17338
J. Phys. Chem. 1995, 99, 17338-17343
A Study of Chemical Exchange in Unequally Populated Systems by Novel NMR Methodologies. Application to the Cis -Trans Isomerization in Furfural Alex D. Bain,* G. J. Duns,? F. Rathgeb, and J. Vanderkloet Department of Chemistly, McMaster University, Hamilton, Ontario, Canada U S 4Ml Received: June 19, 1995; In Final Form: September 18, 1995@
The internal rotation of the aldehyde group with respect to the ring in 2-furanaldehyde (furfural) provides an example of chemical exchange in a two-site system with unequal populations. In a polar solvent, the two isomers are present in unequal amounts. In the present study, rates of exchange for the cis-trans isomerization process of furfural in acetone are measured using a combination of the offset-saturation method for determination of fast rates of exchange, time-domain line shape analysis for measurement of intermediate rates of exchange, and selective-inversion measurements of slow exchange rates. This combination of NMR techniques permits the determination of rates of exchange over 5 orders of magnitude, covering a temperature range of 177-318 K. The utility of the offset-saturation method for fast rate measurement is highlighted in the present system, where the exchange rapidly enters the fast exchange regime. The corresponding values of the activation parameters are the energy of activation E, = 41.9 & 0.9 kJ mol-', the enthalpy of activation AH* = 40.0 i 1 kJ mol-', and the entropy of activation AS* = -26.8 k 5.2 J K-' mol-'.
Introduction The study of chemical exchange processes by nuclear magnetic resonance spectroscopy (NMR) is well established.'-4 In order to obtain optimal values of the thermodynamic activation parameters for an exchange process, it is desirable to measure exchange rates over as wide a range of temperatures as Combinations of NMR methods, each best suited to a particular exchange time scale, have been shown to provide the widest range of temperature^.^,^ Line shape methods, which can be used to over the slow, intermediate, and fast exchange regimes, are most appropriate for the intermediate region, where the exchange rate is of the order of the frequency difference between the exchanging sites and generally in the range 10lo3 s-i.3.4.6.9.10 Methods based on the measurement of the spinlattice relaxation time T I are optimal for providing slower (0.110 s-l) rates,"-13 while experiments for measuring the spinspin relaxation time TZwithout contribution from magnetic field inhomogeneities can extend the upper limit of rate measurement beyond lo3 s-i.6.14-16 Recently, a novel combination of NMR methods was used to obtain values of the activation parameters for the hindered C-N bond rotation in N-acetylpyrrole.g Selective-inversion T I measurements of slow rates of exchange, time-domain line shape analysis for the intermediate exchange regime," and the offsetsaturation methodI6 to extract rate constants from T2 measurements in the fast exchange regime were combined to provide rate constants covering some 6 orders of magnitude with a corresponding temperature range of approximately 150 K. This wide range of rate measurements accordingly permitted accurate determination of the thermodynamic activation parameters for the equally-populated hindered rotation process and provided reasonable estimation of the corresponding errors for the thermodynamic parameters. The study of exchanging systems having unequal populations of the sites is less straightforward. For such systems, an * Author to whom correspondence should be addressed. Present address: Pesticide and Trace Contaminants Laboratory, Agriculture and Food Laboratory Services Branch, Ministry of Agriculture, Food and Rural Affairs. Guelph, Ontario, Canada N1H 857. Abstract published in Aduance ACS Absrracrs, November 1, 1995.
0022-365419512099-17338$09.00/0
0
I
H
Figure 1. Cis-rruns isomerization of furfural.
equilibrium process as well as the overall kinetic or rate process must be considered. The equilibrium constant will accordingly become an additional parameter in the determination of exchange rates for such system^.^,^,'^-^^ Although systems having unequal populations are relatively common, including Nmonosubstituted or N,N-asymmetrically-disubstituted amides, alkyl nitrites, and cyclic alkanes such as derivatives of cyclohexane,2,'8,2'-24 relatively few such systems have been subjected to a detailed dynamic NMR investigation. An example of a dynamic system having unequal site populations is 2-furanaldehyde (furfural) (Figure l), which may exist in solution as an equilibrium mixture of two planar isomers in which the two oxygen atoms are either cis or trans with respect to each other. The spectra exhibit characteristics indicative of a two-site system with unequal populations, as shown in Figure 2. The cis-trans rotational equilibrium has been the subject of some controversy regarding the nature of the more stable of the two i s ~ m e r s . ~ ~A- ~solvent l dependence of this equilibrium has been established, with the cis form predominating in polar Despite the rather large number of studies of 2-furanaldehyde, the only comprehensive NMR measurement of rate data for the rotational isomerism process appears to be the early study by Dahlqvist and Forsen,26who performed a line shape analysis of 2-furanaldehyde in dimethyl ether. In the present study, the isomerization or internal rotation process of furfural in a polar solvent, acetone-& is subjected to a thorough dynamic NMR investigation. A combination of selective-inversion expenments' for measuring slow rates of exchange, time-domain line shape analysis1' for the intermediate exchange regime, and the offset-saturation method for measuring T2,I6 which has previously been shown to be applicable with some relative facility for obtaining fast rates of exchange,s is used to provide rate data over some 5 orders of magnitude. The present paper provides a detailed analysis of a two-site exchang-
0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 48, 1995 17339
Chemical Exchange in Unequally Populated Systems ing system having unequal site populations and highlights some interesting aspects of exchange in unequally-populated systems.
