ch&miccrl in/trumentation
edited by FRANK A. SETTLE.JR. virginia~ilitary~itute Lexington. V A 24450
The Fourier Transform in Chemistry-NMR Part 4. Two-Dimensional Methods Kathryn R. Williams and Roy W. King University of Florida, Gainesville. FL 32611 In previous articles in this series (1-3) the fundamental concepts of pulse NMR have been presented.' Simple single-pulse experiments (1.2) and multiple-pulse experiments such asDEPTand the attachedproton test (3) are all examples of one-dimensional spectroscopy. This article will conclude the series with an examination of some of the mast important types of twodimensional s o h a . These methods have expanded even funher the great powera of nuclear magnetic resonance for the elucidation of molecular structure. The term one-dimensional refers to experiments in which the transformed signal is presented as a function of a single frequency, e.g., the range of Larrnor frequencies of either the orotons or the carbon-13 nucle~in the molecule. By analogy, in a twodimensional spectrum the coordinate axes correspond to two frequencj domorns. In most cases these are two chemical shift ranges, but sometimes one axis represents a range of spin coupling constants. The ohserved simal. which is a function of hoth constitutes a third dimension. There are several ways of presenting the spectral data, as will be shown below.
withlH decoupling added during the second delay period. In 2-D J spectroscopy each segment of the spin echo sequence is called t112, so that the entire evolution period emresponds to the tl time domain. The usual acquisition period now constitutes a second time domain, called t ~(Note . the use of lower case t's to avoid confusion with the relaxation times TIand T2.) In the APT seouence onlv one value is assigned tochedeiay interval'toproduee the desired differentiation of the carbon multiplicities. In J spectroscopy a series of experiments is performed, each with a different tl delay. The tl's are ineremented in a regular manner (e.g., the first tl might he 2.3 ms, in which case the second would be 4.6 ms, the third 6.9 ms. etc.). and a seoarate FID is stored for e k h value. ( ~ o t e ' t h a tfor each value of t l the FID is stored in a separate memory block. This should not be confused with the usual practice of signal-aueraging several FID's for each tl to attain the required signallnoise ratio.) As mentioned above, the two-dimensional data set pro-
duced by this pulse sequence contains two time domains: the acquisition period, tn, during which the FID's are digitized and stored, and the array of variable delays, which is effectively "digitized" by the incremental spacing of the tl values. Suppose that a total of 128 t, values is used, and that they are successively incremented by 2.3 ms. At the end of the experiment there are 128 stored FID's, each of which is then Fourier transformed to give 128 spectra. The fust 12 of these are shown in Figure 2. The frequency axis is labeled fz, because its Fourier partner is the tz domain. In this case the sample (CHCL) consists of only one type of carbon, and each broadband-decoupled spectrum contains a single peak a t 77.0 ppm. The figure shows that hoth the height of the peak and its sign vary regularly with tl. As deserihed earlier in relation to APT, the reason is the J coupling, which modulates the signal during the first half of the t, interval. This periodic behavior is demonstrated (Continued on page A126)
J Spectroscopy Although it is used less than other methods, C H J spectroscopy serves as a good introduction to the fundamental concepts of 2-D NMR. The most common oulse sequence, which is the same as that for the APT experiment, is reproduced in Figure 1,
Figure 1. Pulse seqequence tor 2-0 J sP0cb-oSW (gated dempler method). with the segments renamed according to their usual 2-D designations. As discussed previously (3), the euolution period, which is divided into two equal parts hy the 180' pulse, is the familiar spin echo sequence
Figure 2. l3C O
P
B of~CHCll
showing Me effect of varying Me length of t, in Me 2-D J pulse sequence.
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more clearly in Figure 3, where the 128 heights of the peak a t 77.0 ppm are plotted versus their respective t l values. The regular oscillations give the plot the appearance of an FID, especially since the envelope of the oscillations decays as the length of t~ increases. Indeed, the plot does correspond to an FID, but the time domain variable is the value o f t , instead of real time during data acquisition. Just like a true FID, this time domain function can he subjected toFourier transformation to give the corresponding frequency spectrum. The vector picture for APT (ef. ref 3, eq 2 and Fig. 4) shows that the peak heights have a cosine dependence on the delay interval. This simple trigonometric function transforms directly to give two lines, i.e., the familiar doublet pattern of lines for the splitting of the carbon by one proton. So far only the tl variations at the frequency of the peak in each 13C spectram have been considered. Now suppose that the data are manipulated to Fourier transform the t, domain for the entire f i frequency range. The overall process is shown pictorially in Figure 4. The data points comprising each FID acquired in tn farm a row of a matrix, with iach row rorresponding to a different value of I , . In this example the initial matrix is made uu oi 128 rows of 8192 tl data points, one row ior each of the 128 t~ increments. The first Fourier transformation operates successively on each row to generate the second matrix of 128 frequency (f,) spectra with 4096 real points per row. Looking now a t the second matrix, each column contains 128 data points which are a function of the time tl, e.g., one columncontsins the amplitudes of the peak a t 77 ppm, which vary sinusoidally as shown in Figure 3. To prepare for the second Fourier transformation, the matrix is then transposed so that the columns of the second matrix become the rows of the third matrix. As shown in this example, to save time and disk storage space the number of tl increments was less than the number of data points acquired during tz, as is the normal practice. The appearance and digital resolution of the resulting 2-D spectrum are improved if some zero filling is performed a t this point in the data analysis, and in some 2-D techniques (e.g., H-H correlation) zero filline to form a square matrix is required. In this &ticular example 128 zeros &e added (one zero fill) to each row of the transposed matrix. Because of the relatively small number of tl increments that is usually dictated by time and memory conatraints, special apodizotion functions, such as the sine-bell, are often applied before the second Fourier transformation to enhance the spectral resolution in f, and improve peak shapes. Finally, the 4096 rows are Fourier transformed with respect to t, to give 4096 fi "spectra". The counteracting effects of zero filling and Fourier transformation preserve the 128 points in the f l domain. There still remains the problem of displaying the results in a usable manner. Figures 5a and b show the two common means of presentation. Both have fi plotted horizontally, although this is not always the case. Figure 5a is a stacked plot, in which
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Journal of Chemical Education
the axes for successive f l spectra are displaced horizontally to give a three-dimensional appearance. Stacked plow are sometimes used in J spectroscopy, but for most 2D NMR work a contour plot, as shown in Figure 5b, is preferred. Each contour line represents a certain intensity value, just as a toooeraohical mao shows lines of eaual alti,. tude abuw sea level. Where a peak occurs in the third dimension the contour lines congregate to form a spot. Figure 6 shows a C-H J spectrum of ethyl benzoate. Understandably, the newcomer to 2-D NMR may find the contour plot a bit perplexing. In a C-H J spectrum the carbon chemical shift information (in ppm) is presented along the fi direction (horizontal in this example), and the C-H spin coupling (in hertz) is shown separately in the fi direction. If the fi axis is collapsed, the projection on the f 2axis is a series of peaks a t the various carbon chemical shifts. For convenience a one-dimensional completely decoupled carbon spectrum is presented parallel to the f2 axis. In the Jspedrum the multiplets are effectively turned by 90' about the chemical shifts of the corresponding carbons. The quartet and triplet from the CH3 and CHs resonances are observed at 14 and 61 ppm. They are clearly spread out in the f i direction, and the spacings between the spots (64
.
