I NST R UME NTAT IO N
Advisory Panel Jonathan W. Amy Glenn L. Boornan Robert L. Bowman
Jack W. Frazer G. Phillip Hicks Donald R. Johnson
Howard V. Malmstadt Marvin Margoshes William F. Ulrich
Pulsed and Fourier Transform NMR Spectroscopy T. C. Farrar Institute for Materials Research National Bureau of Standards Washington, D. C. 20234 Certain advantages in pulsed n m r spectroscopy, especially increased sensitivity, make it an attractive technique. With the solution of many of the problems in the spectrometers and associated computer instrumentation, it is safe t o predict it will rival continuous wave-nmr spectroscopy in usage ULSED nmr spectroscopy has been P w i t l i us for almost as long as the more conventional, continuous wave (cw)-nmr spectroscopy; however, it is less familiar to most chemists. This situation is now changing rapidly since it has been pointed out that the induction decay signal obtained in a pulsed nmr experiment and t,he cw-nmr spectrum constitute a Fourier transform pair ( I ) , provided that certain conditions are met. Since potentially one of the most exciting and fruitful areas of research is 13C Fourier-transform (Ft)-nmr spectroscopy, a large part of this articlc will be devoted to that subject. Other problems which are amenable to pulsed nmr methods will be mentioned briefly. The primary purposes of this article are fourfold: (1) t o point, out the ndvantagcs of Ft-nmr spectroscopy, (2) to introduce the reader to some of the jargon used in pulsed and in Fouriertransform-ninr spectroscopy, (3) to attempt to explain in a simple way what pulsed and Ft-nmr spectroscopy are about and how they differ from “normal” or cw-nnir, :inti (4) to give thc render some information about the minimuni requirements necded in the basic instrumcntation of a Ft-nmr spcctrometer.
IMPORTANCE AND LIMITATIONS OF CW-NMR
In the Ixwt six ycars or so a n u n b c r of scicntists havc h e n working with grc:i t succcss in thc area of cw-ninr sprctroseopy. In particular, the elcg:int work of Professor Grant and his conorkcrs :it I-tali, of Professor Lantcrh i r :ind his coworker.: in Yew York,
and of Professor Roberts and his coworkers in California attests to tlie vast wealth of information available froin 13C-nmr spectroscopy ( 2 ) . -4s has been pointed out by these workers, I T - n m r spectroscopy is probably the single most important, tool in determining the structure of organic and biological molecules and, as such, it’ is almost impossible t o overestimate its importance. I n :in overwhelming number of cases where almost no information is available from proton nmr, Y!-nnir spectrn easily show differentiation betweeii t,wo complex molecules which differ only in the subtle rearrangement of a few carbon atoms. The reason for this lies partly in t’he fact that thc range of 13C chemicnl shifts (200 ppm or more) is much greater than for protons (about 20 ppni) and partly becaiise in non-13C-enriched moleciiles only one 13C nucleus is in any given molecule. The primary limitation of the technique has been a lack of sensitivity, duc both to a relntivcly small magnetogyric ratio, y c , and to the fact that has a natural abundance of only 1% . By employing signal-averaging methods and by taking advantage of proton noise-decoupling techniques, great advances have already been made in increasing the signal-to-noise ratio ( S T ) obtainable from 13C-nmr spcctrometers. By utilizing all the tricks a\-ailnble, good 13C spectra have been obtained of relatively comples steroids ( 2 ) . This has been accomplished by signal averaging for long periods of time and by using large amounts of miterial. Often, howel-er, only sinall amounts of inaterial are available. This is especinlly t r w in the c:ise of samples