Theory and Methodology
240 K
Slow Exchange. In the region of slow exchange; the rates may be too slow to result in apparent broadening of the resonances for each of the exchanging sites but are generally comparable to nuclear spin-lattice relaxation times. It is accordingly appropriate in such instances to employ spin relaxation methods or generalizations of the inversion recovery experiment,' -1 which are essentially pulsed NMR analogues of the classic saturation transfer approach pioneered by the balance between Hoffman and F o r ~ e n . ~In~this , ~ approach, ~ spin relaxation and exchange is observed by selectively inverting one of the exchanging sites and observing the resulting intensities or magnetizations of both sites as a function of time during the return to equilibrium governed by spin relaxation. The spin-lattice relaxation times of both sites can be determined by nonselective-inversion recovery experiments. Combinations of nonselective- and selective-inversion experiments have been shown to provide the optimal approach to the study of slow exchange processes. 3.33 In a two-site unequally populated system in slow exchange, both the forward rate, KAB, which takes site A into site B, and the corresponding reverse rate, ~ B A must , be considered in the time dependence of the magnetizations of each site in slow exchange, either explicitly or in terms of either of the rate constants and the equilibrium constant for the rate process. In terms of the present study of furfural, site A corresponds to the major (cis) isomer, while site B represents the minor (trans) isomer. The system can be described by a coupled set of differential equations. For example, the time dependence of the return to equilibrium of the magnetizations in terms of ~ B A and the equilibrium constant K (=PB/PA) is given by
210 K
1
3932933
205 K
195 K
~
3000
ZSSO
W
2900
chemical shift (Mi
Figure 2. Variable-temperature 300 MHz 'H NMR spectra of the aldehyde proton of furfural in acetone-&
:
Y
::
..... ....._._........... .......................................
where MA(~) and k f B ( t ) are the magnetization at time t for sites A and B, respectively, and MA(=) and MB(=) are the equilibrium magnetizations for sites A and B, respectively. The exchange rate can be obtained from a nonlinear least-squares fit to eq 1 which minimizes the sum of squares of the differences between the observed and modeled data.36-38 A nonlinear least-squares variation of the program SIFIT" written in C was used to determine the rate constants. In this program, for each site, a value of the relaxation rate in the a6sence of exchange (UTI) as determined from a standard inversion recovery experiment, a value for the equilibrium intensity, and a value for the intensity at the start of the relaxation, as well as an initial estimate of the rate constant, are used as input parameters for each set of experimental data. The errors in the fitted parameters can also be estimated from the nonlinear fitting procedure, as the standard deviations or square roots of the variances from the variancecovariance matrix of the fit.36-38 For an equally-populated exchanging system, the choice of which site to invert in a selective-inversion experiment is arbitrary. With unequal populations, however, the effects of inversion on each of the sites is less clear. In a simple two-site unequally-populated system, the effects of exchange are larger with respect to the minor site, as evident in the differential broadening experienced by the resonances for the two sites as n the the exchange rate increases. In order to measure k ~ with greatest precision, an analysis of the partial derivatives of the magnetizations (the derivative of the solution to eq 1 with respect to ~ B A )indicates that the optimal result or more sensitive
I/
1'
-50.00 -100.004
0
5
10
15
20
I
25
Time (s)
Figure 3. Results of a selective-inversion experiment on the exchanging aldehyde protons of 2-furfural at 177 K. The points represent the observed magnetizations or intensities as a function of time, while the solid lines represent the best fit to the data. The major site (points represented by asterisks) was inverted, while the x points represent the minor site.
experiment is obtained when the major site is inverted, and the subsequent effects on the minor site are observed.39 An example of a selective-inversion experiment performed on the exchanging aldehyde protons of furfural at 177 K is shown in Figure 3. The major site was inverted by placing the transmitter frequency directly on the resonance for the major site. Further details on the selective-inversion experiments are given in the Experimental Section of this paper. Intermediate Exchange. The exchange rates in the intermediate exchange regime are comparable to the frequency difference between the two sites. In this regime, pronounced line broadening may be observed as the temperature increases from the slow exchange region, and the two resonances eventually coalesce. The well-known approximate formula of Gutowsky and Holm for determining rates at the coalescence temperature' is not in general valid for the case of unequal
Bain et al.