.
Hz far the auartet and 75 Hz for the triolet) are equal rb one-half of the corresponding C-H coupling conatants: Aside from making the J values somewhat easier to measure in a crowded spectrum, the splitting8 in these multiplets provide little new information. For this molecule the greatest benefit of the J spectrum is the assignment of carbon multiplicities, especially for the aromatic peaks which overlap badly in the coupled spectrum (ef. ref 2, Fig. 7). From peak intensities in the 1-D spectrum, we may immediately assign the 130 ppm peak to the suhstituted ring carbon, because saturation and low nuclear Overhauser enhancement both contribute to a reduced peak height. This assignment is confirmed by the appearance of only a single contour spot a t this chemical shift in the J spectrum. The two intense peaks a t 128 and 129 ppm and the weaker peak a t 132 ppm all show the two apots characteristic of methine carbons. Assuming similar TIand NOE enhancement values for the protonated ring carbons, it is legitimate to compare their intensities. The 132 ppm peak has lower intensity in both the l-D and contour plots and corresponds to the 4carbon of the ring. The 2,6 and 3,5 carbon peaks are more intense but are not diatinguiahable from each other in this spectrum. Thereassignments will be refined later m a n ~
~
Figure 5. C-H J spectrum 01 chlwofwm. (a1Slacked plot. Each of Me stacked t, spectra conespondsto a particular value of h; shown are spectra from h = 77.94 to t = 76.06 ppm. (b) Contw plot.
example of another 2-D method. Although 2-D J spectroscopy provides a good introduction t o two-dimensional NMR, it and its homonudear analogue are now seldom used. They were among the first 2-D NMR methods to he developed, and, because of the great importance of multiplicity data in structure elucidation, were once considered an enormous boon to chemists.As was shown for ethyl benzoate (cf. ref 3, Fig. 9 ) , carhon multiplicities can now be obtained via the DEPT sequence. The DEPT sequence is most successful when the tau delay is exactly equal to lI(2Jc.d and, because there is almost always a spread of J wluea,a compromise must usually be made. However, the IIKPT experiment requires an order of mamirude leas time than a 2-D C H d snectruk and. even though " the edited subspectra may show some toreign peaks, DEPT is preferred when instrument time is limiwd, as is almost always the cnse. ~~
~
~.~ ~~
though this simple sequence can he malyzed mathematically without too much difficulty, the effects that are produced cannot be shown bv means of vector nictures. The case followinn &ort exnlanation foi the ~~~~- of a coupled two-proton system may provide the reader with some understanding of the behavior of the nuclei. Readers who are interested in a more in-depth description are encouraged to consult refs 5, 6, and 7, which present the detailed mathematical analysis. As discussed previously for other sequences, the initial relaxation delay and 90: pulse prepare the spin system hy rotating the equilibrium magnetization to the -y axis. At this point the system can be described mathematically as a sum of terns each containing the spin of only one of the two protons. The spins then euolve during the variable t, period, i.e., they precess un~~~
~
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~
~~
der the influences of bothchemical shift and mutual spin-spin coupling. As ohserved previously for J spectroscopy, the precession modulates the signal which is eventuallv ohsewed durine t?.-In - addition. the mutual coupling of the spins has the mathcmatical effect of converting some of the single spin terms into products containing the magnetization components of both nuclei. It is these product terms that eventually result in the desired features of the 2-D spectrum. Following the evolution period there occurs the second 90: pulse, which constitutes another essential part of the sequence; the mixing period, as it is called, has not been encountered in previous pulse sequences. This pulse has the effect of distributing the magnetization among the various spin states of the coupled nuclei. The mathemat(Continued on page A128)
H-H Correlation Spectroscopy (COSY) That J spectroscopy is less popular today than it was formerly is due to the availability of other more useful 2-D experiments. These methods supplement, and have partially replaced, the interpretation of spin coupling patterns for determining the sequence of chemical bonds in a molecule. Relationships among honded atoms can now he obtained much more readily by means of a dass of 2-D methods called COrrelation SpeetroscopY. The anonym "COSY" is sometimes used in reference to this entire family of techniques, hut the name is properly resewed for hamanuclear H-H correlation spectroscopy. The pulse sequence applied to the protons in COSY is: relaxation delay-90:-t,-90:-t,(aequisition) As in 2-D J spectroscopy, the tl interval is successively ineremented and tp corresponds to the acquisition of the FID. Al-
Figure 6. G H J specbum of ethyl benzoate.
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ical description of this romplicatrd system is the sum of n large numher uf terms, many of which involve undetectable components of the magnetization (i.e., they involve multiple-quantum coherenees (3)).Those terms that do result in observable signals during the tz detection period are of two types. The first set, whieh forms a rather uninformative part of the resulting 2-D spectrum, includes the terms in which the magnetization h a s been modulated throughout the sequence by the precession of only one nucleus. In the 2-D plot (to be described in detail below) these terms produce the diagonal peaks. The new and exciting result of the pulse sequence comes from the mathematical transformation of the product terms described above. The resulting expressions contain the Larmor frequencies of both coupled nuclei. The magnetization represented by these terms has been modulated (in a sense "labeled") by the chemical shift of one nucleus during tl and, after the mixing pulse, by the precession of the other nucleus during t?. The resulting off-diagonal peaks, or cross peaks, show the correlations of pairs of nuclei via their spin-spin coupling. To became familiar with the appearance and interpretation of a homonuelear correlation spectrum it is useful to examine the contour plot for a simple molecule, such as the~. 300-MHz oroton-oratan COSY soectrum of 2;J-dibromothiophene, as shown in Figure 7 . Because the proton chemiral shift region is plotted m both directions, the plot ~
~~
The useful information comes from the squares of contour spots that lie entirely off the diagonal. The coordinates of the crws peaks are the chemical shifts of the nuclei that are coupled to each other. For this compound there are just two cross peaks, at 21o1,2080 Hz and at 2080,2181 Hz, on oppositesidesof the diaxonal. In thiasimplecase the chemical shiftshf the counled nuclei are read directlv from the f~. and f? axes.. but.. when interpreting a complex spectrum, it is often helpful to draw lines parallel to the axes to show the relationship of a cross peak to the correlated diagonal peaks. A practical example of the utility of H-H correlation is given in Figure 8, which shows the structure and 300-MHz l-D proton spectrum of the antiviral drug Ribavirin in DMSO-dc. In this solvent the OH orotons do not erchange, and so fhe CH-O'H spin splittings arp virihlr. For structure dctermination of derivatives of this molecule it was necessary toassign all the proton peaks. The singlet at 3.4 ppm is from a water impurity and that a t 8.9 ppm can be assigned with confidence to the triazole proton. The hroader singlets a t 7.86 and 7.64 ppm are most likely from the primary amide NH protons, nonequivaleni because of restrict; bond. The multied rotation about the CN plets near 3.52 and 3.63 ppm may he assigned to the CS methylene group as the most shielded protons in the molecule, nonequivalent because of the chiral nature of the rihofuranoside ring. The remainder of the spectrum consists of three doublets between 5.2 and 6.9 ppm, a triplet at 4.9 ppm, and three very similar quartets between 3.9 and 4.4 ppm.The triplet comes from the C-5 OH, the doublets correspond to the CI praton and the OH protons on carbons 3 and 4, and the quartets arise from the ring protons on C2-C1. The assignments in the C r C l reeion are bv no means clear from the oneZimensionh soeetrum. but each multiolet correrponds to m e proton, and first-order analysis is valid, that is, the quartets arise from splitting by three protons with approximately equal couplrng constants. The protons can be asslgned by analysis of the two-dimensional H-H correlation
.
