indicated a significant deviation from a single exponentiality, whereas the relaxation of the singlet line for which there is no 13C-13C dipolar interaction was found to be exponential. In the present molecule, the cross-correlation effects due to the 13C-13C dipolar and the chemical shift anisotropy interactions can be ignored to a very good approximation, because single-exponential recoveries of carbon-13 magnetization were almost completely obtained even at long delay times as shown by the example presented in Figure 1. This observation suggests that the chemical shift anisotropy of the carboxylate carbon in acetate ion molecule gives a relatively minor component as a posaible relaxation mechanism. It is worth noting that in the case of acetic acid the chemical shift anisotropy mechanism was found to contribute significantly to the relaxation rate of the carboxyl carbon.30 In view of the above-mentioned argument, the more rapid relaxation of the 13C-13C doublet resonances, as clearly indicated in Figure 1, can be attributed to the simple additional dipole-dipole (13C-13C) interaction, and therefore the relaxation rate due to the 13C-13C dipolar interaction may be separated on the basis of the difference between the two relaxation curves: 1
T, (13C-13C)
-
1
T1(1,2-C0)
-
1
Tl(1-CO)
(1)
(26) Werbelow, L. G.; Grant, D. M. In “Advances in Magnetic Resonance”; Waugh, J. S.; Ed.; Academic Press: New York, 1977; Vol. 9, p 189. (27) Vold, R. L.;Vold, R. R. In “Progress in NMR Spectroscopy”; Emsley, J. W., Feeney, J., Sutcliffe, L. H., Eds.; Pergamon Press: Oxford, 1978; Vol. 12, p 79. (28) Canet, D.;Nery, H.; Brondeau, J. J.Chem. Phys. 1979,70,2098. (29) Shimizu, H.J. Chem. ,Phys. 1964,40, 3357. (30)Farrar, T. C.; Becker, E. D. ’Pulse and Fourier Transform NMR”; Academic Press: New York, 1971; Chapter 4.
TABLE I: Carboxylate-13CSpin-Lattice Relaxation Times for 0.5 mol dm-) Solution of Singly (l-13C)and Doubly (l,2-I3C)Labeled Sodium Acetates in ZH,O T,TI(l-CO)/S ( 1 , 2 - C 0 ) / ~ T , ( 1 3 C - ’ 3 C ) / ~
s/K 273.7
18.0 79.8
65.3 66.7
282.6
95.0 94.2
80.8 80.9
287.8
103
89.3 87.4
101 293.0 303.0
106 112 115
93.2
102 104
401 406 av = 404 54 1 573 a v = 577 671 649 av = 660 772 1140
1090 av = 1120
24.6
24.4
-
r
I VI N
‘0
9
24.2
-cc
\
i
24.0
23.8
I
I
3.3
3.4
I
I
3.5
3.6
\ I
l o 3 B-l/K-‘
Figure 2. Temperature dependence of isotropic rotational diffusion constant obtained from rsC-13Cdipolar relaxation for 0.5 mol dm-3 sodium acetate in 2H,0.
where Tl(1430)represents the observed spin-lattice relaxation time for the carboxylate carbon in acetate-1-13C and Tl(1 , 2 4 0 ) corresponds to that in acetate-1,2J3C2. The observed T1 values for the carboxylate carbons in the 1- and 1,2-13C-labeledsodium acetates are shown in Table I. The value of Tl for the doubly labeled species was clearly shorter than that for the singly labeled modification at each temperature; the pure dipolar relaxation times T1(13C-13C),were calculated by use of eq 1 and are shown in Table I. The intramolecular dipolar relaxation time is related to an effective correlation time for molecular reorientation, reff(CC), under an extremely narrowing condition through the following equation: 31 1
The Journal of Physical Chemistty, Vol. 87,
Methyl Rotation Barrier in Sodium Acetate
TABLE I11 : Methyl. 13CSpin-Lattice Relaxation Times and Nuclear Overhauser Enhancement Factors (q ) for 0.5 mol dm-3 Solution of Sodium Acetate-2-l3Cin 'H,O'
TABLE 11: Effective Correlation Times (reff(CC)) and Isotropic Rotational Diffusion Constants (D) for Acetate Dipolar Relaxation, Ion in ZH,OObtained from 13C-13C and Activation Energy ( A E , ) for Overall Molecular Reorientation
273.7 282.6 287.8 293.0 303.0 a
