Multipulse NMR in liquids

Progress in NMR Spectroscopy, Vol. 16, pp. 311-370,1984 Printed inGreat Britain. All rights reserved.

Copyright

MULTIPULSE CHRISTOPHER

0079-6565/8430X0+ .50 @ 1984. Pergamon Press Ltd.

NMR IN LIQUIDS J. TURNER

Department of Chemistry, Cohunbia University, New York, NY 10027, U.S.A. (Receiued 23 March 1984)

1. Aims of the Review 2. One Pulse Techniaues

2.1. General features 2.2. Edge echo 2.3. Delayed acquisition 3. Two Pulse Techniques 3.1. Introduction 3.2. Inversion-recovery 3.3. Composite pulses 3.4. Progressive saturation 3.5. Saturation-recovery 3.6. Miscellaneous methods for 7’rdetermination 3.7. The Hahn echo 3.8. Destruction of steady-state echoes 3.9. The Carr-Purcell echo 3.10. Rotary echoes 3.11. Miscellaneous echoes 3.12. Echo modulation 3.13. Generation of multiple quantum coherence 3.14. Binomial pulse excitation 4. Resolution Enhancement 4.1. Resolution enhancement by spin-echo techniques 4.2. Reduction of the effective sample volume 4.3. Removal of baseline distortion 5. Frequency Selective Pulsed Excitation 5.1. Introduction 5.2. Very low power pulses 5.3. Long pulse techniques 5.4. DANTE 5.5. Tailored excitation 6. Selective Suppression 6.1. Introduction 6.2. Steady-state method 6.3. Presaturation 6.4. Irradiation during acquisition 6.5. WEFT 6.6. Selective WEFT 6.7. Long pulse methods 6.8. Redtield 2-14 6.9. Timeshared Redfield 2-l-4 6.10. Binomial pulse sequences 6.11. Miscellaneous 7. Sensitivity Enhancement 7.1. Introduction 7.2. DEFT 7.3. Steady-state techniques 7.4. Heteronuclear selective population transfer 7.5. INEPT 7.6. DEPT 7.7. SINEPT 7.8. SESET 7.9. J-cross polarization 311

312 313 313 313 313 315 315 315 317 317 318 318 318 320 321 322 322 322 324 325 325 325 325 325 326 326 326 326 327 328 328 328 328 329 329 329 330 330 331 331 332 333 333 333 333 333 334 337 340 341 341 342

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8. Multiplicity Selection 8.1. Introduction 8.2. Homonuclear J-modulation 8.3. Heteronuclear J-modulation 8.4. INEPT 8.5. J-scaling 8.6. Masked projection of 2-D data 8.7. Generation of multiple quantum coherence 8.7.1. General features 8.7.2. INADEQUATE 8.7.3. Uniform excitation of multiple quantum coherence 8.7.4. DEPT 8.75. SEMUT 8.8. Comparison of spectral editing techniques 9. Connectivity 9.1. General features 9.2. Homonuclear selective population transfer 9.3. Double selective population transfer 9.4. Sign-labelled polarization transfer 9.5. Selective excitation transfer 9.6. Spin-echo double resonance 9.7. Chemical shift correlation 9.8. Isotope filtration 9.8.1. Basic echo techniques 9.8.2. Inverse polarization transfer 9.9. DOUBTFUL References

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1. AIMS OF THE REVIEW The purpose of this article is to review the multipulse NMR experiments which have found application in the study of isotropic liquids. This is such a large area that some subjects have had to be excluded in order to keep the review at a manageable size. Firstly, experiments which require double Fourier transformation, i.e. two-dimensional NMR techniques, are not included. This is unfortunate because many of the experiments to be discussed have two-dimensional counterparts. In fact, the same sequences of pulses can often be used for both one- and two-dimensional NMR. However, two-dimensional NMR has often been reviewed. (l-5) Secondly, broadband excitation techniques such as stochastic excitation@,‘) and correlation spectroscopy@p9) are also not included. This work concentrates on “one-dimensional” experiments which are in some sense selective, in that they differentiate between resonances on the basis of position, linewidth, multiplicity, magnitude of spin-spin coupling, or relaxation time. The experiments which are included serve as potential methods of spectral assignment. No previous full review of this subject appears to exist. However, most modern NMR texts devote some attention to this topic. In this review an attempt has been made to cover the subject fully from the simplest sequences up to the most complex ones currently available. The implementation of techniques and the problems inherent in their application are discussed. The treatment of relaxation time measurements is indicative, rather than exhaustive, since it would scarcely be feasible (or indeed useful) to review all the applications of these techniques. Relaxation time measurements have, however, been extensively reviewed elsewhere, see for example references (10-12). This review uses the classical, or semi-classical vector model to discuss experiments involving single quantum magnetization since it provides a simple physical model for these experiments. However, experiments involving the generation of multiple quantum coherence are becoming increasingly more valuable. These experiments, while included in this review, are not conveniently interpreted by such a model. Thus, discussion of how they work is minimized. Other models, such as the product operator formalism, are more appropriate in this case.(r3) Obviously, before any multipulse experiment is attempted, a conventional FT NMR spectrum would be obtained. Text books are available on the practical aspects of this subject,“““) as are