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.
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contour plot whieh is presented in Figure 9. When approaching a 2-D spectrum it is necessary to start from a known point of reference, in this case the Cs methylene group a t 3.s3.7 ppm. Cross peaks connect the methylene multiplets to the triplet at 4.94 ppm (confirming its assignment to the Cs OH) and the quartet at 3.97 ppm, which must belong to the C, ring proton. There is a further correlation between the quartet at 3.97 ppm and that at 4.15 ppm. The latter must come from the C3 proton, which in turn is related to the 5.22 ppm OH doublet. The remaining quartet, at 4.36 ppm, is assigned to the Cz proton by another cross peak with the Ca proton. The only remaining amhiguity is the assignment of the 5.60 and 5.83 ppm doublets, both of which show coupling to the Cz proton. One of these is the C, proton and the other the OH on carbon 2. The splittings of the 5.22- and 5.60-ppm doublets are similar, whieh favors the 5.60ppm peak to he the OH. This assignment was confirmed by a C-H HETCOR experiment (see below). Off-diagonal spots also occur at the coordinates of the peaks that were assigned to the NH protons. This shows that they are coupled, even though no splitting is seen in the l-D spectrum. The NH peaks are broad (ahout 5.5 Hz, probably from unresolved coupling to the 14N) and the two-bond HN-H coupling of about 1Hz is obscured. This example demonstrates the great utility of H-H correlation. One COSY experiment can identifv all oairs of couoled . orotons, whieh otherwise would require a separate 1-Dselective decoupling experiment for each nucleus-a very tedious process. Cross-peaks can be observed for cuuplings that are not ohervablein the l-Dspectrum, for example, hetween the NH prm~nvofHibavirin, or for protons with chemical shift differences too small for spin decoupling to be practical, for example, the Cs methylene protons.
. .
.
Heteronuclear Correlatlon Spectroscopy In the H-H COSY experiment the 90°
Figure 7. Contour plot of me H-H conelation spec. bum (COSY) of 2.3dibrornothiophens. is symmetrical about the diagonal. The coordinates of the diagonal peaks are the same in both directions and occur a t the Larmor frequencies of the protons in the sample; the projection on each axis (not shown) is the ane-dimensional proton spectrum. Along each dimension the mutual coupling splits each proton resonance into a douhlet, and the result is a square of four dots for each diagonal peak. Two of the four spots lie exactly on the diagonal, but the other two are dia~lalaeedfrom it. It is obvious that nothing new is learned from the diagonal peaks, and in many cases the outlying members of a diagonal square can ohscure other more important features of the spectrum.
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Journal of Chemical Education
Figure 8. 300-MHz proton NMR spectrum of Ribavirin in DMSOds. inset: expanslan of 3.4-5.9-ppm region.
pulses are both applied to the protnn spins. If the second 90' pulse in a COSY sequence is accompanied by a ~imultaneous90' pulse on the carbon-13nuclei, the situation is very simrlnr. except that one set of spins ia now rarhon. By monitorini: t h e l T FlD'ndwing t , , followed bv the usual double FT data manipulation, a two-dimensional C-H correlation spectrum can be produced. The basic puke sequence for 2-D G H correlation is: 1 ~ :
Delay-90'-t,-90" 90°-t,(acquisition)
1 3 ~ .
The 90° preparation pulse tips the proton magnetization to the xy plane. During the t~ evolution period the proton spins precess due to their chemical shifts and to coupling to other nuclei, protons and carbons alike, but in this case it is 'H-I3C coupling that produces the desired correlations. The simultaneous SO0 mixing pukes transfer part of the proton magnetization to the carbons. Since this magnetization was "labeled" by the proton precession frequencies during tl, the '3C signals that are detected during tr are modulated by the chemical shifts of the coupled protons. The C-H correlation, or HETCOR, apeetrum of ethyl benzoate is shown in Figure 10. Since the carbon FID's are acquired during t z , carbon chemical shifts are expressed along the fi axis, with the modulating proton shifts along f ~A. contour spot occurs a t the intersection of the shift positions of a directly bonded C-H pair. The plot resembles, but is much simpler than, an H-H COSY spectrum. One reason is the absence of diagonal peaks, which are not produced by a heteronuclear spin aptem. Also, C-H spin coupling is not observed along the fi axis because, according to normal practice, broad-band decaupling of the protons has been applied during tz. (The sequence with decaupling is a little more complicated than that shown above, but the fundamental concepts involved are the same.) H-H coupling does affect the spedrum, broadening the spots somewhat along the fi axis. The low-intensity peak a t 130 ppm has already been assigned to the substituted ring earbon by C-H J spectroscopy. The HETCOR spectrum makes this assignment immediately obvious, because there is no corresponding proton correlation spot, showing that carbon to be quaternary, like the earbonyl. Similarly, the ambiguity between the 5.60- and 5.83-ppm peaks in the proton spectrum of Ribavirin, above, was resolved by a HETCOR spectrum in which the 5.83 doublet showed a one-bond C-H correlation spot while that a t 5.60 did not. As mentioned above, correlation spectroaeopy has largely replaced 2-D J spectroscopy, and the reasons are obvious when one considers the additional infonnarion available from the HRI'COR spectrum. Functional groupaasignrncnt is rnoreritraightforward in the proton than in the earbon spectrum, and proton spectra are easier to integrate accurately. Information from the proton spectrum can then be used to assign peaks in a correlated carbon soectrum. For examole. .~ -~~~~~ ~. thk multinlet at 8.1 onm comes from the two mostvd;shielded.&omaric protons, which must be the crtho pair beenuseof the deahrelding effect of theester group; a spot relates them to the carbon (Continued on page A130)
.~
~~~~~