8.42 6.11 5.15 4.39 3.04
no. of runs
1.98 2.73 3.23 3.79 5.49 AE,/(kJ mol-') = 24 i 2'
where po is the permeability of a vacuum, h is Planck's constant, yc is the magnetogyric ratio for 13C,and rcc is the distance between the two carbons. The effective correlation time for the overall molecular reorientation was evaluated at each temperature by use of eq 2 in which the value of 0.1505 nm32was substituted for rcc. The values of 7eff(cc)are listed in Table 11. Since the Arrhenius plot of 7efftcC)gave a straight line (cf. Figure 2, discussed later), additional information about the anisotropic rotation of the molecule could not be obtained from our experimental data. In the present data analysis, the molecular motion is therefore assumed to be isotropic. When the molecular reorientation is described as a small-step angular diffusion process (the stochastic diffusion model") and the motion of the molecule is isotropic, the effective correlation time is simply related to an isotropic rotational diffusion constant,33D, which characterizes the overall molecular motion:
T, NOE 5 5
282.6 287.8 293.0 303.0
3 3 3 4
7 5 3
11 The estimated
T,(Me)/s 8.60 i 0.35 10.3 t 0.4 11.7 i 0 . 3 12.6 t 0 . 1 14.6 i 0 . 3 uncertainty is
T1-
( 13C-'H)/s
71
1.44
t
0.06
11.9 r 0.9
1.32 i 1.30 i 1.24 i 1.07 i
0.06 0.04 0.09 0.06
15.5 i 17.9 f 20.2 i 27.1 i
1.3 1.0 1.6 2.1
95% confidence limit.
TABLE IV: Effective Correlation Times (Tefff(CH) and Methyl Internal Rotational Diffusion Constants for Acetate Ion in ,H,OObtained from "C-lH Dipolar Relaxation, and Activation Energy ( AE,(int)) for Internal Rotational Process of Methyl Group
(hint)
273.7 282.6 287.8 293.0 303.0 a
13.5 10.3 8.95 7.93 5.91
9.94 11.3 12.4 12.9 15.1 AE,(i,t)/kJ mol-' = 9 . 8 t 1.3'
The estimated uncertainty is 95% confidence limit.
relaxation rate into the dipole-dipole (13C-lH) part, 1/ Tl(l3C-lH), and the others, l/Tl(0), can be accomplished in accordance with the treatment of Kuhlmann et al.: l1
(3)
The values of D estimated by using eq 3 are shown in Table 11. The molecular reorientation in question can be treated as a rate process in analogy with the treatment for the reorientational process of dielectric dipoles in an electric field.34 Figure 2 represents the temperature dependence of D. The data were fitted to a common two-parameter Arrhenius-type equation:
D = A exp(-AE,/RB)
e/K 273.7
a
The estimated uncertainty is 95% confidence limit.
7eff(cc)= 1/6D
No. 18, 1983 3513
(4)
where A and AE, are adjustable parameters, R is the gas constant, and B is temperature. The apparent activation energy for the reorientational process, AE,, was 24 f 2 kJ mol-'. Analysis of the Spin-Lattice Relaxation Times for the Methyl Carbon. In the relaxation data analysis for the methyl carbon, we assumed cross-correlation effects, which might give nonexponential relaxation, to be negligible; the recovery curves were exponential. As discussed by Werbelow et al.,= this assumption is acceptable to a reasonable degree of accuracy for the methyl carbon (unless the methyl group is extremely fast in comparison with the overall molecular rotation36). The observed relaxation times of 13C in the methyl moiety, T1(Me), and the proton NOE factors for the carbon, 11, are listed in Table 111. Separation of the overall (31) Abragam, A. "The Principles of Nuclear Magnetism"; Oxford University Press: London, 1961; Chapter 8. (32) Kwei, K.T.;Ward, D. L. Acta Crystallogr.,Sect. B 1977,33,522. (33) Hubbard, P.S. Phys. Reu. 1963, 131, 1155. (34) Glasstone, S.; Laidler, K. J.; Eyring, H. "The Theory of Rate Process"; McGraw-Hill: New York, 1941; Chapter 9. (35) Werbelow, L. G.; Grant, D. M. J. Chem. Phys. 1975, 63, 4742. (36) Buchner, W. J.Magn. Reson. 1975, 17, 229.
