Harold M. Bell Virginia Polytechnic institute and State University Blacksburg, 24061
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NMR Spectral Analysis An experiment involving complete lineshape analysis of a two-site exchange problem
One of the most interesting aspects of nmr spectroscopy is its application to the study of time-dependent exchange phenomena. This technique has been quite thoroughly covered in the literature (1-51, and some experiments have appeared in this Journal (6, 7). However, several factors contribute to the exclusion of this subject matter from most undergraduate curricula. First, structure determination is the application of nmr which is stressed most a t the undergraduate level, and time may not permit other applications. Second, nmr instrumentation capable of making variable temperature measurements is not likely to be on hand. Finally, the lineshape analysis required to extract kinetic data from the spectra involves computer analysis, and the programs and/or computing facilities may not be available. The experiment described below is designed to remove a t least some of these difficulties.
B E S T TRU
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System Description and Theory
At room temperature, the spectrum of N,N-dimethylactamide shows separate peaks for each methyl group. In dilute 1,1,2,2-tetrachloroethane at 30% these peaks appear at 2.06, 2.93, and 3.04 ppm. The N-methylsignals at 2.93 and 3.04 ppm are discrete, owing to the fact that partial double hond character of the C-N hond restricts bond rotation, and confines the methyl groups in different environments, one cis and the other trans to the carbonyl. The harrier to rotation is low enough that as the temperature is raised, the rate of interchange of the methyl groups by bond rotation increases to the point that they cannot he distinguished on the nmr time scale, and the peaks coalesce. Several methods for the determination of the rate constant for such an interconversion are discussed in the references listed above. In this experiment complete lineshape analysis will he used. The rate constant for bond rotation a t each temperature will be obtained by comparison of computercalculated plots of lineshapes with the experimental curves. The usual Arrhenius plot then provides the energy of activation for the process. Experimental
Measure the spectrum of a 5%solution of N,N-dimethylacetamide in 1,1,2,2-tetrachloroethanea t 0°C. This allows determination of the frequency difference, and linewidths, id the absence of exchange broadening. Measure the spectrum at higher temperatures, such that 34spectra are taken below and 3 4 above the coalescence temperature.' In no case go ahove 120°C. A sweep width should be chosen such that the horizontal scale is about 5-8 Hzlin. Spectral Analysis
Extraction of the "mean lifetime," T , and thus the reaction rate constant, 1/(2r), from an experimental spectrum involves comparison of computer-generated plots of lineshapes (calculated as a function of r ) with the experimental curve. This comparison can be performed visually; the program CLAUTX, written by Binsch is suitable for generating the faimly of theoretical curves needed ( 1 ) . Alternately, the value LFull-sealecopies of 100 MHz spectra are available upon request. 2The program, which is written in Fortran, is available upon request. If a platter is not available, the printed output alone can be used rather effectively.
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DMR R T 63 DEGREES Cornputw plot of expenmentalspecrmm (x),and best least-squaresfit ( s m w h curve) for N.Ndimethylacetarnideat 63'C.
of r can be determined directly by computer, using a leastsquares curvefitting routine. In this case the experimental spectrum is entered in digital form, and the computer finds the value of T corresnonding to the best fit to the exoerimental data. The prugrsm CI.AI:'I'X has hem modified t(, perform this calculation: a s3mdr of the dotter outuut is shown in the figure.2 The activation energy for the hond rotation can he ohtained from the usual Arrhenius plot of In k versus 1/T. A rather good straight-line plot is ohtained, with an activation energy in good agreement with the more reliable literature values (8,9). Additional Work
The rate constant a t the coalescence point, i.e., the temDerature at which the minimum between the methyl signals banishes, can he determined by the equation k = raulJ2. AD is the nonexchanging chemical shift difference, ohtained by measuring the separation between the signals a t O°C.This equation can be easily tested by comparing the rate constant thus obtained with the rate constant taken from the Arrhenius plot at the coalescence temperature. The computer programs discussed ahove can also generate curves for a given r value as a function of Au (and thus Ho). Therefore. - - ~ - - ~ - -the - ~exneriment can he used to illustrate the effect of magnetic field strength on the temperature range amenable to studv. The student should observe that lines which have become too narrow at high temperature for an accurate determination of r would he broadened. and therefore suitable for analysis, if a spectrometer with greater magnetic field strength were used.
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Literature Cited (11 B ~ ~ sG.. c in ~ ."Topin in Stenochornistry."vol. 3. IBdilorr: Eliel. E. L.. end Allinger, N. I,.). Wiley-Inforscience. New Yurk. 1968, pp. 97-192. F. A. L.,and net, R., in ',Determination of Orpnic Structures by Physical (21 Methods." Vol 3. IBd~Lors:Nschod. F. C., and Zuckerman. 1 . J.1. AcadernicPrsss. New Yurk, 1971. pp. 346353. 1%).Johnmn,C. S. Jr., in "Advancer in Magnetic Resonance." Vol. I, IEditnr Waugh, J. S . 1 . A e a d e m i c P r e ~ r . NYork, ~ ~ 1 9 6 5 . p ~ 33-102. . (4) K ~ B I E C H , . . A ~ ~ cPh ~e m . ~ n r e r n o t~. d . 9,219 . 119701. ( 5 ) Juhnson,C. S., Jr., and Moreland. C. G.,J.CHEM. EDUC., 50,477 119731. (6) Sucrates,G.,J. CHEM. EDUC.,dl, 575 (19671. 17) Leyden. 0. E., and Morpan. W. R., J. CHEM. EDUC.,46,169 (19691. 181 Stewart, W. K a n d Sidda1.T. H.111. Chsm. R l u . 70.517 (19701. 19) Neuman.R..and Jonas, V., J. Om Chem.. 39,929 11974).
Volume 53, Number 10, October 1976 / 665