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in/trumentotion peak at 129 ppm. The one-proton peak at 7.45 ppm arises from the para proton and correlates with the carbon at 132 ppm. By elimination, the multiplet st 7.35 ppm is assigned to the meta protons, and a spot relates them to the corresponding carbon peak at 128 ppm. Another simple molecule, tmns-cinnamaldehvde. , ..orovides an examole of the utility of C-H correlation in the concurrent interpretation of "C and ' H spectra. The 1-D ' H and 'C spectra (Fig. 11s and b) are both ambiguous. In the proton spectrum the douhlet at 9.7 ppm is readily assigned to the aldehyde proton, a, and the doublet of doublets at 6.7 ppm arises from the splitting of proton b by both the trans hydrogen c and the aldehyde proton. The problem is the precise location of proton c, which is partly obscured by the aromatic peaks. Likewise, in the carbon spectrum the peak at 193.6 ppm is clearly the aldehyde carbon and that at 152.7 ppm corresponds to one of the alkene carbons, but the other alkene peaklies in the confused region between 128 and 134 ppm and is not easily assigned. The C-H correlation spectrum of cinnamaldehyde, shown in Figure 12, allows the assignment of both proton and carhon resonances. The peak at 134 ppm must be the substituted ring carbon because of the absence of a spot at its shift position. Alkene proton c, whose 1-D doublet is buried in the aromatic ring multiplets, is clearly located by its correlation with the carbon peak at 152.7 ppm. The other alkene carhon, which in the 1-D spectrum is almost coincident with an aromatic peak at 128ppm, is located via its correlation with the doublet of doublets at 6.7 ppm in the proton spectrum. These assignments are in accord with the known parallel chemical shift trends of 13C and 'H in a polarized carbon double bond. It is interestine. ... however. that the oroton huried in the aromatic region does nor mrrespmd to the rarlwn that lies among the ring resonances. C H correlation spectrwcopy makes even more useful the complementary information available from 1-D proton and carhon NMR. The aromatic peaks remain to be assigned. Although the 1-D carbon spectrum was not run under conditions conducive to accurate integration, it is still safe to distinguish peaks corresponding to one and two CH carbons by their relative intensities. Of the almost superimposed peaks near 128 ppm, the more shielded one has already been assigned to alkene carbon b. The other. which isabout twice as intense, relates t i the aromatic proton multiplet at 7.5 ppm, which belongs to the ortho hydrogens. The cluster of proton peaks at 7.4 ppm shows spots corresponding to the 129- and 131ppm carhon peaks. The latter may be assigned to the para carbon because of its lower intensity, leaving the 129-ppm peak as the resonance of the meta ring earhons. Close inspection of the correlation spots shows that the para proton is slightly less shielded than the meta protons. Complete assignment of all 'H and '3C resonances in this simple molecule at 7 T, a common value of Bo,would have been much more difficult without the information provided by the correlation spectrum. A130
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Ftgure 9. W H mlatlon specbvmof Rlbavirln. ia)Fullspectrum. (b)Expanslonof 3-6 ppm region. Dataare pl&d in the absolute value W e
Carbon-Carbon Cowelatlon Probably the mast powerful technique far structure elucidation is 13C-I3C correlation, better known as 2D-INADEQUATE (for Incredible Natural-Abundance QoublE&!Ahturn Transfer Experiment). Anslogous to 'H/13C correlation, INADEQUATE identifies the chemical shifts of directly bonded I3C atoms. The experiment is designed to detect only signals from molecules containing two adjacent '3C nuclei. Since this condition occurs in only about one molecule in lo4, the method suffers from Incredibly Low sensitivity and is used less frequently than H-H COSY or HETCOR. Suppression of signals from molecules containing a single I3C is accomplished by
selective detection of double-quantum eoherences (DQC's (3)),which require that at least two spin-112 nudei be present. The basic I3C INADEQUATE pulse sequence is: Delay-90°-r12-1800-~l%900-tL-900t,(acquisition) The sequence is somewhat different from those encountered so far because a major part, i.e., the entire section from the relaxation delay through the second 90° pulse, is devoted to the preparation of the spin system. The f i s t 90' pulse turns the 13Cz axis magnetization to the xy plane. During the r interval. which is held constant for ~~- all - t. values, the nuclei precess under the influ: ence of both chemical shift and I 3 G Y ! J ~~
~
~
coupling, hut the inclusion of the 180° pulse in the middle of the 7 delay (the familiar spin echo segment) refocuses the chemical shift component. The final preparation step is the second 90° pulse, which converts part of the magnetization of the coupled nuclei into douhle-quantum coherences. During tl, douhle-quantum coherences undergo chemical shift precession; the frequency of rotation is the sum of the precession frequencies of the two coupled spins. At the end of the tl evolution period a 90' pulse converts the DQC's hack to observable magnetization, which is detected during the usual t z acquisition period. A contour plot of the 2-D INADEQUATE spectrum of menthol is shown in Figure 13. Even though this is a homonuclear n r e l a tion experiment, diagonal peaks do not appear because the terms that produce them are eliminated when only double-quantum coherencea are converted into detectable signals. (This hints that perhaps diagonal 'HCOSY can be ~imilarlvsupoeaks in 'H, pressed. The use of douhle-quantumfiltering will he discussed later.) Since a directly bonded pair of carbons (e.g., A and B) is mutually connected by a douhle-quantum coherence in t l , the two nuclei share the same f,. Two small spots, corresponding to the 1% satellites of each nucleus of the pair, appear a t their common fi value. Thus, to determine which nuclei are directly connected, it is only necessary to draw a line between spots a t each fi frequency. To grasp the power of this technique, the reader is invited to construct the carhon skeleton from this plot. I t helps to letter each peak arbitrarily, starting from the least shielded as CA,which from its shift should he the alcohol carhon. Write %"on apiece of paper, then ohserve the line already drawn on the plot to the spots for CB and write "CB" with a bond joining it to CA. Carbon A also correlates with carbon C, and Cc correlates further with CE.Following the remaining correlations will produce the carbon skeleton of menthol absolutely a priori (but with no stereochemical information as shown in the structure in the figure.) Nuclear Overhauser Effect Correlation The three correlation experiments described so far have demonstrated that 2-D NMR is a powerful method for detecting nuclear connections via J coupling, hut there are other ways by which nuclei can he related. One of the most important of these is the dipolar interaction, which is the principal mechanism of relaxation for spin-112 systems. Nuclei that relax each other by the dipolar mechanism can exhibit the nuclear Overhauser effect, in which there is a transfer of spin polarization from one nudeus to the other. The key ward here is transfer. Like J coupling, the NOE can also act as a means of transferring chemical shift information from one nucleus to another in a suitably designed pulse sequence. The ahservation of the nuclear Overhauser effect for two nearby nuclei was described in the second paper of this series (2). In that context the use of the NOE to increase peak intensities in the I3C spectra of small molecules was emphasized. Determination of the presence (and magnitude) of NOE's is also very important in structural studies, especially in the proton systems of macromolecules. The dipolar mechanism is a dired through-space interaction with an