of biological interest. The practical limit, for signal averaging is about, 20 to 30 hr, rest,ricting the number of systems that can be investigated. Furthermore, in the area of biological research, the lifetime of a sample is often such that one has only a few hours in wliicli t o complete an investigation. I n short, the sensit,ivity inherent in 1”-cw-nmr spectroscopy, even using proton noise decoupling and long-term signal averaging, is woefully inadequate. Happily, Fourier-t’ransform techniques, especially xhen used in multiple pulse experiments, afford one a significant increase (in principle, up to a factor of 100 or more) in this sensitivity. I t has been demonstrated ( 3 ) thnt for lH-Ft-nmr, one can obtain a substantial increase in sensitivity. Since one should realize even greater gains in the sensitivity of 13C-Ft-nmr over 13C-cu--nmr, it, is surprising that more work has not been done in this ;area. The reasons for this are probably due to the lack both of good pulsed nmr spectrometers and of good, reliable, and inexpensive dah-Tecording and data-reduction devices (i.e., inexpensive, dedicated comptitcrs suitably interfaced to tlie spectrometer). SOME ADVANTAGES OF FT-NMR
Up t o this point wc have attempted to give some evidence of the importance of I T - n m r spectroscopy, and we have stated that the main limitzition in the technique is its lack of sensitivity. We have also stated that Ft-nnir offers a n a y of obtaining a suhstnntinl increme in sensitivity over that pod-
ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970 * 1 0 9 A
sible via cw-nmr spectroscopy. We now try t,o point out’ why this is so. Basically, pulsed Ft-nmr spectroscopy is just a special form of interferometry and, as is usually the case, to interpret t,he results it is necessary to go t.0 t,he conventional form of spect,ral representation b y means of a Fourier transformation. This can be done eit,her by an analog Fourier analyzer or it can be done by collecting the interferogram digitally and performing the Fourier t,ransformation on a digital computer. The technique consists of the application to the sample of a short,, intense pulse of radio-frequency (r,f,) energy and the measurement as a function of time of the resulting free induction decay signal from the nuclear spins in the sample. Fourier transformation of the free induction signal gives the ordinary highresolution spectrum (3, 4). The advant,age of the Ft-nmr technique is that the free induction decay signal is obtained rapidly, so that in a given length of time it is possible to apply the pulse repetit,ively and add the free induction decay signals coherent,ly in a digital computer or a time-averaging device. The time, T , required to record a spectrum is given sec, where r is the resoluby T /v tion desired (usually about 1 Hz); T is independent of the width of the spectrum, A . The consequence is that sensit’ivity is much higher. The sensitivity enhancement, factor esJ is given by e, ‘v ( A / r ) l / * or, alternat,ively, the time enhancement factor et is given by et ‘v A / r (S/N improves only as the square root of t,he time, or as the number of scans in a time-averaged experiment). Thus, the time required to obtain a spectrum of a given signal-tonoise ratio (S/S) is shorter using the Ft-nmr technique by a factor of et. I n l3C-nmr studies of complex systems, A is typically 200 ppm and r is about 1 Hz, so a t 15 RlHz (at, which frequency many current spectrometers operate), the time enhancement factor, ct, is (200 ppm 15 MHz/l Hz) = 3000. With the newer 13C spectrometers which operate a t 25 MHz or 55 MHz, the time saved is even greater. Also, one can achieve even greater t,ime enhancements (preliminary theoretical and experimental work indicates that an additional factor of about 10 can be realized) by using multiple pulse techniques ( 5 ) . FURTHER COMPARISONS AND APPLICATIONS
The two methods, Ft-nmr and cwnmr, differ primarily in the duration and magnitude of the r.f. field used in 110A
the experiments. I n the pulsed Ft-nmr experiment, an intense (200 G ) r.f. field is applied to the sample, but it is left on only for a very short time (typically, about 1 p e c ) . I n the cwnmr experiment, a rather weak G or less) r.f. field is used, but is allowed to run continuously. The result of this is that in the cw-nmr experiment, one produces an r.f. field, H I , a t a single discrete frequency which perturbs only slightly that line in the spectrum which resonates at precisely this frequency. This frequency is then changed slowly at a rate comparable to the resolution desired. For example, for a resolution of 1 Hz the frequency is changed at a rate of about 1 Hz’sec. For 13C-nmr one works usuallJ- a t a frequency of about 15 LIHz, and in a