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reviews on related subjects, such as the optimization of the NMR acquisition parameters,“s) and digitization and data processing in FT NMR.“‘) Since almost any of the techniques which are reviewed may be used for spectral assignment, it follows that there can be no separate section on assignment techniques. Rather, the review is divided into an introductory section on one and two pulse techniques, which covers the basic building blocks of pulse sequences in the order of increasing complexity. The remainder of the review is divided into sections devoted to a particular task, i.e. resolution enhancement, selective pulse excitation, selective suppression, sensitivity enhancement, multiplicity selection and connectivity. There is considerable overlap between these sections; so the choice of where a particular pulse sequence is discussed has been based on what the sequence was originally designed to achieve. 2. ONE PULSE TECHNIQUES 2.1. General Features A variety of experiments other than normal FT NMR are possible with a single pulse. Three simple techniques include lengthening the pulse, reducing its amplitude or placing the transmitter a long way from resonance. In this context, these are almost equivalent and their effect is a familiar problem in FT NMR, that of finite pulse power. If the value of the 90” pulse width is longer than 1/(4SW) where SW stands for the spectral width of interest, then phase and intensity abnormalities throughout the spectrum become important. GO) This is because increasing the length of the pulse makes it increasingly frequency selective. For some experiments this can be desirable. Such long pulses (sometimes called “soft” pulses to distinguish them from “hard” non-selective pulses) may be used to selectively excite only part of the spectrum. (21) Solvent suppression is a major application of such frequency selective pulses. Frequency selective pulsed excitation is dealt with in Section 5, while selective suppression is discussed in Section 6. As an aside, it may be worth noting that all pulses are in some sense selective. A single weak pulse can generate multiple quantum coherence if it is applied with appropriate power at the position where a multiple quantum transition would appear in a CW experiment.(22) This is mainly a nuisance, since it can give rise to undesired effects (usually phase or intensity distortions) in conventional single quantum experiments involving soft pulses. 2.2. Edge Echo A single long pulse can generate an echo (‘j) (the “edge” echo). When the pulse is long, the process of turning the pulse on and then waiting a long time before turning it off, makes it behave similarly to two separate pulses. This echo may be stimulated by applying a single pulse whose RF power is comparable to the signal offset from the transmitter. The magnetic field must be somewhat inhomogeneous so that this effect is not masked by the normal free induction decay (FID).‘24) The edge echo follows the trailing edge of the pulse at a time shorter than the duration of the pulse. This echo results from the refocusing of isochromats which were dephased during their precession about the highly tilted effective field of the pulse. The refocusing takes the form of a rapid frequency sweep through the NMR spectrum. Separate edge echoes are obtained for each chemically shifted resonance. In contrast, all resonances are refocussed simultaneously in the Hahn or Carr-Purcell echo (neglecting the effects of homonuclear spin coupling). Sections 3.7-3.12 deal with echoes in greater detail. 2.3. Delayed Acquisition

The next simplest extension of one-pulse NMR is the enlargement of the inevitable delay between the end of the pulse and the beginning of the data acquisition. The purpose of this normally short delay (which we will refer to as the “dead time”) is twofold. Firstly it protects the RF receiver (which is designed to detect the minute signals resulting from nuclear induction) from the effects of the trailing edge of the high power pulse. Secondly, it allows any transient response of the probe (often referred

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to as “ringing”) to completely die away before the receiver is switched on, and thus avoid baseline artifacts.‘251 Consequently, it is difficult to detect undistorted NMR signals in the 10 to 2Opec immediately following the pulse. Loss of the initial part of the FID introduces distortions into the resulting FT spectrum which cannot, in general, be removed by further processing of the data. A minimally distorted spectrum can be obtained from the FID following a single hard pulse if certain conditions are met. If td represents the dead time and w, is the maximum frequency of interest (with quadrature detection this is usually equal to half the desired sweep width), then a minimally distorted spectrum can be obtained when (i) the condition td rc
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suppress acoustic resonance are discussed in Section 3 which deals with resolution enhancement. Delayed acquisition has also been used as a method of suppressing solvent signals(34) which have been selectively broadened with a paramagnetic relaxation reagent. Delayed acquisition can be extended into a method of multiplicity selection in proton decoupled 13C NMR spectra by turning the decoupler off during the delay (z) between the RF pulse and start of data acquisition.(35) During the period T the different components of the proton-coupled carbon multiplets precess at their individual frequencies which are governed by their heteronuclear Jcoupling. The recombination of these components when the decoupler is turned back on produces a constructive or destructive interference. It is convenient to define 8 = 27rJcnzrad. The signal intensities are governed by the following equations, in which only the large one-bond couplings are considered : M(CH):Acos8 M(CH,) : OSA(1 +cos24 M&H,)