Figure 10. C-H correlation spectrum of ethyl benzoate inverse sixth-power dependence on the internuclear distance. As a consequence, the observation of an NOE for a certain pair of protons is a gwd indication that they are Located close to one another (within ahout 0.5 nm) in the molecule. Nuclear Overhauser effects mav he measured in a one-dimensional experiment by selectively irradiating one proton resonanre and observing any intensity changes of the other proton peaks, in the same way as selective decoupling is used to detect J cou~
~
~~~~
~
plings. This technique is very tedious, requiring exacting adjustment of the irradiation power and frequency. NOESY, the NOE (and rhyming) equivalent of COSY, allowsall NOE's, and hence all spatial correlations, to he observed simultaneously with only a single instrumental setup. In the 2-D NOESY spectrum the cross peaks occur at the chemical shifts of nuclei that relax each other hv the dioolar mechanism and which must therefore be in close spatial proximity. (Continued on page A132)
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Inftrumentotlon The NOESY pulse sequence is similar to that for H-H correlation (COSY), but in NOESY the mixing period also involves a delay internal, called ,r and a third 90° pulse is needed. The resulting sequence is: Equilibration Delay-9O0-t,-90°7,-90°-tz(acquisitian) As in COSY, the equilibration delay and initial 90° pulse prepare the nuclei by tuming z axis magnetization to the xy plane. During the variable tl evolution period the nuclei are frequency-labeled by their chemical shift precession. (J coupling also occurs, but the ohsenration of such effects is not the desired result in NOESY. The elimination of COSY cross peaks is a major concern in the design of an actual experiment.) The second 90' pulse rotates part of the magnetization hack to the z axis. During the r, interval (usually constant) the longitudinal magnetization is allowed to relax. This produces a mixing of the magnetization of nuclei that are related by the dipolar relaxation mechanism, thus correlating their chemical shifts. The third 90° pulse is needed to rotate the vectors hack to the xy plane, where they can be detected during the tz acquisition period. In general, the NOESY technique is most important in the study of biological macromolecules, in which secondary and tertiary structures are dictated by interactions of nonbonded atoms (8).Fortunately, these are also systems for which NOESY is mast experimentally feasible. The long correlation times (short TI'S) of large molecules result in negative NOE's whose absolute magnitudes are often larger than those of the positive NOE's found in small molecules
~ i g ~Ir1.e(a) 1 0 and (b) 1 0 1%
of mnsclnnamaldehyde
(9).
With careful adjustment of mixing times, etc., NOESY spectra of small molecules can still be obtained, and often can be quite useful. An interesting example is the m e t h a w late ion, a very simple molecule, but one in which it is not possible tomake an unamhiguous assignment of the methylene protons on the basis of coupling constants alone. The NOESY spectrum of sodiummethacrylate in DzO is shown in Figure 14. As expected for a small molecule, the NOESY cross peaks are very weak. The only ones visible in the spectrum are indicated by circles; they relate the methylgroup at 1.8 ppm to the methylene proton a t 5.3 ppm. This is a good indication that the nuclei are close together in space, i.e., that the 5.3-ppm methylene proton is the one cis to the CHB. A chemical shift calculation using standard emprrrcal rules agrees with this assignment, which will be dircussed more fully in connection with phase-senaitive 2-D NMH.
Experlmental Conslderatlons In 2-D NMR In the second paper in this series (2) severa1 important experimental considerations were described. Two-dimensional work introduces a number of new complications that should properly he introduced a t this point; however, this section may be skipped on first reading and referred to when the reader is about to tackle a real 2-Dproject.
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Figure 12. C-H wrrelatlon apecbwn of m~innamaldehye.(a) h~llspectr 154gprn region.
(b) Expansion of
me 126
tion hack to its original position at the start oft,. It is then detected during ts as if it had never evolved during tl. This is the equivalent of a dc signal at the detector, which in a 1-D spectrum is observed as azero-frequencyglitch (asignal exactly at the spectrometer frequency). In 2-D work the result is an objectionable row of contour spats at the exact center of the f i axis. Fortunately, these aria1 peaks may he suppressed hy shifting the phase of the ini) tial 90" pulse by 180° (e.g., +x, - x , +x, in alternate FID's acquired for each tl value. Addition of the FID's cancels the constant magnetization, hut the mathematical terms that give rise to the cross peaks are unaffected. This is an example of the use of a phase cycle to produce or suppress a particular feature in an NMR spectrum. The alternate 180° shift of the 90' pulse is analogous to the part of the four-step CYCLOPS phase cycle used to cancel the zero-frequency glitch in a 1-D spectrum (2). Phase cycles can hecome quite complicated in 2-D NMR, sometimes reaching 32 steps, and the cycle must be repeated foreach tl increment. This is unimportant if a large number of transients must he accumulated for each increment to improve the signallnoise ratio, hut the extra repetitions can result in a considerable increase in the total experiment time if no signal averaging is otherwise needed.
. ..
Flgue 1 3 . 2 0 INADEQUATEapscbum of mntlml.
Flgurs 14. NOESY spsctrunof d l u m methawlam In DzO.Thediagonalpeaksat 4.8.3.3, and 1.0 ppmere due to HDO and unknown lmpurltles. The data ere planed In tha absoluh,value mode.