17340 J. Phys. Chem., Vol. 99, No. 48, 1995 populations. A complete line shape analysis, which in general is the optimal method for determining rates of exchange in the intermediate exchange regime,3.4.6.9is thus required. In the present system, the intermediate exchange regime is rather narrow, so that line shape analysis is in effect of limited use. Some rates were determined close to the region of coalescence. however, using a new method of line shape analysis.I7 This method makes use of the fact that line shapes, even near coalescence, retain Lorentzian characteristics.jO These lines, or coherences. are each defined by an intensity, phase, position, and line width, and for each line in the spectrum, the contribution of that particular line to the overall free induction decay (FID) can be calculated. The solution to the set of coupled differential equations defining the time dependence of the coherences M A and M B for the general two-site case is given by"
where
and w ~W ,B are the Larmor frequencies of sites A and B, R2i\ and R ~ are B the corresponding spin-spin relaxation rates in the absence of exchange, and AB and k B A are the forward and reverse exchange rates, respectively, in eq 3. The imaginary and the real parts of the eigenvalues of A give the oscillation frequencies and the decay rates, while the real and imaginary parts of the coherences at time t = 0 can be determined from the eigenvectors of A. For the present work, a simulated FID is calculated by means of a computer code written in C. This FID is processed analogously to the FID of the corresponding experimental spectrum,I7 and the two spectra are compared simultaneously and superimposed on the computer display Below coalescence, the position of each line can be obtained directly, while above coalescence, the chemical shifts are obtained from extrapolation of the temperature dependence of the chemical shifts below coalescence. The small (approximately 1 Hz) long range scalar couplings between the aldehyde proton and the ring protons are not included in the line shape computations, having a negligible effect on the line shape in the vicinity of coalescence. Fast Exchange. In the fast exchange regime, the rate of exchange between two exchanging sites is greater than the chemical shift difference between the two sites. The corresponding spectrum is thus a single line, with a contribution to the observed line width from exchange broadening. The measurement of relatively fast rates of exchange is accordingly limited by the ability to measure the spin-spin relaxation time T2 when the exchange broadening becomes less pronounced at faster rates of exchange, primarily due to restrictions of magnetic field inhomogeneity. Pulse spin-echo techniques such as the CPMG experiment6.4'.'2 and TI method^'^,^^ have successfully been employed to measure faster exchange rates which are beyond the upper bounds of line shape analysis, but these methods in general have proven difficult to implement. The offset-saturation method16 has recently been shown to be a viable method for studying fast chemical exchange, with the capability of measuring exchange rates on the order of IO5 s-l or greater.8 The offset-saturation method has the additional advantage of relative ease of implementation compared to CPMG or TI, methods. The offset-saturation method as described in detail previouslyI6 measures the z component of the magnetization by irradiating the resonance of interest with a saturating rf field B2 produced by the homodecoupler of the
,
spectrometer. This irradiation is placed at some resonance offset (wg - w ) for a period of time of approximately TI, where TI is the spin-lattice relaxation time of the observed spin, until a steady state is achieved. The decoupler is then gated off, and a delay time z, which is approximately 10% of TI,is introduced to allow for partial relaxation of spin system prior to the application of a 90" observation pulse. The recorded FID is then Fourier transformed, and the intensity of the corresponding signal gives a measure of the partially saturated 7: magnetization M:. The experiment is then repeated for a series of different decoupler resonance offsets. The resulting plot of the zmagnetization as a function of resonance offset gives a curve which is described by the Bloch equation for M- in the presence of a saturating rf field B2 as
where M(=) is the equilibrium magnetization. Both TI and Tz are obtained from a single offset-saturation experiment, with errors on the order of 5% at the 95% confidence level, by means of a nonlinear least-squares fit to eq 4,as described previously.'6 The value of B' in eq 4 can be determined with good precision using the single-spin double-resonance experiment.'6,13-46 Importantly, the value of T, as obtained in the presence of the saturating rf field is free from any contributions from magnetic field inh~mogeneities.~'Thus, in the assumption that T I = Tz in the absence of exchange, the only other contribution to T? can be attributed to the underlying exchange process. For an exchanging system having unequal site populations, the differing intensities of the two sites will have interesting implications for measuring exchange rates from offset-saturation experiments. The contributions of the magnetization of each individual site to the total or single observed 7: magnetization will differ according to the population difference in the sites, as reflected by the relative intensities of the two individual resonances in the slow exchange regime. Gutowsky and coworkers'." showed from the Bloch equations early in the development of chemical exchange that for two sites A and B in fast exchange. the total observed magnetization M is the sum of the individual magnetizations of each of the sites, M.4 and M B , weighted by the individual site populations p 1 and p~