: o.m(3

COS 8-COS

= A cos’ 0 38)

=

A COS3

8.

Quaternary carbons are essentially unmodulated. Thus, if the delay t is set to l/J (about 7-8 msec for aliphatic carbons), this leads to a pairwise separation of multiplicities. Quaternary carbon singlets and CH, triplets have the opposite phase to CH doublets and CH, quartets. However, the use of simple delayed acquisition results in severe frequency dependent phase shifts across the spectrum, which are normally unacceptable. Section 7 discusses other methods of multiplicity selection. 3. TWO PULSE TECHNIQUES 3.1. Introduction A sequence of two pulses separated by a delay can be used to investigate Tl or T2, to generate multiple quantum coherence, and also as a method of solvent suppression (see Section 6.10). To some extent, all these effects take place simultaneously and must be separated by appropriate delays or phase-cycling. 3.2. Inversion-Recovery Arguably the most familiar NMR pulse sequence to chemists is the inversion-recovery method(36s37) for the measurement of the spin-lattice relaxation time (Ti). In this type of experiment, the equilibrium magnetization is first inverted by a 180’ pulse which rotates it from the +z axis of the rotating frame onto the -z axis. At a time t(r < 7’i) after the inversion pulse, the magnetization has partially recovered. If a read pulse (usually a 90” pulse for reasons of sensitivity) is applied and the resulting FID collected and Fourier transformed, the relative intensities of the various lines in the spectrum reflect their individual relaxation times. The experiment can be summarized by the following sequence : ( T-180“~r-90°-ACQ), where T represents the preparation period; this should be long compared with Ti. n is the number of FID’s for each value of z. At the end of the sequence, any particular resonance may appear positive or negative, depending on whether the read pulse is applied before or after the magnetization has passed through zero. In principle, two different measurements suffice in order to determine Tl. However, better data are retrieved from a set of spectra obtained by varying z. The first major modification to the basic inversion-recovery sequence was designed to remove non-linear (and thus incorrigible) phase errors associated with short r-values.(38) These are caused by the non-ideal inversion pulse. An ideal 180” pulse would not excite any transverse magnetization. At a time r < T,*, the transverse magnetization generated by the non-ideal 1800 pulse has not decayed to zero when the read pulse is applied. The resultant FID will have an additional transverse-component

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which introduces a phase shift. The size of the phase shift will be inversely proportional to the line-width of the resonance. Since line-widths usually vary amongst the resonances of a particular compound, this phase error will also vary. The most elegant solution to this problem is to alternate the RF phase by 180” on every other read pulse. The sequence now becomes : (T-1800(X+90=(X)-(

+ )ACQ-T-180’(X)-r-90°(

- Xt( - )ACQ),.