Axial P& So far the effecta of relaxation on twodimensional spectra have been ignored. As in 1-D work, relaration proves to he a twoedged sword. A short TIgreatly reducea the total experiment time, an important factor in 2-D spectroscopy, because relaxation delays can he reduced or eliminated. On the other hand, if TI is not large compared to t l ,
some relwtion will occur during the 2-D evolution period. This mean8 that a certain amount of z magnetization will have built up when the t, interval ends. One might think that this would merely reduce the amplitude of the signal observed during tl, but in H-H and C-H correlation experiments the 90° mixing pulse rotates this magnetiza-
Frequency Dlscriminatlon in t, and PhaseSensitive Data Acqulsltlon For reasons described in ref 2, it is desirable to place the transmitter frequency, fa, at the center of the spectral window in a 1-D spectrum. Quadrature detection is then needed to determine the direction of rotetion of the magnetization vectors relative to the rotating coordinate frame. Since quadrature detection is standard on modern FTNMR spectrometers, it is used routinely to acquire FID's in tz. However, it is also necessary in 2-D work to use a data acquisition method that is sensitive to the direction of rotation of magnetization in t ~Some . ~ technique ia therefore needed to achieve the same effect in tl as is performed hy conventional quadrature detection in tl. Ina Ptandard quadrature detector the signal passes simultaneously through two phase-sensitive detectors whose reference The2-D equivasignal. are90°0ut of lent involves acquiring two successive FID's for each tl increment with a 90" phase difference between the pulses which precede the tl interval. These two phase shifts are combined with 180" shifts (for axial peak suppression) to yield a minimum four-step phase cycle for each tl value. In the simpler, hut less desirable, operational mode the signals are comhined prior to storage in memory. Unfortunately this scheme for fi sign discrimination produces 2-D peaks with very undesirable shapes (4, pp 205, 206). In a simple 1-D experiment, Fourier transformation of the FID produces peaks that are linear combinations of the absomtion (real part of the transform) and dispersion (imginnrypart) modes. It is relativelv eaav. bv adiustine the combinations. to phase-cob& the spectrum so that pur; absorption peaks are displayed. (2). However, when two successive Fourier transformations are performed, the absorption and dispersionmodes are inextricably mixed, and it (Continued on page A134)
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in/trurnentotion is impassible to separate them by any presently available phase-correcting procedure. In order to eliminate the phase problem without resorting to the outmoded practice of placing the transmitter frequency at the edge of the spectrum, the data may be presented in the absolute mlue mode, where the signal is the square root of the sum of the squares of the real and imaginary parts. Since the amplitude information is always positive, no phase correction is necessary. Unfortunately the absolute value display causes considerable peak broadening (cf. ref 2, Fig. 6d) which can cause severe overlap problems in complicated spectra. The peak tailing can he reduced by the use of suitable nnodizotian before Fourier transformation. -r hut, as in l-D spectroscopy, the improvement in resolution is offset by a considerable loss in signallnoise ratio. The phase problems partially solved by the ahsolute value method can he eliminated entirely by the use of phase-sensitiue data acquisition. Two FID's are collected with phase-shifted pulses, exactly as described above for tl sign discrimination, except that they are stored in separate blocks of memory in mueh the same way as the signals from the two channels of a quadrature phase detector. After separate Fourier transformations the frequency data are combined in a prescribed manner. The real part of the resulting matrix contains only ahsorption-mode components, with pure dispersion-mode signals in the imaginary part. If the real part is displayed, the peaks are mueh narrower than those produced by the absolute value calculation. The t, sign discrimination occurs naturally, because the contributing spectra have opposite symmetry and the unwanted peaks (corresponding to quadrature images in a 1-D spectrum) cancel in the process of combining the spectra. At present two experimental procedures exist for the acquisition of phase-sensitive data. Both methods, and the data treatment, are described in a veryreadahle paper by Keeler and Neuhaus (10). The contour plot of a phase-sensitive HH correlation spectrum of Rihavirin is shown in Figure 15. Mathematical analysis of the COSY pulse sequence reveals that the cross and diagonal peaks have opposite phase character; if the cross peaks are displayed in the absorption mode, as they are here, the diagonal peaks must he in dispersion. The signs of the spots alternate in the cross peaks, although signs cannot he seen in amanachrome plot such as this. The resolution of the cross peaks is considerably hetter than in the conventional absolute-value COSY plot of Figure 9h. However, the overlap of the dispersion-mode diagonal peaks produces the familiar "angel-wing" patterns, which ohscure some of the cross peaks visible close to the diagonal in Figure 9h. In addition to the benefits of the narrower widths of absorption mode peaks, the phase sensitive spectrum provides the spectroscopist with valuable information that is Lost in the absolute value display. An example is the NOESY spectrum of sodium methacrylate. In the absolute value mode of display it is always difficult to determine if very weak cross peaks, such as those observed in Figure 14, are true NOESY signals. The
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Figure 15. Contour plot of H-H COSY specrmm of Ribavirln obtained in the phase-sensitive made: expansion of me 3-Wpm region.
Figwe 16. NOESY spectrum of sodium memacrylate obtained in the phasesensitive mode NOESY mixing time, 7,. also provides a period for transfer of magnetization by chemical exchange of the nuclei. Indeed, the same pulse sequence is the basis of 2-D exchange spectroscopy, which is very useful in the study of such reactions (4, pp 242-2431, In NOESY work there is always a possibility that cross peaks may be due to exchange processes instead of the desired dipolar relaxation effects. In addition, if experimental conditions are not ideal, cross peaks due to J coupling (COSY peaks) may appear. The long tails of absolute value diagonal peaks can also intersect to produce spurious contour spots. The situation is clarified if the phase properties of the spectrum are known. Figure 16 shows the phase-sensitive NOESY spectrum of sodium methacrylate. All the
peaks, bath diagonal and cross, appear in the ahsorption mode. As noted ahove, this would not be possible if the cross peaks originated from the J coupling correlations that m e COSY peaks. Although they cannot he observed in Figure 16, the positive and negative signs of the contours are also quite informative. Mathematical analysis of the pulse sequence shows that chemical exchange peaks must have the same sign as the diagonal peaks, whereas opposite signs are predicted for NOE peaks in small molecules (11). macromolecules the NOE is neea. (For . " tivr, and the diagonal and cross praks haw the same s i p . ) Separate plots of positive and negative conwursshow that if the diagonal peaks are made positive, then the eontours for the methylene-methyl cross peaks are negative, confirming that the cross
fied to reduce such interferences by adding an extra 90' pulse and some phase cycling. The modified version is:
DeIay-900-t,-900,900-t~(aquisition) in which the third 90° oulse follows the setond as fast as the instrument will allow. In this representation the subdcriprs showing the dirertionl of che pulses are omitced he. cause they are the subjects of the phase cycle and vary according to which step they occupy in the cycle. (The two successive 909 pulsea have different phases and are not eauivalent to a sin& 180' nulse.) 'AS was stated the end of the tl interval in a simple COSY experiment the spin system is described hy a complicated sum of mathematical terms, which are affected differently by the second pulse. Part of the magnetization that produces the desired cross peaks is converted into doublequantum coherence hy the second 90' pulse, while none of the magnetization that gives rise to the diagonal peaks follows the DQC pathway. In the simple COSY experiment, the magnetization that has been converted into DQC's is not detected, whereas the third 909 pulse in the modified sequence converts some of this "lost" magnetization hack into observable form. The phase eycling reinforces signals from the DQC pathway a t the expense of thase (the diagonal peaks) that are never involved in a DQC. This version of COSY is called Double Quantum-Filtered Wrrelation Spectroscop y (DQF-COSY), by analogy with the use of a filter to reduce noise in a quadrature detection system (2). Figure 17 shows the 3-6-ppm region ofthe DQF-COSY spectrum of Rihavirin (cf. Fig. 9b). Double-quantum filtration has completely suppressed the diagonal peak at 3.4 ppmfrom the water impurity and has accentuated the cross peaks relative to the diagonal peaks. An even greater benefit of DQF is the production of absorption-mode peak shapes for both the diagonal and cross peaks. Elimination of the dispersion-mode "angel wings" (cf. Fig. 15) further reduces the interferences from diagonal peaks in complicated spectra. In essence, the modified experiment uses both (1) a suitable pulse sequence to create the needed coherenees among the coupled spins and (2) a phase cycle to provide the required "pathway" for the desired part of the magnetization to reach the detector in preference to the undesired part. Multiple QuontumFilters, those in which coherenees ofmore than two coupled spins are selected, have been used to simplify spectra of large molecules, especially those of biological interest (13). ~~~
~
~
~~
~
~~~~~~~~~~~~at
Figwe 17. Do~bleqmnhlmfiltwred COSY specbum of Ribavirin: expansion of the 3-6-ppm region.
