The Fourier Transform in Chemistry Part 2. Nuclear Magnetic Resonance: The Sifigle Pulse Experiment Roy W. King and KaUwyn R. Wiiiiams UniversiIy of Florida, Gainesville, FL 3261 1 Thefirsttxtide in this series (1)discussed the fundamental concepts of pulse NMR spectroscopy. In this paper the use of FTNMR to obtain a single-pulse proton or carbon spectrum will he described. In this context "single" means that only one RF pulse is issued for each accumulated FID.
Data Acqulsltlon Figure 1 shows a typical sequence of events for a ~inglepulse and its associated data acquisition. After an initial delay to set up the in~trumentalconditions, the pulse is applied to the nuclei with the receiver off to prevent overload. Then the receiver is turned on, and after a very short dead time the free induction decay is digitized and added into the computer memory. The acquisition time should he long enough for the FID to have*decayedto a negligible level (a few times TJ,and, as shown in Figure 1, an optional delay may he needed to allow for TI relaxation.
pulses, given hy Ernst's equation (2, pp 16.5 166)
where a is the tip angle and tmpis the pulse ~enet.ition time. s~ectrometers will ..r.. ~ . ~Manv . ,~ ~ calculate the Ernst and? and the optimal pulse width from freD and a TIestimate 8 1 1 plied hy the operator. Like IR spectroscopy, NMR fits the definition of a "detector-noise-limited" measurement (3, which means that the process of time-meraging a large number of FID's results in a theoretical improvement in signallnoise ratio hy a factor equal to the square root of the numher of acquisitions, W/z. Because of this dependence it is relatively easy to improve the signallnoise ratio (whichis the factor that determines whether or not a peak i~visible) hy one or two powers of 10, hut any further increme requires an impractically long experiment time. It is, of course, vital that the relation of the spectrometer frequency and the Larmor frequencies of the nuclei not change during the accumulation process. Any spectral drift will a t hest cause line broadening, and at worae result in N superimposed, hut distinct.. s~ectra.In nractice this ~rohlemcan arise hecause of temperature.dependent chemical shifts, drift in the m8gnet. or movement of nearby magnetic objects such a the operator's chair. Of these effects, all but the first can be compensated hy field. frequency locking. The f=equency of i rewnance in the sample (usually from deuterium in the solvent) is compared to a fixed frequency derived from the master clock used to generate the spectrometer frequency, and any deviation is converted into a correction to Bo(2, pp 44-46). ~
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Figure 1. Seqmnca of events in a singie-pulsw experiment.
Signal Averaging The p&lacqui~itionl(delay) sequence is then repeated N times until the desired numher of transients has heen accumulated. To avoid saturation, the sum of the acquisition time and the relaxation delay, if used, hut the resulting should he ~everaltimes TI, long experiment times may make unreasonable demands on the available i n s t m e n t a l resources. For hest sensitivity there is an optimum combination of the tip angle, the TI relaxation time, and the time between
in the ranze of zero to a b u t lI3l.Wil Hz. ~ C c o r d i n ~ L ~ y q u i stheorem t'n (3),'mavoid aliasing (see helow) the sampling frequency (digitiza~ion rate)must be at least twice the highest frequency to he acquired. In modern spectrometers the RF pulse is always apuld he detectable. It i* tonoadvintage increase the input voltage so that the signal from a minor peak is acceptably digiti7ed. hecause the strong signal would then he truncated. A "clipped" FID leads to severe distortions and artifacts in the transformed spectrum (Fig. 3b), so automatic gain setting is often used in routine work to prevent overflow. Intense solvent resonances must be reduced in some way before digitizatiou, if a smallsample peak is to he observed. One way of doing this is to preaaturate the solvent peak hy selectively irradiating it for a time comparable to its TI with a low RF level (which is the Fourier equivalent of a narrow band of frequencies). A short intense RF pulse is then applied to excite all nuclei and the FID is acauired. Manv other techniques of solvent suppression are in use, especially for water elim~nationin samples of hiologicd interest. Another problem can arise from accumulating a large number of transients into memory so that the capacity of the computer word is exceeded. For example, it is not possible to add more than Z4 (i.e., 16) FID's containing a 12-hit fnU-scale sample signal into a 16-hit word hefore the word overflom. Since this also leads to severe prohlems in the transformed spectrum, word lengths of 20 to 32 hits are often used in NMR computers.