Subtraction of the alternate FID’s annihilates the undesirable X component of the transverse magnetization. This sequence was introduced before quadrature detection became commonplace and thus, strictly speaking, would only be optimal for single-phase detection. With the introduction of quadrature detection, the sequence has been modified accordingly and now requires a minimum of four transients. The phase of the inverting pulse is held constant while the phase of the read pulse is cycled in 90” steps simultaneously with the receiver reference phase. Further improvements to this four transient phase cycling scheme have been suggested(39) which involve periodically incrementing the phase of the inversion pulse by 90” every 4M transients (where M is an integer). The resultant sequence requires a minimum of 16 transients. This is a general result for a two-pulse sequence. For an N pulse sequence, the optimum phase cycle will have 4* steps. Fortunately, in most pulse sequences, this alarmingly high number is reduced by the need to have specific phase relationships amongst the various pulses within a sequence. However, the general result does emphasize the need for easy control of the RF phase during pulse sequence generation, preferably by some form of integer arithmetic. Systematic errors may occur if the preparation period T is not sufficiently long for the spin system to relax between adjacent sequences of pulses. (40)Depending on the accuracy requirements, a time of 3-5T, is often used.‘37) This time can be reduced (41)if the first (or first few) FID’s are not collected and if the transverse magnetization is allowed to decay (T > 3T,*). Under these conditions, the preparation time (T) can be lowered without loss of accuracy. This technique has been called Fast Inversion-Recovery (FIR). (41) An analysis of the optimization of FIR experiments has been published.‘42) A Modified Fast Inversion-Recovery method has been proposed.(43) Whereas the FIR method employs a time T between successive 180°-~-900 sequences, the modified FIR method uses a fixed value D = T + t so that T decreases as 7 increases. Both FIR and modified FIR methods have been shown to be capable of nearly equal precision under conditions of ideal 900 and 180’ pulses. But with imperfect pulses the modified FIR method circumvents certain systematic errors inherent in the FIR method. Further sources of systematic errors arise from imperfections in the RF pulse. In practice, there are three major imperfections which affect these experiments. Firstly, the spatial inhomogeneity of the RF field generally makes it impossible to maintain the same flip-angle over the whole sample. The radiofrequency field homogeneity is often checked by comparing the nuclear spin response to 900 and 270“ pulses. A more sensitive method is to follow the response to a train of closely spaced phase-cycled 900 pulses.‘44) Secondly, there is a related problem of the finite strength of the RF field. When the transmitter is set sufficiently far off-resonance that the effective field in the rotating frame is appreciably stronger than the applied RF field (and tilted with respect to the x axis), it may be practically impossible to achieve any inversion at all. Chemical shift ranges in the high fields of present day magnets are such that these off-resonance effects cannot be avoided. Thirdly, there may be systematic changes of the RF phase during the pulse. There are other pulse imperfections which are equally common but whose effects are eventually averaged out, with some minor loss in the efficiency of time-averaging. These include jitter in the pulse length or instability in the timing between pulses, changes in the amplitude of the pulse when its RF phase is shifted, maladjustment and/or lack of reproducibility of the RF phase shifters. During simple time-averaging of normal FT experiments these effects may actually be advantageous since they add a stochastic process which helps prevent the formation of steady-state echoes (see Sections 3.7 and 3.8). This is desirable since it prevents the formation of phase abnormalities with lines from small molecules, such as solvents and reference compounds like TMS, under conditions when timeaveraging is proceeding at a rate which is faster than T2 of these small molecules, i.e. when the data

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acquisition parameters have been optimized for a much larger (solute) molecule. However, this lack of reproducibility leads to problems with any form of difference spectroscopy and causes “Tr noise” in two-dimensional NMRj4’) The problems caused by this irreproducibility should not be underestimated. In any form of difference spectroscopy a significant fraction of the total time may be spent on reducing the artifacts caused by incomplete suppression of unwanted peaks. The systematic (rather than the random) pulse imperfections may have a cumulative effect when the preparation period in inversion-recovery experiments is set less than 2T,.‘46) A major improvement in the inversion-recovery technique has been the introduction of composite pulses. 3.3. Composite Pulses These are series of pulses linked together, which attempt to compensate for their own imperfections. Unfortunately, it proves difficult to simultaneously compensate for the effects of inhomogeneous RF fields and off-resonance effects. The simplest composite 180” pulse(46) is a 90”(X)-180’(Y)-90”(X) pulse with the shortest practical delay between pulses (cu. 1Ousecs) to minimize free precession. Clearly, when the pulse length has been accurately adjusted, and there are no off-resonance effects, the overall effect is that of 180“(X). It is easy to visualize that for a small proportional error in all three pulses, the rotation about the y axis compensates for the errors in the first and last pulses. In a way, this resembles the Meiboom-Gill modification of the Carr-Purcell echo (see Section 3.9.). This discussion focuses on the use of composite pulses for inversion. However, they are of quite general utility. Since these composite pulses can get quite complicated, a simplified nomenclature is necessary. Thus, the 90’(X)-180’(Y)-90”(X) sequence may be written as XYYX where each element represents a nominal 90° rotation about the appropriate axis. The use of the X or Y symbol denotes a 90” pulse about the -x or - y axis respectively. Composite pulses have been demonstrated to be useful in relaxation time measurement,‘47s48) spin-echo formation, (4g) two-dimensional spectrosc~py,‘~~*~‘) and broadband heteronuclear decoup1ing.(52-54) Not surprisingly, efforts to improve the simple XYYX sequence originally concentrated on one type of pulse imperfection at a time, either RF inhomogeneity or off-resonance effects. For instance, three-, five- and nine-pulse sequences have been suggested. These suffer from a drawback. Increased compensation for one type of imperfection is obtained at the expense of an increased sensitivity to another type.‘55,56) These sequences were built up of “right-handed” rotations, usually about one of the orthogonal axes x,y, - x, - y, if a “left-handed” rotation were to become available then a better inversion sequence could be constructed from X[X] - ‘, where [Xl- ’ stands for a “reversed nutation” pulse about the -x axis. However the sense of the nuclear precession (for a given nuclear species) is fixed, and the effect of a reversed nutation pulse can only be achieved by a stratagem. A physical interpretation of this is that the phase shift errors produced by the first pulse are reinforced, rather than compensated, by the final pulse in the XYYX sequence. These ideas have led to the production of the 3XzX sequence which has a comparable range of offset compensation as the basic sequence but is much less sensitive to errors in the phase shifts. (57*5s)The problems of inaccuracy and instability of the RF phase are usually worse with analogue phase-shifters than with the more modern approach of digital phase-shifting at an intermediate frequency. A systematic procedure has been developed for the construction of related families of composite pulses which are increasingly insensitive to RF inhomogeneity. One of these sequences, YXPXXPXY, has been shown to provide excellent compensation of pulse length error over a moderate range of resonance offsets.(5g) The production of composite pulses which have truly dual compensation has recently been described. This is the 3X4XYw4YX sequence .@O)Further improvements have been promised.@‘) 3.4. Progressive Saturation If a spin system is subjected to a sequence of repetitive 90” pulses, a dynamic equilibrium will eventually be established in which the effect of the RF pulses and that of the relaxation balance each