where and PB are the fractional populations of sites A and B respectively such that PA p~ = 1. Expressions for determining rate constants from exchange contributions to observed line widths for unequally populated systems in the fast exchange limit have been derived from the formal solutions to the Bloch equations modified for chemical exchange.48-50 These equations relate each rate constant to the site populations, chemical shift difference between sites, and spin relaxation times TI and Tz. For example. the forward rate ~ A - \ is B given by3.48
+
k,, = p p ~ ~ ( A u ~ , ) ' ~ ' ~
cch
where is the exchange contribution to the measured T2. It is assumed that TI = Tr in the absence of exchange and that the values of TI for each site are equal, i.e. TI = T ~ = A T ~ Bso , that can be calculated from the following relationship
ch
1 - 1
zxchT2
1 TI
(7)
where T I and TZ are the relaxation times measured directly by
Chemical Exchange in Unequally Populated Systems
J. Phys. Chem., Vol. 99,No. 48, 1995 17341
1."" M. the offset-saturation method in the present case. In eq 6 , AWAB is the chemical shift difference between sites in units of radians 0.90per second. Approximate expressions for determination of fast 0.80rate constants such as those above were scrutinized by numerical calculations by Gutowsky and c o - ~ o r k e r s and ' ~ shown to be 0.70accurate for the determination of fast exchange rates, but they 0.60are subject to serious systematic errors if used to obtain rates in the region near coalescence. Accordingly, the offsetsaturation technique was employed in the present case only in the fast exchange region well above the point of coalescence, at temperatures above the point of maximum exchange broadening. 0.10 In order to calculate rate constants for the cis-trans isomerization of furfural from offset-saturation experiments in the fast exchange regime by means of eq 6, it is necessary to know the 0.OO-b 260 4bo 600 ado Idoo12bo Irradiation Resonance Offset (Hz) relative site populations or the equilibrium constant. The use of population-weighted stereospecific long range scalar coupling Figure 4. Example of an offset-saturation experiment performed on constants has long been used in conformational analysis to the aldehyde proton of 2-furfural at a temperature of 262.5 K. Data points are indicated by x, and the solid line represents the best-fit data. determine the relative populations of rotamers or conformers Irradiation time was 75 s, preacquisition delay time was 1.O s, and the and barriers to rota ti or^^'-^^ and has been applied to the strength of the irradiating field yB2/2n was 92 f 2.4 Hz. T I = 16.8 conformational analysis of 2-furanaldehyde and similar 0.05 S; Tz = 2.5 f 0.04 S. m o l e ~ ~ l e s A . convenient ~ ~ ~ ~ alternative ~ ~ ~ ~ to~ the ~ use ~ ~of ~ ~ - ~ ~ small averaged coupling constants in the fast exchange regime TABLE 1: Rate ConStants k,-, for the Cis-Runs Isomerization of Furfural as a Function of Temperature is provided by the exchange-averaged chemical shift. For a two-site system in the fast exchange limit, it is well known that T(K) K k-t % error method a single exchange-averaged line will occur at the population177 0.1 0.2 6.5 selective-inversion weighted mean resonance frequency, which may be given in 182 0.1 0.44 7.3 selective-inversion terms of the chemical shifts and populations for each of the 190 0.11 1.6 10 selective-inversion individual sites3~18~20 as 195 0.13 3.25 10 line shape line shape 205 0.15 11.3 10 210 0.2 30 10 line shape = P A W A + PBWB (8) 215 0.3 48 10 line shape x lo2 15 offset-saturation 230 0.32 1.12 where Wobs is the experimentally observed or exchange-averaged 235 0.32 2.63 x lo2 10 offset-saturation resonance, P A and p~ are the temperature-dependent fraction 240 0.36 4.16 x lo2 3.4 offset-saturation populations of sites A and B, respectively, and W A and w g are 250 0.44 8.60 x loz 2.0 offset-saturation 262.5 0.5 2.79 x 103 1.5 offset-saturation the chemical shifts for the individual sites A and B, respectively. 3.2 offset-saturation 275 0.68 7.28 x lo3 In order to determine W A and W B , in the fast exchange regime, 282.5 0.8 1.08 x 104 2.5 offset-saturation it is necessary to extrapolate the low-temperature chemical shifts 3.8 offset-saturation 292.5 0.86 1.64 x lo4 into the region of fast exchange, assuming the difference AWAB 5.7 offset-saturation 300 0.97 2.71 x lo4 is invariant with t e m p e r a t ~ r e . ~ , The ' ~ , ~low-temperature ~ alde6 offset-saturation 310 1.2 4.05 x 104 317.5 1.5 6.03 x lo4 hyde chemical shifts for the cis and trans isomers varied linearly 10.5 offset-saturation with temperature, as measured with respect to internal TMS, The rate constants were measured using the technique indicated in and the chemical shift difference of approximately 50 Hz was the method column as described in the text, and the errors in each rate independent of temperature within experimental error. The lowconstant are given in the error column. The errors quoted for the rate constants determined by the offset-saturation and selective-inversion temperature aldehyde chemical shifts were extrapolated into the methods represent approximately 2 standard deviations, while the errors fast exchange regime, and the equilibrium constants (K= ptra,,l for the line shape fits were determined visually. pcis, where prransand pcis are the relative populations of the