J. Phys. Chem. 1984, 88, 2675-2678
2675
Gas-Phase Nuclear Magnetic Resonance Investigation of Chemical Exchange in N,N-Dimethylacetamide. Medium Effects on Kinetic Parameters Brian D. Ross, Nancy S. True,* and Gerald B. Matson Department of Chemistry, University of California, Davis, California 95616 (Received: September 16, 1983)
Temperature-dependent first-order rate constants for chemical exchange in gaseous N,N-dimethylacetamide (DMA) obtained from analysis of exchange-broadened 'H NMR spectra are approximately 25 times faster than correspondingrates for liquid samples. The limiting chemical shift difference between the two aminomethyl resonances, 0.0468 (4) ppm, which is 2.6 times smaller than the correspondingvalue observed for the neat liquid, necessitated studies at 500 MHz. Gas-phase rate constants obtained over a 30 K range are consistent with the following kinetic parameters: Eact(m), 16.5 (1.1) kcal/mol; AGZ9*,15.3 (0.1) kcal/mol; AH*298.15.8 (1.1) kcal/mol. Previously obtained values of corresponding parameters for the neat liquid and in various solutions are ca. 2-3 kcal/mol higher. Faster gas-phase rates and lower gas-phase kinetic parameters are consistent with a process proceeding via a transition state which has greater steric requirements than the molecules' equilibrium configuration.
Introduction This paper reports gas-phase kinetic parameters for internal rotation in N,N-dimethylacetamide and compares them with solution and neat liquid data. Our recent studies of gas-phase conformational dynamics in cyclohexane,',* sulfur tetrafluoride: N,N-dimethyltrifluoroacetamide,4and N,N-dimethylnitrosamine5 demonstrate that the gas-to-liquid shifts in the associated kinetic parameters correlate with the relative size of the transition state proposed for each process. Associated exchange rates for both ring inversion in cyclohexane and for pseudorotation in SF4 are ca. 2-3 times slower in the gas phase than in solutions. This trend is consistent with expected solvent internal pressure effects associated with proposed sterically smaller transition-state models for these systems. Conversely, for the internal rotation processes in N,N-dimethyltrifluoroacetamide,for which free rotation about the C-N bond occurs in the transition state, gas-phase exchange rates are ca. 25 times faster than those observed in solution^.^ Conformational processes generally do not proceed via transition states with dipole moments which differ significantly from the equilibrium configurations. In many cases packing forces in solution appear to be the dominant factor in determining the direction of gas-liquid shifts associated with the kinetic parameters describing chemical exchange in most conformationally exchanging systems.6 Exchange in DMA has been studied extensively in the liquid phase with N M R spectro~copy.~-~~ The small limiting chemical shift difference, ca. 10 H z at 60 MHz, and its temperature and solvent dependence complicated many early studies.15 Neglect of long-range coupling also introduces significant systematic errors.l0 More recently reported kinetic parameters, which appear (1) Ross, B. D.; True, N. S . J. Am. Chem. SOC.1983, 105, 1382-3. (2) Ross, B. D.; True, N. S. J.Am. Chem. SOC.1983, 105, 4871-5. (3) Spring, C. A.; True, N. S . J . Am. Chem. SOC.1983, 105, 7231-6. (4) Ross, B. D.; True, N. S.;Decker, D. L. J. Phys. Chem. 1983,87,89-94. (5) Chauvel, J. P., Jr.; Leung, D.; True, N. S . J. Mol. Struct., submitted for publication. (6) Chandler, D. J. Chem. Phys. 1978,68, 2959-70. (7) Drakenberg, T.; Dahlquist, K.-I.; Forsen, S . J. Phys. Chem. 1972, 76, 2178-83. ( 8 ) Reeves, L. W.; Shaddick, R. C.; Shaw, K. N. Can. J. Chem. 1971,49, 3683-91. (9) Neuman, R. C., Jr.; Jonas, V . J. Am. Chem. SOC.1968, 90, 1970-5. (10) Drakenberg, T.; Carter, R. E. Org. Mugn. Reson. 1975, 7, 307-8. (11) Gutowsky, H. S.; Cheng, H. N. J. Chem. Phys. 1975, 63, 2439-41. (12) Waghorne, W. E.; Ward, A. J. I.; Clune, T. G.; Cox, B. G. J . Chem. SOC.,Faraday Trans. 1 1980, 76, 1131-7. (13) Martin, G. J.; Gouesnard, J. P.; Dorie, J.; Rabiller, C.; Martin, M. L. J. Am. Chem. SOC.1977, 99, 1381-4. (14) Nagata, C.; Tanaka, S . Nippon Koagaku Kaishi 1975, 4, 579-82. (15) Jackman, L. M. In "Dynamic Nuclear Magnetic Resonance Spectroscopy", Jackman, L. M., Coton, F. A. Eds.; Academic Press: New York, 1975; Chapter 7, pp 203-52.