peak8 do indeed arise from NOE effects. The phase-sensitive spectrum also shows prominent cross peaks from the =CHZ protons larrowed). In the absolute value display (Fig. 14) these spots are obliteraced by the taih of the dragonal ppaks. These are by far the most intense cross peaks in t h spec~ trum, as expected from the inverse sixthpower dependence of the NOE on the internuclear distance and the close proximity of the geminal protons to each other. ~,
~
Artifacts in 2-0 NMR Often 2-D plots exhibit spurious peaks, which are collectively referred to as artifacts. Although there are several sources of artifacts, one of the most common is t l noise. Its causes are various long-term instrumental instabilities such as an unstable field-frequency lock, fluctuations in receiver gain, ncmreproducihle transmitter pulses, and irregular t, increments (12). Such instabilities are usuallv unnoticeable during- the short tz acquisition period, but they can hecome significant in the much longer period over which t, is ineremented. The effects, therefore, show themselves mainly in the fi dimension of the 2-D spectrum as undesired modulation of the fi peaks. This causes spurious ridges parallel to the f l axis wherever there are strong diagonal peaks, e.g., from solvent resonances. In Figure 14 the ridge parallel to fi on the 1.8-ppm CH3 peak is lengthened hy a t l noise contribution. (The phenomenon of t, "noise" should not he confused with the detector noise that is seen in one-dimensional spectra and that may be reduced by time-averaging. The signals producing t l artifacts in two-dimensional spectra have amplitude and phase characterisa cannot tics similar to the eenuine ~ e a k and be eliminated by signal awrapmg.) A wmmon technique for reducing artifacts in sperrra that are s,wmrtrical about ~~~~~~
~
~
the main diagonal (H-H COSY) or the middle of the f l axis (2-D J spectroscopy) is gymmetrizotion (also known as foldinghut not to be confused with false peaks arising from an improper digitization rate). Each point in the spectrum is compared to the corresponding point reflected across the midline, and, if both are nonzero, then they are both set to the same value. If the intensity on one side is zero, it is likely that the other point represents an artifact, and hoth points are zeroed. Because this procedure can give deceptive results, it is important to examine the spectrum before symmetrization as well as after (4, pp 224-225). Selection of Coherence Pathways In addition to the use of phase-shifted pulsea to achieve quadrature detection in tl, previous sections have shown the importance of phase cycling for the removal of troublesome signals in both one-dimensional (CYCLOPS) and two-dimensional (axial peak suppression) NMR spectroscopy. The pulse sequence for 2-D INADEQUATE also requires considerable phase cycling to isolate the double-quantum coherences. In any phase cycle the desired signal is selected preferentially over the undesired magnetization by its variation as the phases of the pulses of the sequence are varied. Almost any result can be obtained by devising a pulse sequence and accompanying phase cycle to select a certain coherence pathway to the final FID's. Although one must have a working knowledge of the quantum behavior of nuclear spin systems in order to understand these pulse manipulations, the fallowing concrete example should indicate the utility of such methods. mod deal of useIn -~ H-H COSY svectra. a ful information ran he masked hy strong diagonal peaks, often from the solvent resonanrea. The COSY requence may be modi-
Time Requirements By now it is clear that a 2-D NMR spectrum takes Longer to ohtain than a 1-D spectrum, since a 2-D plot is derived from an array of 1-D spectra. The run times for the 1-D and 2-D spectra shown in this series of papers are collected in the table. Some of these times are very long, stretching to 8 h or more. The situation is aggravated by the frequent need to repeat a run because of sample prahlems or unoptimized parsmeters. (It has heen said that 2-D stands for "twice-done".) The chemist will therefore (Continued on page A136)
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inrtrumentotion try to get all the information possible from 1-D spectra hefore attempting all but the most routine 2-D experiments. The total run time of a 2-D experiment is not simply the product of the acquisition time of a typical 1-D scan and the number of tl increments. In order to prevent the data from exceeding the available storage space, the number of data points in each tr acquisition is reduced fiom the 1600044000 used in a normal 1-D experiment. This degrades the digital resolution in the fn dimension, but in much 2-D work the resolution need only he enough to distinguish one chemically sbifted nucleus from another, without concern for spin splitting. Often 512 to 2048 data points are taken in the fi dimension, hut, as the tahle shows, nowhere near this numher of t l increments was used far any of the examples in this series. One must usually live with even less digital resolution in the f, dimension than in f2, or suffer extended acquisition times. For a constant spectral width, the digitization time is proportional to the number of data points acquired for each FID in tn. Thus, reducing the number of data points should result in a decrease in the time for each FID. However, this ignores the need to allow sufficient time for TIrelaxation, as indicated in the fifth column of the tahle. In most 1-D work a certain amount of saturation is permissible, and the tip angle is often optimized far beat signallnoise ratio with a zero relaxation delay ( E r s t angle). However, in 2-D work full 90" and 180' pulses are usually required by the pulse sequence. Failure to allow time to achieve equilibrium z-axis magnetization prior to the next repetition of thesequence leads toannoyingartifacts that may interfere with vital features of the spectrum.
Another factor leading to long experiment times is the phase cycling required by many 2-D sequences, sometimes as many as 32 transients for each tl increment. This dietates a minimum time per t~ increment, even for concentrated samples where signal averaging may not be needed to improve the signal/noise ratio. Finally, some experiments, such as 2-D INADEQUATE, have such intrinsically low sensitivity that many accumulations must be taken for each increment, even with a concentrated solution. The 2-D INADEQUATE example in the tahle has an acquisition time of over one day, which is not uncommon for this h e of exoeriment. Run times much longer than this are not really practical. since the signal, noise ratio is only proportional to the square r w t of the numher of accumulations. Long runs also tie up an expensive instrument for an appreciable fraction of its lifetime and are vulnerable to interruption by disasters, natural and otherwise. The time requirements of 2-D NMR are a major drswhack tocompletely routine useof the methods. Run timed can bederreased by increasing sample concentration, isotopic labeling, or even by buying an instrument with a higher magnetic field, all of which reduce the need for time-averaging. Hawever, there is a lower limit on the run time, which is dictated by the particular pulse sequence, the relaxation properties of the sample, and the digital resolution desired. The restrictions imposed by the computer system have not been considered, since they are steadily being lifted by improvements in technology.
..