cis and trans conformers, respectively) were determined from the chemical shift difference between sites in frequency units and observed average (a&) and extrapolated chemical shifts for the equilibrium constant determined in each case from the each site as19920351 observed and extrapolated chemical shifts according to eq 9. An example of offset-saturation data is given in Figure 4 for K = w A - webs an experiment performed at a temperature of 262.5 K. Ad(9) - wB ditional details regarding the implementation of offset-saturation experiments and the analysis of data are given in the Experiwhere Webs is the chemical shift of the major (cis) isomer, and mental Section. CUB is the chemical shift of the minor (trans) isomer. Anet and B a d 9 have proposed a method for obtaining Results and Discussion equilibrium constants and exchange rates from the point of maximum line broadening in systems which are very unequally The assignment of the major isomer as the cis conformer in acetone25,28~29~31 was verified by an NOE difference experiment populated (> 10: 1). It is interesting to note that the validity of at 170 K. Additionally at 170 K, the TI for the minor site as such an averaging of NMR parameters in the fast exchange limit has recently been a source of some controversy.60s61The offsetdetermined by an inversion recovery experiment was 2.8 s f 5.7%, while that of the major site was 2.3 s f 5.1%, where the saturation method was accordingly applied herein to the errors represent the 95% confidence limits. exchange-averaged aldehyde proton resonance over a temperRate constants for the cis-trans isomerization process &-, ature range from approximately 230 to 320 K, with rate constants for the cis-trans isomerization kc-, calculated from determined at various temperatures are given in Table 1, together eq 9, with a value of AVAB= 2n AWAB= 50 Hz used for the with any associated error, the equilibrium constant, and the I
::"
+
Bain et al.
17342 J. Phys. Chem., Vol. 99, No. 48, 1995 TABLE 2: Values of the Thermodynamic Activation Parameters for the Internal Rotation of the Cis-Trans Isomerization of Furfural" AH* (kJ mol-') AS* (J K-' mol-') E, (kJ mol-') 40.0 i 1.0 -26.8 i 5 . 2 41.9 i 0.9
" The errors represent two standard deviations
\
4
k--20.00 -
"1,IC
-30.001 -35.004 0
1
2
3
4
5
6
lOOOfT
Figure 5. Eyring plot of In(k,-,lT) vs (lOOO/n for the cis-trans isomerization of 2-furfural. The rates have been reduced by the preexponential factor. Points x represent experimental data, and the solid line represents linear regression line about the average of the values of 1000/T. k~ is the Boltzmann constant, and 12 is Planck's constant. The general agreement between the three distinct methods of rate measurement. as evident in the overall linearity of the data, is apparent. method by which the rate constants were measured. The errors in the table represent the 95% confidence limits. The error in the line shape fit is estimated to be on the order of lo%, as determined visually. As indicated in Table 1 and illustrated in Figure 2 , the extent of the intermediate exchange regime is rather small, with the fast exchange regime entered rapidly as the temperature is increased. Line shape methods are thus of limited applicability in the present system. It may be seen that the rate constants given in Table 1, as obtained over the temperature range of some 140", cover several orders of magnitude, from 0.2 to 6 x loJ s-I, with the rates determined using the offsetsaturation method alone spanning a temperature range of almost 90". The utility of the offset-saturation method in this particular study is accordingly apparent. The thermodynamic parameters for the internal cis-trans isomerization process can be determined from the rate data given in Table 1, using linear regression methods, and standard Arrhenius or absolute rate theory. These parameters are given in Table 2, where the errors represent 2 standard deviations. The energy of activation E, for the barrier to rotation for the isomerization was determined from the slope of an Arrhenius plot of In(/& vs UT. The linear regression yielded a value of 41.9 k 0.9 kJ mol-' for E,. Using absolute rate theory, the enthalpy of activation AH* and entropy of activation AS* were obtained from an Eyring plot of l n ( k , - , / ~ vs UT. AH* was determined from the slope of the Eyring plot, and a corresponding value of 40.0 f 1 .O kJ mol-' was obtained for this quantity. A value of -26.8 f 5.2 J K-' mol-' was obtained for AS* from the intercept of the Eyring plot. The error in AS* has been determined by a procedure previously described8 for shifting the origin of the Eyring plot to remove any covariance between slope and intercept.3R The Eyring plot, as shown in Figure 5, has been corrected for the pre-exponential factor h(kB/ h), where k~ is the Boltzmann constant and h is Planck's constant.?* The barrier obtained in the present study is in reasonable agreement with that of Dahlqvist and Forsen,26who obtained a