0022-3654/84/2088-2675$01.50/0
in Table I, demonstrate that rates and activation parameters for chemical exchange in DMA are medium dependent. AG* (kcal/mol) is 18.1, 18.0, 18.6, and 19.3 for neat DMA7 and solutions in acetone-d6, DMSO-d,, and HzO, respectively. The increase in AG* for this series of solvents correlates qualitatively with increases in solvent cohesive energy density. Solvent cohesive energy densities (atm) are 5743, 3890,6955, and 22703 for DMA, acetone, DMSO, and H,O, respectively.16 DMA exchange rates increase with applied pressure. At 350.2 K rates range from 32.5 at 50 bar (AG*, 17.71 kcal/mol) to 22.5 at 1500 bar (AG*, 17.96 kcal/mol) .17-18 Recently a 360-MHz N M R study of DMA at its equilibrium vapor pressure (ca. 1 torr) in ca. 380 torr of acetone-d6 yielded a AG*29g of 15.34 (0.1) kcal/m01.'~ The poor signal/noise ratio coupled with the small limiting shift difference at this spectrometer frequency precluded determination of the associated thermodynamic parameters. The potential function for internal rotation in DMA, calculated by ab-initio methods at the STO-3G level without geometry optimization, has a barrier of 14.93 kcal/mol.20 Experimental Section Gas-Phase IH NMR measurements were made with a Nicolet spectrometer with 'H observation at 50 MHz. Additional 'H NMR measurements were made with a Nicolet spectrometer with 'H observation at 360 MHz. All spectra were acquired in an unlocked mode. Spectrometer drift at 500 MHz was typically 4 Hz/h in an unlocked mode and was compensated for electronically. All measurements were made on spinning samples. Typically 1200 free induction decays were acquired and stored in 8K to produce frequency domain spectra with signal/noise ratios of ca. 50/1. Acquisition times were 1.02 s/transient with a 0 5 s delay and a 74.5' pulse angle (6 ps). Temperatures were controlled with a 0.1' pyrometer which was calibrated against a copper-constantan thermocouple. In the region below the spinner the temperature was found to be constant within 0.2 OC and samples were constrained to this area by placing vortex plugs in the sample tubes. Samples were allowed to equilibrate for 10 min prior to spectral acquisition. DMA (HPLC Grade) was purchased from Burdick and Jackson Laboratories, Inc., and its low volatility, ca. 0.8 torr at 300 K, necessitated addition of an inert bath gas in order to produce good quality N M R spectra. A sample containing 0.8 (16) Dack, M. R. J. Chem. SOC.Rev. 1975, 4, 211-29. (17) Rauchschwalbe, R.; Volkel, G.; Lang, E.; Ludemann, H.-D. J . Chem. Res. (S) 1978, 448-9. J. Chem. Res. (M), 1978, 5323-43. (18) Ludemann, H.-D.; Rauchschwalbe, R.; Lang, E. Angew. Chem., In?. Ed. Engl. 1977, 16, 331-2. (19) Feigel, M. J . Chem. SOC.,Chem. Commun. 1980, 456-7. (20) Peters, D.; Peters, J. J. Mol. Strucl. 1978, 50, 133-45.
0 1984 American Chemical Society
2616
The Journal of Physical Chemistry, Vol.88, No. 12, 1984
Ross et al.
TABLE I: Kinetic Parameters for Exchange in N,N-Dimethylacetamide Ea,,,
kcal/mol 0.8 torr of DMA in 1000 torr of SF,b 1 torr of DMA in 380 torr of a ~ e t 0 n e - d ~ ~
16.5 (1.1)
14.9 mol % in CC14d 20 mol in CC14c neatf 9.5%in D M S O 4 2 10% in acetone-d6g 10% in D,Og 9.9% in formamideo
16.85 (0.4)
"NMR rates,
K
=
AG*298,' kcal/mol Gas Phase 15.3 (0.1)
as*,
AH*, kcal/mol
cal/(mol K)
15.8 (1.1)
1.5 (1.8)
15.34 (0.1)
19.6 (0.3) 20.6 (0.3) 19.6 (0.3) 19.8 (0.1)
Liquid Phase 17.33 18.7 18.2 18.6 18.0 19.31 19.3
16.26
-3.59 (1.23)
19.0 20.0 19.0 19.1 20.3
2.7 4.7 3.2 -0.8 3
bThis study. CReference19. dReference 8. eReference 14. /Reference 9. EReference 7.