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other. Therefore, this can be used as a method for measuring Ti. Al) This steady-state situation is usually reached after three or four pulses. This means that the first few FID’s should be discarded. Apart from this, the experiment requires no other provisions and a set of spectra are obtained by simply varying the pulse interval. The progressive saturation method lends itself to situations where for sensitivity reasons, a large number of transients are to be collected. The method is, however, restricted to T1 values which are not substantially shorter than the acquisition time. This sets a lower limit to the pulse interval. Moreover, in order to prevent the formation of steady-state echoes (see Section 3.8), no transverse magnetization should exist before the subsequent pulse in the sequence. Therefore, the method is limited to situations where T, (N.B. T, not T:) is much shorter than Tl. There is also the undesirable possibility of generating multiple quantum coherence in spin coupled systems (see Section 3.13). In order to eliminate either (or both) of these problems the minimum time between pulses should be greater than 3Tz. The use of CYCLOPS (see Section 3.8) phase cycling reduces this time by a factor of four. Even this requirement can be circumvented by the introduction of a momentary degradation of the magnetic homogeneity (a “homospoil” pulse)@‘) since the spins can be expected to dephase rapidly in an inhomogeneous magnetic field. The use of homospoil pulses often necessitates a delay of the order of 0.001-0.1 set for the recovery of the magnetic field homogeneity. Ideally, some form of randomization of the position of the homospoil pulse in the sequence should also be applied. Thus, the sequence can be summarized as : (T-90”ACQ-HSP), not sampled

( T-90°-ACQ-HSP),

where HSP stands for a homospoil pulse. 3.5. Saturation-Recovery The characteristic of this technique is the initial total elimination of the spin magnetization. most commonly used sequence (62,63)which accomplishes this can be written as:

The

(90°-HSP-r-90”ACQ-HSP),. After the destruction of the initial z-axis magnetization with a 90” pulse, the xy magnetization is likewise destroyed by spoiling the magnetic homogeneity. This has the effect of dispersing the transverse magnetization. After a time z < T,, the z-magnetization has partially recovered and can be measured with a read pulse. 3.6. Miscellaneous Methods For T, Determination The variable nutation angle method’64-66) is essentially a modification of the progressive saturation method and consists of varying the flip-angle of the pulse while keeping the delay between pulses constant. It is subject to the same problems as progressive saturation with the added complexity of requiring a calibration of the whole flip angle range. An intriguing method for the measurement of very long relaxation times is to observe the build up of the magnetization after the sample is placed in the probe. ~‘1 This is a mechanical analogy of the saturation-recovery sequence discussed in Section 3.5. Various implementations of the above methods are available. (i6*17)Comparisons of the various methods’68*69)show that the optimum precision in Tl per unit time is obtained with either FIRc41’ or modified FIR’43) combined with three-parameter exponential regression.‘70*71’ The INEPT pulse sequence (see Section 7.5) may also be used to measure the Ti of either of the two nuclei involved in the polarization transfer.‘72-74) 3.7. The Hahn Echo

The decay of the transverse magnetization after an RF pulse is determined by the spin-spin relaxation time T2, as long as the magnetic field is homogeneous. If a small enough sample could be

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319

(b)