value of approximately 44.8 kJ mol-' for the barrier to rotation of 2-furanaldehyde in dimethyl ether over a much smaller temperature range (about 25 "C) using exclusively line shape analysis. In the transition state, the plane of the C=O aldehyde moiety is probably oriented at approximately 90" with respect to the plane of the furan ~ i n g , ' ~ . and ' ~ the relatively low rotational barrier may be attributed to the loss of resonance stabilization between the n electron systems of the furan ring and the carbonyl group in the transition state.?,'*." The value of -26.8 & 5 . 2 J K-' mol-' obtained for the entropy of activation of the internal rotation for the isomerization process implies a relative ordering of the transition state, perhaps due to increased interactions between the transition state and the solvent molecules. Large negative entropies of activation ( 5-20 J K-' mol-') have been observed for push-pull alkenes or ethylenes in polar solvent^,^.^"^^ which have been attributed to strong polar interactions between the transition state and the solvent, whereby the polarity of the solute is larger in the transition state than in the initial or ground state, which increases order in the solvent shell around the molecules in the transition ~ t a t e . ~The . ~ ~transition state in the present case may be subjected to a combination of electrostatic or dipolar and hydrogen-bonding interactions with the solvent.
Conclusions A combination of NMR methods, each best suited to the slow, intermediate, or fast exchange regimes, has been shown to be applicable to relatively simple unequally-populated exchanging systems, as demonstrated for the cis-trans isomerization of 2-furanaldehyde. The combination of offset-saturation method for determining fast exchange rates from T2 measurements, in conjunction with line shape methods and selective-inversion experiments for measuring slow and intermediate exchange rates, respectively, gives access to a range of rate constants extending over several orders of magnitude. The utility of the offset-saturation method in particular, which is able to extend the upper limit of rate measurement beyond that accessible by line shape analysis, is highlighted in systems such as that studied here, where the exchange is predominantly in the fast exchange regime.
Experimental Section The furfural was obtained from Aldrich and used without further purification. A sample of approximately 10 wt 9% furfural in acetone-& (MSD Isotopes, 99.8 atom % D) with a drop of tetramethylsilane (TMS) added as an internal reference for chemical shift and line width measurements was prepared in 5 mm medium-walled NMR tube, degassed with several freeze-pump-thaw cycles, and sealed under vacuum. The NMR experiments were performed on a Bruker AC-300 spectrometer at a magnetic field of 7 T, using a 5 mm 4 nucleus probe, with 'H being the observed nucleus in all the experiments reported herein. Temperatures were controlled with a BVT 2000 temperature controller and checked by inserting a copperconstantan thermocouple in a 5 mm NMR tube into the probe. The temperature was controlled to within f 0 . 5 K. The selective-inversion experiments were performed using a n/2--t-,z/2 excitation sequence.I3 The transmitter frequency was placed on the resonance corresponding to the major site, as discussed above, and the value of 5 was set to 1/(2AV4~), where AVABis the difference in frequency between the two lines, measured as 50 Hz. Following the excitation, the system was allowed to relax for a delay time, and the spectrum was then acquired with a x/2 pulse. Typically, 15-20 delay times were used per experiment. The selective-inversion data were ana-
Chemical Exchange in Unequally Populated Systems lyzed with the C program CIFIT version of the program SIFIT," using a 486 personal computer. The free induction decays for the spectra used for the line shape analysis in the intermediate exchange region were transferred from the spectrometer to an IBM PSI2 microcomputer using the program NMRLINK and then processed offline with the spectral-processing computer program NMR286 on a 486 personal computer using the time-domain fitting procedure described above.17 The offset-saturahon experiments were performed as described previously, using the proton homodecoupler in the highpower range to provide the saturating rf. The irradiating field yB212n was calibrated using the single-spin double-resonance experimentI6 as described previously, using the isolated TMS resonance signal, and the values employed were on the order of 100 Hz. Satellite signals adequate for decoupler calibration could readily be observed in a single scan. For the offsetsaturation experiments, the TI for the exchange-averaged aldehyde proton signal varied from approximately 12 s at the lowest temperature to 30 s at the highest temperature. Thus, irradiation times ranged from approximately 60 s to 150 s, with a preacquisition delay time ranging from 1.0 to 3.0 s, respectively, used prior to acquisition of the signal. The free induction decays were then acquired using a n12 pulse with a sweep width of 10 kHz or a dwell time of 50 p s . The combination of B2 and sweep width or dwell time was chosen to ensure that relatively small decoupler flip angles were used.'6,66 The offsetsaturation experiments were performed without spinning of the samples. An average of 16 scans was accumulated for each experiment. An average of 30 irradiation resonance offset values was used in each offset-saturation experiment and distributed around the resonance position according to the partial derivative sampling criteria,I6 with the majority of the offsets located close to the expected value of the half-width at halfheight of the curve of intensity or M,as a function of irradiation offset. The intensities or z magnetizations were measured relative to the value of the irradiation resonance offset furthest from resonance, which was used as an absolute intensity standard. The computer program DIPPER,I6 a nonlinear least-squares fitting procedure utilizing the linearization technique for nonlinear a n a l y s i ~ ~written ~ - ~ ~in Turbopascal, was used to determine the T I and T2 values from the offset-saturation data, using a 486 personal computer.