Zero Filling The concept of zero filling has heen introduced in a previous article (3). Because of the constraints on the acquisition time and spectrum width, the FID sometimes does not fit the FFT miterion that the numher of data mints be a Dower of two. In such a case zero filling tothenext higher powerof twois necessary, and most instrum~ntsperform this step automatically. At the discretion uf the operator, zero filling to one or more still higher powers of two can also help to improve the appearance of a spectrum that, hecause of a short acquisition time, was acquired with a limited numher of data points lcf. .~ eo ~,2). . The added zeros have the effect of interpolating extra poinL3 into the spectrum and of improving the dtgilol rewlution (the frequency interval hetween data point& 7ero filling is not a. cure-all, however. The FID should be sampled until it reaches a negligible value (several times G), but sometimes this is not practical. When the acquisition time is considerably less than this ontimum. the numher of mints acquired will not he suffic~entto describe the line shape adequately, and residual magne. tization in the xy plane may cause disturbances in the base line. No amount of zero filling after acquisition can rectify these
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problems.
Apodization The next step in the data processing is apodization, which was discussed at some length in relation to FTIR (5). The apodization functions are considerably different in NMR work, because the FID is a decaying signal. If the FID decays below the noise level much hefore the end of data acquisition, then a constant level of noise, hut no
signal, will be sampled in the latter pan of the Fll). To reduce the contribution of thk noise the FID is often multiplied by a de. creasingexponentid function, e+Ia (where= is equal to for hest sensitivity) prior to transformation. As sbovtn in Figure 4, when exponential multiplication is wed, the signallnoise ratio is im~roved.hut a t the expense of some additiGna1 lin; hroadenmg. A c~>mpromine among t he parameters of resoIut~nn,sensitivity, and experiment time is very common in spectral and analytical measurements. Most spectrometers allow the user to specify the value of the exponent in terms of the degree of line broadening produced. If the user is interested in improving resolution, the Lorentz-Gauss apodization (2, pp 2626) can be applied, but the original signallnoise ratio must he good for the technique to he useful. Many other apodization functions have been proposed (6, pp 9%111), but all have some disadvantages, including a need for intensive computation.
Phase Correction After multiplication hy the desired apodization function. the FID is subiected to Fourier transformalion a9 descriged previously in reference toquadraturedetection. I n that discussion it was assumed that the FIWs in the two data blocks represented the real and imaginary components of the magnetization with no mixing of the two form. This ided situation would produce absorption mode Loreutzian lines (Fig. 5a), which arise from the real uart of the transform. or dis~ersion m o d ~ l i ~ e s ( ~ i g u r e ifthei'magi&ry 5b), pan of the frequency spectrum were used. l'ure absorption mode line9 are required for spectral interpretation, since dispersion mode lines cannot be integrated and their hipolar nature and very long tails make closely spaced peaks difficult to distinguish. In practice pure ahsorption or dispersion mode lines are not nroduced. and the neak shanes in the two parts of the transformed spectrumare3kewed (Figure6a8b1due tocontribution* from both modes. This behavior oc. cum hecawe of an arbitrary difference in phase angle between the nuclear precession signal and the detector reference signal (not
Figure4. Atypical 13CNMR peak (a)wilh noap~lzalionand (b) subjeclec to exponentlai muitipil~tionwiorto Fouriertranslormation.The line broadening laam was 1.0 Hz.
b
F i p e 5, ~
n
I ilnezshapes. ~ (a) Abswplion mcde and (b) d i s p ~ i m d e . The ilne is 12 Hz wide at hall height.