FIG. 1. Vector diagram for the formation of a Hahn (or eight-ball) echo with a 90”-r-900 sequence of pulses of the same RF phase. Notice that a very different result would be produced if the phase of the second pulse was shifted by 90”. studied, where field inhomogeneity could be neglected, this natural decay rate could be observed directly. Unfortunately, in real magnetic fields with normal sized samples the non-uniformity of the magnetic field across the sample causes the magnetization in different parts of the sample (called “isochromats”) to precess at different frequencies, leading to an additional but reversible destruction of the total observed transverse magnetization. Spin echoes occur when this dephasing process is reversed. They were first demonstrated and explained by Hahn, (“) who used a sequence of two equal RF pulses of the same phase, separated by a delay 7. The reappearance of an NMR signal is called a spin echo. Hahn named this the “eight-ball” echo; however, it is more usually named after its discoverer, especially when two 90” pulses are used. There is some confusion in the literature over the use of the name Hahn echo, since it is sometimes taken to mean a Carr-Purcell (method A) echo, i.e. a 90°-7-180° echo, see Section 3.9. In a Carr-Purcell echo the phase of the second pulse need not be identical to that of the first. The convention adopted here is that the name Hahn, (or steady-state), echo is used when the flip angle and the phase of the two pulses are equal. Figure 1 produces a vector model for the formation of this echo. The net magnetization is represented as the sum of many isochromats in the xy plane of the rotating frame. These are aligned along they direction immediately after the initial 90” pulse (Fig. la), but fan out in the xy plane during the delay 7. Here we follow two typical isochromats which each dephase to arrive at the positions shown after the delay 7 (Fig. lb). The subsequent 90“ pulse rotates them to lie in the xz plane (Fig. lc). During the second delay 7 they again precess through their original angle to arrive on the surface of a figure-of-eight pattern produced by all the other isochromats originally lying in the xy plane (Fig. Id). During the delays only the xy components of the magnetization precess. The z components can be neglected. Though this pattern is very similar to a figure-of-eight, the lines do not cross as in a figure-of-eight. The shape is somewhat like that which might be produced if one attempted to pick up a whole, soft, pizza pie by two diametrically opposed points. Notice that a very different result would be predicted if the second pulse was phase-shifted by 90”. The vector model would predict no echo in this case. This prediction turns out to be true only for the study of spin l/2 nuclei in an isotropic liquid. 90“ pulses are not prerequisite requirements to generate Hahn echoes. The maximum available echo amplitude occurs with two 120° pulses. A sequence of three RF pulses(75*761gives rise to secondary echoes: the position of these are shown in Fig. 2. If the separation of the first and third pulses is T, and 27 < T < T,, then echoes appear at T+7,2T-27,2T-7 and 2T. Two types of echoes appear. The echoes at 2T-27, 2T -7 and 27 are ordinary echoes. Hahn

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320

A

V t 7

t 2r

t

f

t

T

T+r

2T-27

t 2T-7

t 2T

FIG. 2. Position of the echoesfrom three 90”pulses of the same phase.

referred to these as “primary” echoes. The echo at 2T arises because of the first and last pulses of the three pulse array. The echo at 2T-27 can be explained by considering the first primary echo at 27 as effectively a pulse with which the third pulse of the sequence gives a further echo. The echo at (T+z) is often called the “stimulated” echo of the three-pulse sequence. If r is short compared to T, and smaller than T,, Hahn(75) showed that the stimulated echo amplitude could be used to measure T,. The stimulated echo decay also has a different time dependence for the effect of diffusion from the primary echoes. A sequence of four RF pulses(77) generates a total of twelve echoes. In the general case when a regular sequence of equal RF pulses of the same phase is repeated at a rate faster than T2, but slower than T,*, a steady state is produced. A negative half-echo appears just before each pulse with a positive half-echo just after the pulse.‘78*79’ 3.8. Destruction of Steady-State Echoes The Hahn echo gives rise to phase and intensity abnormalities in one-pulse NMR, if the experiment is repeated fast enough. The repetitive sequence of pulses which is being used for the purpose of time-averaging causes a steady state to be set up. These problems are normally minimized by the use of a phase-cycling technique@‘) named CYCLOPS which was originally introduced to reduce receiver imbalance and cancel systematic noise. This CYCLically Ordered Phase Sequence advances the phase of the transmitter by 90” for each transient. It also alters the data routing from the two phase sensitive detectors to the computer locations where the data from channel A and B are stored. This process minimizes the “quadrature image” which appears symmetrically disposed about the transmitter position on the opposite side from the real peak. The quadrature image should be less than one percent. In spectra with a high dynamic range, the quadrature image may still be so large that the only solution is to place the whole spectrum on the same side of the transmitter. The resultant quadrature image falls outside the region of interest. The CYCLOPS phase-cycling procedure minimizes the formation of steady-state echoes since it is the time between pulses of the same phase which controls the Hahn echo, thus the sequence effectively multiplies the time between pulses by a factor of four. Another method for the destruction of spin-echoes involves the incorporation of a random delay into the sequence.(78) This varies the interval between pulses, which in turn varies the position of any residual magnetization in the xy plane. After a large number of pulses, the effects of the residual transverse components should be averaged to zero. The disadvantages are that many pulses are required for the averaging to be effective. This method cannot be used where timing between pulses is critical as in Tl measurements. Echoes can also be suppressed by the homospoil technique. (34)A pulsed magnetic field gradient is applied to the sample to destroy the momentary signal amplitude. In practice, this is accomplished by applying a pulse to one of the shim coils. Diffusion will transfer nuclei in a random manner to locations with different magnetic field strength. This destroys the phase memory of the precessing spins and eliminates echoes. However, echoes can also be generated as a result of magnetic field pulses,@‘) so the effectiveness of homospoil pulses might be improved by randomizing the time for which they are applied. This would add another stochastic process to help limit the phase memory of the spins. The disadvantages of homospoil pulses are that they severely perturb weak lock signals and