Acknowledgment. This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). References and Notes (1) Gutowsky, H. S.; Holm, C. H. J. Chem. Phys. 1956, 25, 12281234. (2) Jackman, L. M.; Cotton, F. A. Dynamic Nuclear Magnetic Resonance Spectroscopy; Academic Press: New York, 1975. (3) Sandstrom, J. Dynamic NMR Spectroscopy; Academic: London, 1982. (4) Kaplan, J. I.; Fraenkel, G. NMR of Chemically Exchanging Systems; Academic: New York, 1980. (5) Anet, F. A. L.; Bourn, A. J. R. J . Am. Chem. Soc. 1%7,89,760768. (6) Inglefield, P. T.; Krakower, E.; Reeves, L. W.; Stewart, R. Mol. Phys. 1968, 15, 65-86. (7) Orrell, K. G.; Sik, V.; Stephenson, D. Prog. Nucl. Magn. Reson. Spectrosc. 1990, 22, 141-208. (8) Bain, A. D.; Duns, G. J.; Ternidden, S.; Ma, J.; Werstiuk, N. H. J. Phys. Chem. 1994, 98, 7458-7463. (9) Szymanski, S.; Witanowski, M.; Gryff-Keller, A. M. Annu. Rep. NMR Spectrosc. 1978, 8, 227-289. (IO) Binsch, G. J . Am. Chem. SOC.1969, 91, 1304-1309. (11) Muhandiram, D. R.; McClung, R. E. D. J . Magn. Reson. 1987,7I, 187-192. (12) Gesmar, H.; Led, J. J. J. Magn. Reson. 1986, 68, 95-101.
J. Phys. Chem., Vol. 99, No. 48, 1995 17343 (13) Bain, A. D.; Cramer, J. A. J. Magn. Reson. 1993,A103,217-222. (14) AUerhand, A.; Gutowsky, H. S.; Jonas,J.; Meinzer, R. J. Am. Chem. SOC.1966,88, 3185-3194. (15) Deverell, C.; Morgan, R. E.; Strange, J. H. Mol. Phys. 1970, 18, 553-559. (16) Bain, A. D.; Duns, G. J. J . Magn. Reson. 1994, A109, 56-64. (17) Bain, A. D.; Duns, G. J. J. Magn. Reson. 1995, A112, 258-260. (18) Sutherland, I. 0. Annu. Rep. NMR Spectrosc. 1971, 4, 71-235. (19) Gutowsky, H. S.; Saika, A. J . Chem. Phys. 1953, 21, 1688-1694. (20) Eliel, E. L. Chem. Ind. 1959, 568. (21) Stewart, W. E.; Siddall, T. H. Chem. Rev. 1970, 70, 517-551. (22) Kessler, H. Angew. Chem., Inr. Ed. Engl. 1970, 9, 219-235. (23) Hofner, D.; Lesko, S. A.; Binsch, G. Org. Magn. Reson. 1978, 11, 179- 196. (24) Neuman, R. C.; Woolfenden, W. R.; Jonas, V. J. Phys. Chem.1969, 73, 3177-3180. (25) Abraham, R. J.; Siverns, T. M. Tetrahedron 1972,28,3015-3023. (26) Dahlqvist, K.-I.; Forsen, S. J . Phys. Chem. 1965, 69, 4062-4071. (27) Internal Rotation in Molecules; Orville-Thomas, W. J., Ed.; John Wiley: London, 1974. (28) Martin, M. L.; Roze, J.-C.; Martin, G. J.; Fournari, P. Tetrahedron Lett. 1970, 39, 3407-3410. (29) Roques, B.; Combrisson, S.; Riche, C.; Pascard-Billy, C. Tetrahedron 1970, 26, 3555-3567. (30) Chadwick, D. J. J . Chem. Soc., Perkin Trans. 2 1976, 451-452. (31) Petrongolo, C. Chem. Phys. Lett. 1976, 42, 512-516. (32) Led, J. J.; Gesmar, H. J . Magn. Reson. 1982, 49, 444-463. (33) Orrell, K. G.; Sik, V. Annu. Rep. NMR Spectrosc. 