INSTRUMENTATION
Advisory Panel Jonathan W . Amy Glenn L. Booman 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. F a r r a r Institute for Materials Research National Bureau of Standards Washington, D. C. 20234 Certain advantages in pulsed nmr spectroscopy, especially increased sensitivity, make it an attractive technique. With the solution of many of the problems in the spectrometers and associated computer instrumen tation, it is safe to predict it will rival continuous wave—nmr spectroscopy in usage
Ρ ULSED nmr spectroscopy has been
with 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 in duction decay signal obtained in a pulsed nmr experiment and the cw-nmr spectrum constitute a Fourier trans form pair (1), provided that certain conditions are met. Since potentially one of the most exciting and fruitful areas of research is 1 3 C Fourier-transform (Ft)-nmr spectroscopy, a large part of this article 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) to point out the advantages of Ft-nmr spectroscopy, (2) to introduce the reader to some of the jargon used in pulsed and in Fouriertransform-nmr spectroscopy, (3) to at tempt to explain in a simple way what pulsed and Ft-nmr spectroscopy are about and how they differ from "normal" or cw-nmr, and (4) to give the reader some information about the mini mum requirements needed in the basic instrumentation of a Ft-nmr spectrom eter. IMPORTANCE AND LIMITATIONS OF CW-NMR
In the past six years or so a number of scientists have been working with great success in the area of 13 C, cw-nmr spectroscopy. In particular, the ele gant work of Professor Grant and his coworkers at Utah, of Professor Lauterbur and his coworkers in New York,
and of Professor Roberts and his co workers in California attests to the vast wealth of information available from 13 C-nmr spectroscopy (2). As has been pointed out by these workers, "C-nrar spectroscopy is probably the single most important tool in determining the structure of organic and biological molecules and, as such, it is almost impossible to overestimate its impor tance. In an overwhelming number of cases where almost no information is available from proton nmr, 13 C-nmr spectra easily show differentiation be tween two complex molecules which differ only in the subtle rearrangement of a few carbon atoms. The reason for this lies partly in the fact that the range of 13 C chemical shifts (200 ppm or more) is much greater than for pro tons (about 20 ppm) and partly be cause in non- 13 C-enriched molecules only one 13 C nucleus is in any given molecule. The primary limitation of the tech nique has been a lack of sensitivity, due both to a relatively small magnetogyric ratio, yc, and to the fact that 13 C 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/N) obtainable from 13 C-nmr spec trometers. By utilizing all the tricks available, good 13 C spectra have been obtained of relatively complex steroids (2). This has been accomplished by signal averaging for long periods of time and by using large amounts of ma terial. Often, however, only small amounts of material are available. This is especially true in the case of samples
of biological interest. The practical limit for signal averaging is about 20 to 30 hr, restricting the number of systems that can be im'estigated. Furthermore, in the area of biological research, the lifetime of a sample is often such that one has only a few hours in which to complete an investi gation. In short, the sensitivity inher ent in 13 C-cw-nmr spectroscopy, even using proton noise decoupling and long-term signal averaging, is woefully inadequate. Happily, Fourier-trans form techniques, especially when used in multiple pulse experiments, afford one a significant increase (in principle, up to a factor of 100 or more) in this sensitivity. It has been demonstrated (3) that for 1 H-Ft-nmr, one can obtain a sub stantial increase in sensitivity. Since one should realize even greater gains in the sensitivity of 13 C-Ft-nmr over 13 C-cw-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 data-recording and data-reduction devices (i.e., inexpen sive, dedicated computers suitably in terfaced to the spectrometer).
SOME ADVANTAGES OF FT-NMR
Up to this point we have attempted to give some evidence of the impor tance of 13 C-nmr spectroscopy, and we have stated that the main limitation in the technique is its lack of sensi tivity. We have also stated that Ft-nmr offers a way of obtaining a substantial increase in sensitivity over that pos-
ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970 ·
109 A
Instrumentation
sible via cw-nmr spectroscopy. We now try to point out why this is so. Basically, pulsed Ft-nmr spectros copy is just a special form of interferometry and, as is usually the case, to interpret the results it is necessary to go to the conventional form of spec tral representation by means of a Fourier transformation. This can be done either by an analog Fourier ana lyzer or it can be done by collecting the interferogram digitally and per forming the Fourier transformation on a digital computer. The technique consists of the application to the sample of a short, intense pulse of radio-fre quency (r.f.) energy and the measure ment as a function of time of the re sulting free induction decay signal from the nuclear spins in the sample. Fourier transformation of the free in duction signal gives the ordinary highresolution spectrum (3, ,£). The advantage of the Ft-nmr tech nique 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 repetitively and add the free induction decay signals co herently in a digital computer or a time-averaging device. The time, T, required to record a spectrum is given by Τ ~ r _ 1 sec, where r is the resolu tion desired (usually about 1 Hz) ; Τ is independent of the width of the spectrum, Δ. The consequence is that sensitivity is much higher. The sen sitivity enhancement, factor ts, is given by es ~ (Δ/r) 1 ' 2 or, alternatively, the time enhancement factor t ( is given by et ^ Δ / Γ (S/N improves only as the square root of the time, or as the num ber of scans in a time-averaged experi ment) . Thus, the time required to ob tain a spectrum of a given signal-tonoise ratio (S/N) is shorter using the Ft-nmr technique by a factor of tt. In 13 C-nmr studies of complex systems, Δ is typically 200 ppm and r is about 1 Hz, so at 15 MHz (at which fre quency many current spectrometers op erate), the time enhancement factor, ct, is £ t ~ (200 ppm · 15 MHz/1 Hz) = 3000. With the newer 13 C spec trometers which operate at 25 MHz or 55 MHz, the time saved is even greater. Also, one can achieve even greater time enhancements (preliminary theo retical 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 110 A ·
typical experiment this frequency would be changed slowly from a value of „„ to a value of v0 + 3000 Hz. The field, of course, is "locked" to a fixed value given by the expression 2 irv0 = Wo = y c H 0 , where yr. is the magnetogyric ratio for 13 C. The amplitude, /(ω), of the signal induced is recorded as a function of the frequency, ω , and the result of a sample of H313CC1 is the ,3 C-nmr spectrum shown in Figure la. In the pulsed nmr experiment, the sample is perturbed very much indeed by the very large H x field. This has the effect of irradiating the sample not with a single discrete frequency, as is the case with cw-nmr, but with a band of frequencies centered at 15 MHz and covering a range of about (1/4 τ) Hz where r is the time duration (in
the experiments. In 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 jusec). In the cwnmr experiment, a rather weak ( 1 0 - 3 G or less) r.f. field is used, but is al lowed to run continuously. The result of this is that in the cw-nmr experi ment, one produces an r.f. field, ΗΛ, at a single discrete frequency which per turbs 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 13 C-nmr one works usually at a frequency of about 15 MHz, and in a
(a)
s
iM
I
f•«—••—m
tea
ιΐ[
V
·»
û(t)
tss=0
Figure 1. (a) depicts a "normal" MC cw-nmr spectrum of H313CCI. The chemical spectrum shift from a given reference frequency, ω„, is a Hz and the 10C—Η spincoupling constant is β Hz. f(w