(Continued on page A246)
shows spin-pin splitting due to the protons attached to many of the cmbons in the a m nound. One-bond 13C-'H c o u ~ l i n econrelated to the required 90Âphme difference between thc two phase detectors in q u a d m ture).Because the phasccrror contains hnth frequency-independent and frequency.de. pendent components, the peak shapes change progressively with increasing or decreasingchemical shift. The major contributors to the frequency-dependent error are the time lag hetween the application of the p d e and the start of the sampling of the FID (the "dead time" in Figure 1) and the effects of the pulse not being at the exact Larmor frequency of every nucleus. The phase aberrations can he corrected (Figure 6c) hy displaying a weighted sum (adjusted hy the operator or hy automatic phase COIrection software) of the real and imaginary parts of the transform. Usually the frequency-independent weighting is done on the most intense peak, and the frequency-dependent weighting is adjusted so that remote peaks are comectly phased. An alternative mode of display, which is often used in two-dimensional NMR, is the absolute "due spectrum shown in Figure 6d. This line shape represents the square r w t of the sum of the aauares of the real and imzwinarv .. parts. No phme correctLon 1s required, but the peak is .whsmtially wtder than the phased line in Figure 6c.
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The Frequency Spectrum A properly phased 13C spectrum of ethyl henzoate is shown in F i e 7. Prohahly the most noteworthy feature is the ohsewed nuclew itself. Carbon-13 has a natural ahundance of only l.l%, and, without isotopic enrichment, its resonances can harely he discerned from the n o i ~ in e a CW spectrum. The greatly improved signallnoke ratio of the F T spectrum is made possible hecause a large number of FID's (4lW in this example) can he accumulated. The total acquisition time was 11min, longer than the wan time of a swept spectrometer, hut the gain in spectral information is well worth the investment in time.
Spin I3ecoupling The ethyl henzoate awctrum in Figure 7
20 Hz and not alwam easy to distinguish from each other. Two-bond coupling to the adjacent methylene protons can just he ohserved in the expanded methyl quartet in Figure 7. In contrast. Fiewe 8 is the roto on-decoup l e d s p e c t m ~orethyl benzo&. During the acquisition of the "C spectrum (at 75 MHz in the 7.05 T magnetic fieldl, a second RF transmitter was used to irradiate the protons at 3GQ MHz. The proton irradiation was p u l e and phase-modulated to increase its effective bandwidth to cover the entire ranee of G H Droton chemical shifts. When suhTectedb kntinuous irradiation..the nro. tons are stimulated to flip their spins very rapidly. As a result of this broad-bad decoupling, the carbons experience only the average magnetic moment of the protons, and the resulting 13C resonances are not split. Without the complicationof spin-pin coupling the 13C chemical shifts are much easier to interpret, since a methyl quartet can extend over 375 Hz ( 5 nnm a t 75 MHz). The splntt~ngpattern5 In the coupled spectrum reveal the number of protons attached to each carhon, but the overlap of the spin multiplets from carbons close in chemical shift makes interpretation of the undecoupled spectrum of a large molecule almmt impossible. Of course, when only the decoupled spectrum is obtained, the coupling information is lost. In the past the technique of off-resoname decoupling was used to overcome this problem. A continuous-wave RF irradiation of lower power than that used for broad-hand decoupling is applied just outside, hut close to, the proton spectral region. The T!-'H multiplets appear partially collapsed, though somewhat distorted, and the carhon multiplicities can usually he determined because of the reduced overlap. Unfortunately this technique is not useful a t proton frequencies above 1GQ MHz because the decoupling effect falls off as the separation of the irradiating frequency and the proton resonance increases. Today much more satisfactory multiplicity assignment may he achieved by use of multiple-
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pulse tachniques such as the DEPT spectral editing m e t h d to be demribed in the third paper in this serie~. Aside from the decoupling, the spectra in Figures 7 and 8 were obtained under identical conditions. Comparing the two, there is an ohvious improvement in the signallnoise ratio in the decoupled spectrum. The increase in '3C aignal intensity may he seen most clearly hy comparing the heights of the methyl (13.9 ppm) and methylene (60.5 ppm) carhan peaks to that of the CDCh solvent (77.0 ppm). The solvent resonance, which k split into a k1:l triplet hy the deuterium (I= I), is not affected hy the proton decouplii process. In Figure I the central methyl and methylene peaks are only ahout one-fourth as high as the CDCL triplet, hut in the decoupled spectrum the ethyl group resonances are ahout 10 times as intense a8 those of the solvent. Part of this imnrove: men1 comes from the summing of all mem. hers of each spin multiplet into a single peak. Howevet, the increaw in peak tntensi. ty appears greater than would he expected solely on the basis of the collapse of the spin multiplets, and integration results prove that this observation is not simply an artifact of examining peak heights instead of areas.