torr of DMA, ca. 30 torr of Me4Si gas, and 1000 torr of SF6 was used to obtain first-order rate constants. Additional samples containing 0.8 torr of DMA and amounts of SF6between 50 and 1000 torr were prepared and used for pressure-dependent studies. All samples were prepared in 5-mm N M R tubes by previously described methods.'-5 Rates were calculated with the computer program DNMRsz1 which uses a nonlinear least-squares regression analysis to obtain the best fit of the experimental spectrum. All free induction decays were multiplied by an exponential line broadening factor of 1.5 H z and spectra were zero-filled to 32 K. Typically 990 experimental points were used in the analysis of each spectrum. The digital resolution was 0.342 Hzlpoint below 25.8 OC and 0.244 Hz/point above 25.8 OC. The effective line width parameter, Tz, was measured at 0 and 100 O C and was estimated by assuming a linear temperature dependence at each temperature where experimental rate data was obtained. The line width of the gaseous Me4Si resonance was used to estimate the field inhomogeneity contribution to T2 at each experimental temperature. This factor and the exponential line-broadening contributions were added to each interpolated Tz value. A limiting chemical shift difference of 23.4 f 0.2 H z (0.0468 (4) ppm) is consistent with spectra obtained between 0 and 10 O C . Useful spectra below 0 OC could not be obtained due to low sample volatility. Within our uncertainity limits, limiting chemical shifts are not temperature dependent for gaseous DMA.22 The 4-Hz natural line width of each methyl resonance exceeds the expected contribution from respective anti and syn 'JHH coupling constants of 0.5 and 0.2 Hz.l0 Therefore neglect of long-range coupling incurred negligible error in our rate calculations and DMA was analyzed as an uncoupled A3X3system. Rates obtained from our exchange-broadened spectra have ca. 6% uncertainties 5-7 OC from coalescence and ca. 25% uncertainties ca. 15 O C above coalescence due to the small limiting chemical shift value and uncertainties in T2, resonance positions, baseline irregularities, and our experimental signal/noise. The temperature dependence of the rates was used to determine the activation energy and associated thermodynamic parameters in the customary ~ a y . l - ~ Reported uncertainties are two standard deviations.
*
Results Figure 1 shows slow exchange 'H 500-MHz NMR spectra of gaseous DMA (0.8 torr in 1000 torr of SF,) (a) and liquid DMA (10% w/v) in CC14 (b) at 0 OC. These spectra demonstrate that the limiting shift difference is much smaller in the gas phase. In the liquid the three proton resonances, from low to high field, are assigned to the aminomethyl groups anti (3.014 ppm) and syn (2.834 ppm) to the carbonyl group and the methyl group (1.964 (21) Stephenson, D. S.; Bunsch, G. QCPE 1978, 10, program 365. (22) See, for example: Jameson, C. J.; Jameson, A. K.; Cohen, S. M.; Parker, H.; Oppusunggu, D.; Burrell, P. M.; Willie, S.J . Chem. Phys. 1981, 74, 1608-12.