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that the magnetic homogeneity takes time to recover which sets a lower limit on the delay before the next event in the sequence. 3.9.

The Carr-Purcell Echo

A rather more familiar echo is that due to Carr and Purcell, (**)who used the sequence 90°-t-180° (Method A) and multiple refocusing 90°-(r-180%), (Method B) in order to minimize the effects of diffusion. The formation of such an echo is shown in Fig. 3. Here, the pulse has been applied on-resonance. After a time r, the isochromats have become diffuse (Fig. 3a). This is because the inhomogeneity across the sample causes some isochromats to precess slightly slower than the average, and some slightly faster. The 180’ pulse flips them into their mirror image along the -y axis. Now the dephasing process is reversed (Fig. 3b), so that at a total time of 27 all the isochromats are back in phase. This results in an echo. This configuration resembles the start of the experiment. Thus, further refocusing pulses at times 32, 5, etc. will generate further echoes at times 4r, 62, etc. This is called a Carr-Purcell train of spin echoes. The amplitude of these echoes is now independent of field inhomogeneity provided that a given spin does not diffuse into an appreciably different magnetic field in the interval 22. Multiple refocusing at a rate faster than the chemical shift difference between any spin-spin coupled nuclei that are present also prevents the formation of echo modulation (see Section 3.12). The decay of the echo amplitude can be used to measure spin-spin relaxation times. The spin-echo can be thought of as two free induction decays back to back. In practice, the time between refocusing pulses might be of the order of milliseconds. After many (possibly hundreds or thousands of) refocusing pulses the sequence is interrupted and the last echo collected. However, when multiple refocusing is used even small inaccuracies of the 180’ pulse width will lead to a cumulative error, i.e. the magnetization will eventually be forced completely out of the xy plane. In order to avoid this, the phase of the 180° refocusing pulses is shifted by 90” with respect to the phase of the 90” pulse. This is the principle of the Meiboom-Gill modification.‘83) The Carr-PurcellMeiboom-Gill (CPMG) sequence compensates for miscalibration of 180’ pulse, RF inhomogeneity and small off-resonance effects on all even numbered echoes, but breaks down in the presence of homonuclear spin-spin coupling (see Section 3.12 on Echo Modulation). Spin echoes have been discussed in much greater detail elsewhere.(“*‘*) As the delay between refocusing pulses is reduced the CPMG sequence resembles the “spin-locking” experiment(84*85) where a continuous RF field is applied along the y axis of the rotating frame. In practice, it is difficult to generate a sufficiently strong RF field for a period of seconds without

x

Pulse

Refocusing

FIG. 3. Formation of a Carr-Purcell echo with a 90’~r-1800 sequence of pulses with the same phase. Notice that refocusing would still occur if the phase of the 180” pulse was shifted by 90’. The echo would then be formed along the +y axis. JPNHRS 16:3/4-I