Tim Nuclear O v e d u s e r Effect The extra enhancement of the NMR signal is due to the nuclear Owrhauer effect (NOE), which is another result of the irradiation of the protons. In addition to the immediate effect of averazinz .. of the roto on magnetic moment.., the decoupling process also saturates the 'Htransitions after a icw proton TIperiod8 (a few seconds). This equalization of the proton spin populations gives rise t o the nuclear Overhauser effect. As shown in Figure 9 a and h, irradiation of the protons results in a spin distribution which is contrary to thermal requirements. The system attempts to reestablish the equilibrium populations hy TI relaxation processes (Fig. 3c). Provided that r e l a t i o n occurs by the dipolar mechanism described previously ( I ) , a net increase in '3C signal intensity can he produced. The m b o n and proton do not have to he spin-pin coupled, hut, because they must relax each other by
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Figwe 6. A Iypleal NMR llne shape: (a)arX (b) the two prts of the transform& FID, ( 0 )the peak aflwr phaw m c t l o n , (d) the absolue value llne shape.
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Journal of Chemical Education
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the dipolar mechanism, the two nuclei must be in close spatial proximity. This means that careful proton-proton NOE studiw can provide useful information ahout internuclear distances within molecules and hence decide questions of configuration and conformation (2, Chapter 5). Quantitatively the nuclear Overhauser enhancement is expressed in terms of the relative increase in signal intensity, NOE = ( I - Io)lIo
(4)
where I and 10are the intensities with and
without the enhancement. The maximum value of the NOE is given by = o.bin170b
(5)
where 7in170bis the ratio of the magnetogyric ratios of the irradiated and observed nuclei. This ratio is 4.0 if protons are irradiated while l3C is observed. Thus, for 13C spectra the maximum NOE is 2, which means that the signal intensity is tripled. However. the maximum NOE is achieved only when qtrict requlremenb are met The r~quiqited ~ p o I e 4 ~ p oTI l e relaxation pathway is usually dominant for small molecules
in nonviscous solvents, hut when other mechanisms contribute to relaxation, less thanmaximum NOE is achieved for some or all of the observed nuclei. This can be an extreme disadvantage in spectra of nuclei, such aa 15N,with negative magnetogyric ratios. Irradiation of the protons then causes a negative NOE, which, if it is less than the maximum (which results in negative-going peaks), can lead to phial or complete loss of the signal. Quantitatlon In 13Cspectra the NOE can b8 very helpful in increasing sensitivity, hut, if the mbons have different NOE's, integration results will he erroneous. To avoid the problem of varying NOE's, the decoupler can he used in thegated mode, that is, it is activated only during the acquisition of the F D (Fig. 10). The p ~ o t o mare irradiated and experience rapid spin flips, but, hecause the spin populations change in a time of the order of the proton TI (which is usually longer than the acquisition time), there is little or no NOE. Quantitative '3C spectra may be obtained in this way, but a t the expense of sensitivity, since long delays hetween pulses are needed to allow any residual NOE to decay. On the other hand, if a fully coupled spectrum with NOE enhancement is desired, the decoupler is turned on during interpulae delays and cut off during data acquisition. Proton spin flipping stops instantly when the decoupler is turned off, whereas the abno~mal'~C ~ o ~ u l a t i distrion bution persists through the acquisition of the FID. (Continued on page AZ48)
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Fluure 7. '% NMR sDemm of ethyl benzoate obtained at 75 MHz without roto on decou~lino. , " Four hundred FlD's were accumulatd uina an acaulsltion time of 1.64 s and no relaxation delav. The total data methylene protons.
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