A
I
,
I
, , , , , , , ~ , , , ~ , , , ~ , , , , , , , 1 , , , 1 , , , 1 , , , ~ 3.2
3.a
2
,
~2,fi
2,q
2.2
2.4
1.8
I . ~ ~ P P M
Figure 1. 'H500-MHz NMR spectra at -0.2 O C of (a) gaseous (0.8 torr with 1000 torr of SF6) DMA and (b) liquid (10% w/v in CC14) DMA. In the gas phase, the three methyl resonances are at 2.905, 2.859, and 1.893 ppm referenced to gaseous Me$i (0.000 ppm). In the liquid, the three methyl resonances occur at 3.014,2.834,and 1.964ppm, referenced to liquid Me4Si (0.000 ppm), The gaseous Me4Siresonance is 2.554-ppm downfield from the liquid Me4Si resonance. TABLE 11: Exchange Rate Constants of Dimethylacetamide Gas (0.8 torr + 1000 torr of SFs) T , OC k , s-l T , OC k, S-I 23.3 13.9 (1.2) 41.2 69.0 (5.5) 25.8 17.7 (1.4) 43.2 88.1 (7.7) 27.9 26.6 (1.4) 45.1 109 (23) 131 (28) 30.1 30.5 (1.9) 47.1 31.9 35.5 (2.0) 49.1 169 (37) 33.3 39.9 (2.5) 51.1 181 (46) 35.3 46.2 (2.5) 53.1 227 (80) 37.3 52.0 (3.3) 55.1 273 (96) 39.2 59.2 (3.3)
ppm) on the carbonyl carbon, respectively,I6 referenced to liquid Me4Si (0.000 ppm). In the gas phase the three methyl resonances are at 2.905, 2.859, and 1.893 ppm, referenced to gaseous Me& (0.000). The gaseous Me4Si resonance is 2.554-ppm downfield from that of the liquid, consistent with an expected shift due to the bulk susceptibility difference for cylindrical gas and liquid samples oriented parallel to BQZ3 Since we were unable to resolve long-range couplings or to discriminate a significant difference (23) Becconsall, J. K.; Dayes, G. D., Jr.; Anderson, W. R., Jr. J . Am. Chem. SOC.1970, 92, 430-1.
The Journal of Physical Chemistry, Vol. 88, No. 12, 1984 2617
Medium Effects on Kinetic Parameters
gaseous DMA. The smaller limiting chemical shift difference in the gas phase is also of interest. These topics are discussed below. Tables I and I1 and Figure 2 demonstrate that the rates and activation parameters associated with chemical exchange in DMA are strongly medium dependent. AG*29g is 15.3 (0.1) kcal/mol in the gas phase and 18.2 kcal/mol for the neat liquid as calculated from observed exchange rates by using a transmission coefficient of 1/2. Temperature-dependent studies demonstrate that this results primarily from lower energy requirements in the gas phase and that the entropy contribution to AG* is small. The very small activation entropy, AS*,of 1.5 (2.0) cal/(mol K) is appropriate for a conformational exchange process in the gas phase. The ca. 3 kcal/mol phase-dependent difference in AG* is consistent with expected medium-dependent effects on an internal rotation p r o ~ e s s .The ~ activation volume, A V , for an internal rotation process is typically large and positive? Pressure-dependent liquid-phase studies which obtained exchange rates for DMA inversion between 74 and 83 OC at applied pressures ranging from 50 to 2000 bars were consistent with a A V of 10.3 (1.0) cm3/ m01.17J8These studies used a sample which contained 60% DMA, 20% Me&, and 20% acetone-d6. A V for this process is solvent dependent, and additional experiments in other solvents yield the following values for A V (cm3/mol): neat, 7.6; 60% CCl,, 5.5; 80% CsD.5, 9.0; 80% (CD3)2SO, 6.8; 80% CDjCN, 9.3; 80% CD30D, 7.6, 80% DzO, 1.6. For any process A V can be factored into an intrinsic contribution and a contribution from solvent effects. The intrinsic contribution to A P for internal rotation in DMA is ca. 13 cm3/rno1.l7 Since A P is large, solvent internal pressures, which arise from local packing forces, can be an important factor contributing to the phase dependence of AG*?6 The partial derivative of AG* with respect to pressure equals the activation volume for the process.6
T(K)
\
\
1 ,
2.8
I
1
I
I
3.0 3.2 1000/T( K 1
I
(S(AG*)/SPiT) = A V
I
3.4
Solvent internal pressures range from ca. 1500 to 5000 a t n z 7 If ideally is assumed, the internal pressure of a gas is zero. Therefore Figure 2. Arrhenius plots of exchange rates for DMA: (a) 0.8 torr and for a A V of 10 cm3/mol, (AGllqmd-AGgas)can range from ca. 0.5 1000 torr of SF,; (b) 14.9 mol %' DMA in CCl4 (ref 16); (c) 9.5 mol % to 5 kcal/mol, based solely on internal pressure effects. This factor DMA in DMSO-d, (ref 17). only partially accounts for the experimentally observed differences, A(AG*) 3 kcal/mol, obtained in this study. Dielectric effects in Tlbetween the two aminomethyl resonances a definitive must be relatively important in this system. gas-phase assignment cannot be made. It is interesting to compare this result to previously