typical experiment, this frequency would be changed sloivly from a value of l - o t o n value of v G 3000 Hz. The field, of course, is “locked” to a fixed value given by the expression 2 r u G = w G = ycHG, where y c is the magnetogyric ratio for 13C. The amplitude, f ( w ) , of the signal induced is recorded as n function of the frequency, w, and the result of a sample of H313CC1 is the 13C-nmr spect.rum shown in Figure la. In the pulsed nmr experiment, the sample is perturbed very much indeed by the very large H I field. This has the effect of irradiating the sample not with a single discrete frequency, as is the cnse with cw-nmr, but with a band of frequencies centered a t 15 LZHz and covering a range of about ‘(1/4 T ) Hz where is the t.ime durabion (in
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Figure 1. (a) depicts a “normal” ”C cw-nmr spectrum of H23CCI. The chemical spectrum shift from a given reference frequency, w 0 , is (Y Hz and the ‘T-H spincoupling constant is p Hz. f ( w i ) is the intensity of the signal at the position w 1 (= 2 7 u t ) in the spectrum. (b) depicts the interferogram of H,’”CCI. The C-H spin-coupling constant is proportional t o l / y , and the chemical shift is proportional t o 1/6
ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
Instrumentation
seconds) of the pulse used. For a 1p e e pulse, then, the pulse covers the frequency range 15 MHz i 120 kHz. The result is that the nuclei associated with the various lines in the spectrum are induced to radiate their characteristic r.f. signals simultaneously and, as is the case whenever one mixes a number of signals simultaneously with different frequencies, an interference pattern is obtained. The result for H,13CCl is shown in Figure l b . This is usually referred to as ar. interferogram or the Ft-nmr spectrum or a “timedomain” spectrum. Since the interferogram shown in Figure Ib, even in this simple example, is much more difficult to interpret than the frequency spectrum shown in Figure l a , we desire some method of transforming Figure l b into l a . The transformation from l b to l a is given according to the formula
It is, of course, possible to go from the form in Figure l a to Ib. In this case the proper procedure is given b y
An alternative, at least in principle, to the pulse technique is a manychannel experiment. I n this method one could, for example, apply 3000 transmitter frequencies from u0 to (vo 3000) Hz and use 3000 phase detectors to detect separately each one of the individually induced signals. This experiment, too, would give one a time-enhanc.ement factor, c f j of 3000 since one is doing 3000 cw-nmr experiments simultaneously. I n t,his esperiment. one could also use a single phase detector and obtain an interferogram just as in the usual pulsed Ft-nmr experiment. I n addition to the Ft-nmr application, there are a number of other problems amenable to pulsed nmr techniques. By measuring the spin-lattice relasation time, T I , and t,he spin-spin relasation time, T 2 , as a function of temperature, one can get a wealth of information about a given molecule system in the solid, liquid, or gaseous state, ranging from a determination of both activation energies and frequencies of motion of a given molecular species to the study of the “structure” of liquids and the determination of correlation times for angular momentum. A variety of multiple pulse t,echniques now exist for mensuring self-diffusion coefficients and the Carr-Purcell-
Figure 2. A simplified block diagram of a typical pulsed nmr spectrometer
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hleiboom-Gill pulse experiment can be used to study chemical kinetics over a wide dynamic range. An escellent recent review (6) gives a number of applications in these areas. INSTRUMENT REQUIREMENTS
One remark and one question that we are often asked these days is as follovis: “I would like to get started in the arcn of Ft-nnir. What, arc some of the more important considerations to keep in mind when buying equipment 1” I n the hope that it’ will serve a useful purpose, I would like to comment on what I believe are some of the essential requirements to look for in a pulsed nmr spectrometer and in a signal averager or “dedicated” computer to be used with it. -4simplified schematic diagram of R typical pulsed nmr system is shown in Figure 2. The pulse programmer dctermines the sequence of pulses in an experiment, the width of each pulse, and the repetition rate betaeen sequences. It, also provides a synchro-