1993,27, 103171. (34) Forsen, S.; Hoffman, R. A. J . Chem. Phys. 1963,39, 2892-2901. (35) Hoffman, R. E.; Forsen, S. Prog. Nucl. Magn. Reson. Spectrosc. 1966, 1, 15-204. (36) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes in C. The Art of Scientijic Computing; Cambridge University Press: Cambridge, 1988. (37) Seber, G. A. F.; Wild, C. J. Nonlinear Regression; Wiley: New York, 1989. (38) Draper, N. R.; Smith, H. Applied Regression Analysis, 2nd ed.; John Wiley and Sons: Toronto, 1981. (39) Bain, A. D.; Cramer, J. A. J . Phys. Chem. 1993, 97, 2884-2887. (40) Reeves, L. W.; Shaw, K. N. Can. J. Chem. 1970,48,3641-3653. (41) Allerhand, A.; Gutowsky, H. S. J . Chem. Phys. 1964, 41, 21152126. (42) Reeves, L. W. In Dynamic Nuclear Magnetic Resonance Spectroscopy; Jackman, L. M., Cotton, F. A., Eds.; Academic: New York, 1975; p 83-130. (43) Stilbs, P.; Moseley, M. J. Magn. Reson. 1978, 31, 55-61. (44) Anderson, W. A. Phys. Rev. 1956, 102, 151-167. (45) Baldeschweiler, J. D. J . Chem. Phys. 1964, 40, 459-472. (46) Tomlinson, G. J. Magn. Reson. 1983, 52, 374-385. (47) Abragam, A. The Principles of Nuclear Magnetism; Clarendon Press: Oxford, 1961. (48) Piette, L. H.; Anderson, W. A. J . Chem. Phys. 1959, 30, 899908. (49) Meiboom, S.; Luz, Z.; Gill, D. J . Chem. Phys. 1957, 27, 14111412. (50) Swift, T. J.; Connick, R. E. J. Chem. Phys. 1962, 37, 307-320. (51) Pople, J. A.; Schneider, W. G.; Bernstein, H. J. High-Resolution Nuclear Magnetic Resonance; McGraw-Hill, Inc.: New York, 1959. (52) Sheppard, N.; Turner, J. J. Proc. R. Soc. London A 1959,252,506519. (53) Gutowsky, H. S.; Belford, G. G.; McMahon, P. E. J . Chem. Phys. 1962, 36, 3353-3368. (54) Schaefer, T.; Veregin, R. P.; Laatikainen, R.; Sebastian, R.; Marat, K.; Charlton, J. L. Can. J . Chem. 1982, 60, 2611-2616. (55) Dahlqvist, K.-I.; Forsen, S. J . Phys. Chem. 1965, 69, 1760-1761. (56) Benassi, R.; Folli, U.; Mucci, A.; Schenetti, L.; Taddei, F. Magn. Reson. Chem. 1987, 25, 804-810. (57) Roques, B.; Combrisson, S. Can. J . Chem. 1973.51, 573-581. (58) Fraenkel, G.; Kolp, C. J.; Chow, A. J . Am. Chem. Soc. 1992, 114, 4307-4314. (59) Anet. F. A. L.: Basus. V. J. J. Maan. Reson. 1978, 32, 339-343. (60) Jones, D. H.; Kurur, N. D.; Weiteiamp, D. P. Bull. Magn. Reson. 1992, 14, 214-218. (61) Anet, F. A. L.; Freedberg, D. I. Chem. Phys. Lett. 1993,208, 187192.
(62) Dreir, C.; Henriksen, L.; Karlsson, S.; Sandstrom, J. Acta Chem. Scand. 1978, B32, 282-285. (63) Berg, U.; Sjostrand, U. Org. Magn. Reson. 1978, 11, 555-560. (64)Meinpeter, E.; Heyndenreich, M.; Chattejee, S. K.; Rudorf, W. D. Magn. Reson. Chem. 1994, 32, 473-479. (65) Sandstrom, J. Top. Stereochem. 1983, 14, 83-181. (66) Bain, A. D.; Duns, G. J. Bull. Magn. Reson. 1993, 15, 64-69. JP951678H