obtained The small limiting chemical shift difference restricted the results for N,N-dimethyltrifluoroacetamide(DMTFA). For this temperature range over which useful rate data could be obtained molecule (AG*llquld - AG,,,) is ca. 1.5 kcal/mol, S V is ca. 16 to ca. 30 "C. Associated rates range from 13.9 (1.2)/s at 23.3 cm3/mol and internal pressure effects can completely account for OC to 273 (96)/s at 55.1 OC and are listed in Table 11. Coathe observed d i f f e r e n ~ e .The ~ 3 cm3/mol difference in intrinsic lescence occurred at 32.5 O C . In order to ensure that the obtained A V s for DMA and DMTFA is due to differences in van der are first order, pressure-dependent studies near the coalescence Waals radii of H (1.2 A) and F (1.35 A) used in the calculations. temperature were performed. Within our experimental uncerThis molecule is considerably less polar than DMA since the CF3 tainity rates for samples with SF6partial pressure ranging from 100 to 1000 torr were the same. Model RRKM ~ a l c u l a t i o n s ~ ~ and CO dipole moment orientations result in a net cancellation. An interesting observation is the phase dependence of the limsupport this conclusion. Gas-phase vibrational frequencies as well iting chemical shifts of the aminomethyl resonances of DMA. The as moments of inertia obtained from infrared band contour limiting chemical shift difference between the two aminomethyl analyses25 were used in these calculations. Methyl tops were proton resonances obtained for gaseous DMA is 23.4 Hz at 500 included as free internal rotors. For a threshold energy of 17.0 MHz. This value is 2.66 times smaller than corresponding values kcal/mol, the unimolecular K ( E ) is 1 X 108/s and if we assume obtained in solution. Smaller gas-phase limiting chemical shifts a kinetic cross section of 3 A, the falloff pressure, defined as the were also observed for N,N-dimethyltrifluoroacetamide. The pressure where the rate has declined to 1/2 its infinite value, is limiting chemical shift difference for N,N-dimethyltrifluoropredicted as ca. 75 torr. acetamide in the gas phase is 0.0980 ppm and in liquids its value Since both experimental data and RRKM calculations clearly is solvent dependent and averages around 0.1233 ppm. We have establish that the rates obtained for our high-pressure samples been unsuccessful in resolving the dimethylamino resonances of are pressure independent, it is valid to apply transition state theory dimethylformamide in the gas phase at 500 M H Z . ~The ~ 'H and calculate Eyring parameters for the exchange process. These dimethylamino resonances are separated by 0.150 ppm in liquid parameters appeartin Table I. Figure 2 displays Arrhenius plots dimethylf~rrnamide.~~ Early studies of chemical shifts in subfor gaseous DMA as well as previously obtained liquid-phase stituted formamides emphasized magnetic anisotropies associated results for comparison purposes. with the C=O bond.jO The anisotropy of a C-H group is Discussion Significant medium-dependent differences obtained in this study (26) Ouellette, R. J.; Williams, S. H. J. Am. Chem. SOC.1971, 93, 466-51 1. include faster rates and associated lower kinetic parameters for (27) Dack, M. R. J. Chem. SOC.Rev. 1975, 4, 211-29. (28) Conboy, C. B.; True, N. S.,unpublished results.
-
(24) Hase, W. L.; Bunker, D. L. QCPE program 234. (25) Jones, R. L. J . Mol. Spectrosc. 1963, 11, 411-21.
(29) Rabinovitz, M.; Pines, A. J . Am. Chem. Sot. 1969, 91, 1585-9. (30) Hooper, D.L.; Kaiser, R. Can. J . Chem. 1965, 43, 2363-71.
2678
The Journal of Physical Chemistry, Vol. 88, No. 12, 1984
sizeable3' and when both effects are taken into account a splitting of 0.09 ppm is predicted for the amino methyl resonances of N,N-dimethylformamide,32 somewhat smaller than the observed liquid-phase differences. The very small limiting chemical shift
Additions and Corrections differences observed in gaseous dimethyl acetamide is consistent with anisotropies associated with the C=O and C-CH3 groups which are nearly equivalent.
Acknowledament. This research was suuuorted bv the National
ADDITIONS AND CORRECTIONS 1983, Volume 87
P.A. Monson and K. E. Gubbms*: Equilibrium Properties of the Gaussian Overlap Fluid. Monte Carlo Simulation and Thermodynamic Perturbation Theory. Page 2852. Figure 1 of this paper was inadvertantly reproduced twice as both Figure 1 and Figure 3. Figure 3 should be replaced with the figure below. The statements in the text concerning Figure 3 apply to the corrected figure.
P'