nizing pulse to start the time base drive in a recording instrument such as an oscilloscope, a gated boxcar integrator, or a signal averager. The programmer should be flexible enough so t,liat almost nny sequence of pulses can be generated. Since the timing in many espcriments, for example, the D E F T ( 5 ) experiment, is extremely critical, a digital programmer is to be preferred. I n this case it is preferable to have a clock frequency of 2 MHz or higher to minimize radio frequency interfcr~ n c e ( R F I ) problems. I t is iniportant that the puke viidtlis bc adjustable to a precision of 1% or better from 1 psec up to 1 nisec or longer. The longer pulses are needed for rottiting reference frame esperiments. The r.f. gate unit and transmitter should be capable of generating enough ive pulse ividths of 1 . Thio is an important requirement because if the pulse widths are too long, say much greater than 3 or 4 psec for lW-nmr, the assumption that pulsed nmr and cw-nmr form a Fourier-transform pair begins to break
ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
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Instrumentation
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down. Of course, it is necessary that the r.f. gate unit supply a coherent r.f. reference signal t o drive the ring demodulator in the r.f. phase detector. The total system recovery time a t 15 MHz should be 15 p e c or less and the preamp-receiver combination should have a voltage gain of 120 db or more. The entire system should be extremely well shielded to avoid RFI problems arising from clocks in the signal averager, pulse programmer, or computer. For maximum flexibility the digitizer in the A/D converter of the computer should have a t least 10 bits or more and it should have a digitizing rate of at least 20 kHz or more. For 15 MHz 13C-nmr, a writing speed of 6 kHz is required [from sampling theory one knows that to cover a spectrum of “z” Hz (in our case 5 = 3000 Hz), i t is necessary to sample a t a rate of “2 2’ Hz]. If one samples for 1 sec (to obtain a resolution of 1 Hz), then 6000 data channels are required in which to store the data. To make use of the FFT (fast Fourier transform) computer programs available, one needs a signal averager and/or computer with a capacity of a t least 8192 words for data storage; the word size should be a t least 18 bits although 16 will do. Of course, another 4000 words of memory are needed in the computer to carry out the Fourier transformation. After the cw-nmr spectrum has been calculated, a D/A converter is needed to plot out the final cw spectrum. I n summary, the field of 13C-Ft-nmr spectroscopy is developing a t a very rapid rate. Although there have been many problems, they have, for the most part, been solved. With the rapid development and ever-decreasing cost of small computers, it seems safe to predict that the time when Ft-nmr spectrometers are as ubiquitous as the cw-nmr spectrometers is not far away. References
(1) I. J. Lowe and R. E. Norberg, Phys. Rev., 107, 46 (1957). (2) J. D. Roberts. et al.. J . Amer. C h e m . -Sot., 91,7445 (1969); D . Grant and B. Cheny, ibid., 89, 5315-19 (1967) ; P. C.
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112A
ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
Lauterbur, in “Determination of Organic Structures Bv Physical Methods,” F. C. Tachod and Mr.D. Phillips, Eds., Vol. 2, Academic Press, New York and London, 1962, Chap. 4. Other helpful references arc given in these three papers. (3) R . R. Ernst and W. A. Anderson, R e v . Sei. Instr., 37, 93 (1965). ( 4 ) A . Abragam, “The Principles of Xuclear Magnetism, Clarendon Press, Oxford, 1961. (5) E. D. Becker, J. A . Ferretti, and T. C. Farrar, J . Amer. C h e m . SOC., 91, 7784 (1969). (6) J. Jonas and H. S. Gutowsky, “Annual Reviews of Physical Chemistrv,” Vol. 18 (Eyring, H., Ed., Annual Reviews, Inc., 1968).