where the extremely narrowing condition is applied and yH is the magnetogyric ratio of proton. The dipolar relaxation times, T1(13C-'H), thus obtained are shown in Table 111. Equation 7 gives a relation between the relaxation time, T1(13C-'H), and an effective correlation time for the rotation about the c-H axis, 7eff(CH),in analogy with eq 2: 1
where nH is the number of protons directly attached to the carbon atom and rCH is the distance between the carbon nucleus and the proton. In general, Teff(CH) is expressed as a quite complicated function of the molecular geometry and parameters characterizing the intrinsic motion of the molecule. The present analysis was restricted by the following assumptions: (1)the molecule approximates an axially symmetric ellipsoid; (2) the overall molecular tumbling is isotropic; (3) the internal rotation of the methyl group and the overall molecular tumbling are stochastically independent; and (4) the methyl group undergoes small-step angular diffusion around the symmetry axis and the motion is characterized by an internal rotational diffusion constant, Dint. These assumptions make it feasible to give a simple relationship between Teff(CH) and the rotational diffusion constants: Teff(CH)
--
(3 cos2 a 240
a cos2 a + 3 sin2 + -34 6D + Dint
sin4 a (8) (6D + 4Dj,t)
3514
1
I
3.3
3.4
I
I
3.5
3.6
28.:
-
28.C
c
I VI N
5 \ 4
u
Kakihana et al.
The Journal of Physical Chemistry, Vol. 87,No. 78, 1983
27.E
0 C
+
27.6
lo3
$-'/K-'
Flgure 3. Temperature dependence of methyl internal rotational diffusion constant obtained from '%-'H dipolar relaxation for 0.5 mol dm-3 sodium acetate in 2H20.
where a is the angle between the symmetry axis of the methyl group and the C-H bond. The value of 7&(cH) was estimated by putting rCH = 0.1095 nm3' into eq 7 and the value of Dintwas calculated by substituting the D value obtained from eq 3 into eq 8; here we assumed a to be a tetrahedral angle. The values of 7,ff(CH) and Dintat each temperature are shown in Table IV. The Arrhenius plot of Dintis shown in Figure 3. The apparent Arrhenius activation energy for the internal rowas evaluated by linearly aptational process, proximating the plot; the value obtained was 9.8 f 1.3 kJ mol-'. We attempted to calculate the torsional vibrational frequency for the methyl group, which is expected to be observed in the far-infrared frequency region (300-50 (37) Chen, D. M.; Reeves, L. W.; Tracey, A. S.;Tracey, M. M. J . Am. Chem. Soc. 1974, 96,5349.
cm-l), in order to compare it with the result of a qualitiative Raman work reported by Spinner.3s The force constant relating to the torsional vibration, H,, is derived from the following relation: 39 H, = 9 v 3 / 2 (9) where V3 is the threefold potential barrier for the methyl group. The Arrhenius activation energy, can be related to the V3 barrier. Kowalewski and Liljefors40 treated hindered internal rotation as a rate process according to Eyring's absolute rate theory34 and showed that from V3was small, around 2-4%. the deviation of We assumed that V , in eq 9 could be replaced by The torsional frequency was calculated by using the value of H, and the structural parameters of acetate ion reported in the literature; 32 the calculated frequency was 204 cm-l. Spinner38observed two Raman bands at 247 and 228 cm-' in the far-IR frequency region for solid sodium acetate, the former frequency being tentatively assigned to the torsional vibration with some ambiguity. Since absorption bands due to lattice vibrations are often observed in the far-infrared spectral region for solid samples, conclusive assignments for fundamentals due to torsional vibrations cannot be easily given. In view of this, the present result gives valuable information on the torsional vibration for the methyl group. At the present stage, the Arrhenius activation energy reported here seems to be a reasonable alternative to the V3barrier for acetate ion. It is worth noting that the V3 barrier for acetate ion estimated in the present study is much higher than those for acetic acid reported in the literature (a typical value is 2.0 kJ mol-' (ref 41)). Acknowledgment. We heartily thank Professor A. Yamazaki of the University of Electro-Communications for his helpful discussions and advice. Thanks are due to Mr. T. Suzuki, Mr. K. Kushida, and Mr. M. Murata of Analytica Corp. for the use of the Varian XL-200 NMR spectrometer and their technical advice for the NMR spectral measurements. Registry No. Sodium acetate-lJ3C, 23424-28-4; sodium acetate-2-I3C, 13291-89-9; sodium acetate-1,2J3C2, 56374-56-2;
sodium acetate, 127-09-3. (38) Spinner, E. J . Chem. Soc. 1964, 4217. (39) Fateley, W. G.; Miller, F. A. Spectrochim. Acta 1961, 17, 857. (40) Kowalewski. J.: Liliefors. T. Chem. Phvs. Lett. 1979. 64. 170. (41) Chadwick, D.; K a d b , A.'J. Mol. Struc; 1974, 3, 39.