Three-Dimensional NMR The 2-D spectra presented in this article
have been limited to simple, but instructive, examples. The pulse sequences cited are of greatest use in the structure elucidation of much more complicated molecules, such as those derived from natural products. Twodimensional NMR is used extensively in the study of biological macromolecules, and such investigations are becoming iucressingly popular with the availability of 400and 500- (and even 600.) MHz spectrometers. However, even with the greater spectral dispersion of the high-field instruments, 2-D contour plots from large molecules can he very complicated and hard to interpret. Just as overlap in a 1-D spectrum can be alleviated by adding another dimension, one answer to this problem is the use of a third frequency domain. The fundamental concepts of 3-D NMR are the same as those already set out for 2-D work. There are now three time domains: two of them (tl and tz) are successively incremented and the FID is acquired during tl. a t the end of the seouence. The total data analysis requires three aueceasrve Fourier transfornations to produce a spectrum wnh three perpendicular frequency domaim A typical 3-D pulse sequence can he considered as two 2-D sequences joined as links in a chain. In the example shown in Figure 18
COSY
/
I
Homo-J Spec
I
/IUl
Figure 18. Slmpllfied pulse sequence for Ihreedimn~lonalH-H COSYN spemoscopy.
Acuulsltlon rimer, ol Exwrlmenle Used In Thls Serlesa Part.
Figure
Experiment 1 0 Prom 1 0 Carbon 1 0 Carbon. no NOE
Compound
#of Transients
# ot tncrements
RelaxatlMl Delay (s)
Acquisition Time (h:m:s)
Ethyl Benzoate
Comments Optimal (Emst)tip angle use
Ethyl Benzoate
Ethyl Benzoate
Gated decoupllng, on during very long delay. to allow quantitatlon. Four spectra acquired. Dela needed lor peak Cancellation in edited spectra.
Emyl Benzoate
C-H Jspeotrum
tl-H COSY ti4 c o s y C H HETCOR G H HETCOR
2 0 INAOEOUATE NOESY PhassbensitiveCOSY
Long relaxanon delay required due to large T,. Rlbavirln Ethyl Benzoate han~4innamafdehyde Menmol
ne& Many ac~~m~latlons to compensate for very lo sensitivitv.
Sodlum Memacrylate Rlbavlrin
Doublelenglh data set fw all phase-sen~itl~e spectra.
Phasesensitive NOESY 4.17
Sodium Mmhaclylate Ribavlrln
WF-COSY (Phasesens.) 16 7.05 T i n 5 mm tuber on concernratedsolutions, i e . . 10.20%
All spectra were run at
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2
6:02:00
Wv, me parameters used weretypical, buf n n necessarily aptlmal.
-
the first 1ink.whichcontains the r l evolution period, is the H-H COS Y sequence. 'The 90° mixing pulse at the ~ n of d the COSY segment is also the start of the 2-D J sequence. After the ts evolution period the FID is acquired (ta). In the thrice-tramformed spectrum the proton chemical shifts are plaited in the fi and f i domains. with J couoline plortedin the jjdirertion.' In practice thr timp needed toacquire a 3Dsprctrumcan br prohibitively long (several days is not uncommon), because tl and tz must be incremented in a nested fashion, i.e., a full set o f t * increments must he obtained for each successive tz value. The data storage and computational requirements are also immense.. orocessine times of 6 h heing common. And, i i a 2-D contour plot p u b spots hefore your eyes, do not hazard a look at a full-blown R-D spectrum. The sheer volume of data presents a challenge to the human eye and mind! These experiments are more tractable if dataareacquired and/oran&zed in a selective manner. For examnle. in studies of bioloeical molecules the o;o&ns of interest are often thwe bonded to the amide nitrugens and the carbons alpha and beta to the peptide linkages in aprotein. A pulse that selectively excites only the nuclei in one of those regions can be used in the preparation period of the sequence. The spectral width (and hence the number of t l and tz increments) can then he decreased, thus reducingexperiment timm and data storage and processing requirements. The resulting spectra are also much easier to interpret. Readers who are interested in the details of 3-D NMR are referred to the recent article by Griesinger et al. (14). This brief overview of 3-D NMR eoneludes the oresent series of articles on the use of the gourier transform in oulse NMR spectrnscopy. The pulse sequences described in this and the previous paper represent onlya small fraction of the manymultiple pulse experiments now available, and new versions are regularly appearing in the NMR literature. At the time of writing, the most concise listing of t h e myriad sequences, with their respective acronyms, purposes, and major applications, is to be found in the article by Kessler et al(6). The interested reader is encouraged to consult that paper and the other excellent references cited in this series.
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Literature Cited 1. King, R. W ; Williams, K. R. J Chem.Educ. 1989, 66, A213. 2. King. R. W.; Wil1iams.K. R J Cham. Educ. 1989.66. A243. 3. Williams, K.R.: King, R. W. J. Chem. Edur. 1990,67, I.
.A..
Derome. A. E. Modern NMR Techniquesfor Chemistry Research: Pergamon: New Ymk, 1987. 5. Brey. W. S., Ed. Pulse Methods in ID and 2D LiquidPhas~NMR:Aeademic:San Diepo. 1988. B. K w l c r . H.: Gehrke. M.: Grieainger. C. Angem. Cham. Imt. Ed. Engl. 1988,27,490. 7. Emst. R. n.;Bodenhsu~cn, G.:Wakaun, A. Principles o/ Nuclear Magnetic Resomnee in Ons and n"o Dimansions: Oxford U n i ~ m i t y Oxford, 1987. 8. WBthrich. K. Acc. Chem.Rer. 1985.22.36. 9.
Morris,G.A.Mogn.Res. Chem. 1986,2d,371.
10. Keeler, J.; Neuhaua, D. J.Mag. A m 1985.63,454. 11. Crosnmun, W. R.:Csrlson.R. M. K. Tun-Dimensional NMR Spectroscopy; VCH: New York, 1987. 12. Freeman, R. A Hondbook of Nurhor Mopnelir Resononce'pp 27528%
N.: Ern% R R.; WBthrich, K. J Am. Chrm. Snc. 1986. IOB, 6482. 14. G r i m i ~ g e sC.; Sbrenaen. 0.W.: Ernst, R. R. J. Mag. Rex. 1989.84.11. 13. MUller.
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Acknowledgment We wish to thank W. S. Brey, Jr., for his continuing help and encouragement during the preparation of these articles.
' Phrases Mined In Uw glossary of NMR tenns (4are Italicized of their first appearance In the text. 2The pulse sequence (gated decoupling mem cd) used fathe ethyl benzoate C H J spscnum produces fi peaks separated by JIZ. An alternate pulse sequence (me spin flip methcd (5.pp 14-17)) can be used to produce heieronuclsar J spectra extra resolution Is needed. separated by J. if 3This need arises in experiments where the amitude 01 the f, signal is modulated as a functlon of 1,. e.g., H-H and C H correlation, INADEQUATE, NOESY, and C-H J specbosmpy with proton decoupling during ~cquisition.In hornonuclsar J specnoscopy and C H J spectra withoui decoupiing in 1, me signal is phase-modulated, and me sign discrimination occurs naturally.
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