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appreciably heating the sample, and thus the CPMG sequence at high repetition rate is more useful for liquids. The compensation of the CPMG sequence can be improved by phase-alternation’86) of the 180° pulse so that the sequence becomes 90’(X)-(r-180’(Y)-2r-180”( -Y)-r),. This helps compensate for large off-resonance effects. However, the most important improvement in these experiments comes from the use of composite 180’ pulses,‘4g) since these composite 180’ pulses remain effective in the presence of homonuclear coupling. When the simple Carr-Purcell echo (method A) is being used, it should be phase-cycled over a 16 transient cycle, so that each pulse uses all four RF phases, in order to compensate for misset pulse lengths. This technique has been called the EXORCYCLE,‘87) and was introduced as a method for the elimination of artifacts in 2D J spectroscopy. 3.10. Rotary Echoes The rotary echo (88) is a completely different form of echo. This was one of the first techniques concerned with refocusing not the magnetic inhomogeneity but the inhomogeneity of the RF field. The RF field is applied long enough to rotate the magnetization vectors many times in the yz plane of the rotating frame. While the RF field is on the inhomogeneity of the magnetic field can be neglected. However, inhomogeneities in the RF field cause a loss of phase coherence in the yz plane. Rotating the phase of the transmitter by 180” reverses this, putting faster isochromats behind slower ones, causing a rotary echo. In practice, the experiment is initiated by a 90’ pulse so that the rotary echoes are formed along they axis. An alternative method of generating high resolution NMR rotary echoes has been demonstrated (8g)which involves the use of magnetic field pulses. 3.11. Miscellaneous Echoes In the special case of solution spectra of a quadrupolar nucleus with spin I = 1, (or in a solid) the problems resulting from the inability to record the initial part of the FID may be circumvented by the “quadrupolar”, or “solid” echo technique. (‘O)This consists of two 90’ pulses with the RF phase of the second pulse shifted by 90”. This cannot be adequately described by the vector model. The second pulse of the sequence causes a complete refocusing of the nuclear magnetization as long as irreversible effects due to resonance offset, static magnetic dipolar interactions with other nuclei, or fluctuating quadrupolar and dipolar interactions may be neglected. (‘I) Under these conditions the signal starting at the peak of the echo is identical to the FID following a single pulse. Thus, if the echo still has appreciable amplitude beyond the receiver dead time following the second pulse it is possible to avoid the distortions due to a finite receiver dead time. All the echoes discussed so far, have been single quantum echoes. Multiple quantum spin-echoes can be generated in a similar manner. (22) A related echo phenomena is that of coherence transfer echoes and anti-echoes.“‘) These echoes can only be observed in coupled spin systems. One type of such echoes results from coherence transfer between two different nuclear species. Since the gyromagnetic ratios are different, the times for defocusing and refocusing will be unequal, and in the ratio of their respective gyromagnetic ratios. These echoes have important ramifications in twodimensional experiments.(g3) Another form of this echo appears when coherence is transferred from a multiple quantum transition to a single quantum transition generating a sequence of several echoes, the number and timing of which reflect the number of coupled spins. (g2)Coherence transfer echoes will also contribute to the signal amplitude in multiple refocusing experiments on spin-coupled systems. 3.12. Echo Modulation One of the most useful features of spin-echoes is that they provide a method for the separation of the effects of spin-spin coupling from those of the chemical shift. For this reason spin-echoes have become an essential part of modern pulse sequences.

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(d)

FIG. 4. Vector diagrams illustrating the modulation of the amplitude of a Carr-Purcell echo. (a) Initial 90’ pulse at time zero. (b) Spin-spin coupling causes the magnetization to break up into a fast (0~)and a slow component (fi), each exhibiting a spread of magnetization due to the inhomogeneity in the static field. The chemical shift causes

a net precession of the mean frequency. (c) At time z a 180°pulse rotates all the vectors into new positions that are refiections in the y.zplane. (d) If the coupling is to a non-resonant nucleus, a conventional spin-echo is formed at time 22 with its amplitude independent of coupling constant, magnetic field inhomogeneity and chemical shift. (c’)If the coupling is to a resonant nucleus, then the 180”pulse at time r inverts the spin-states of that nucleus, interchanging the fast and slow components of the observed nucleus. (d’) At time 27, chemical shift and inhomogeneity effects are refocused, but spin coupling causes a continued divergence of the fast and slow components, leading to a modulation of the echo amplitude according to cos (xJT).

Homonuclear coupling gives rise to a modulation of the echoes,(g4*g5)which is sometimes called “J-modulation” or “phase-modulation”. Consider the case of two coupled protons (an AX system). After a 90” pulse the transverse magnetization from the A nucleus (Fig. 4a) will precess away from the y axis of the rotating frame because this nucleus is slightly off-resonance. But it will also be split into two components because of spin-coupling to the X-nucleus. One half of the doublet will be further from the transmitter frequency than the other, thus it will move faster in the xy plane. Both components of the doublets will become diffuse due to the inhomogeneity of the magnetic field (Fig. 4b). A 180” pulse is then applied, in this case about the y axis. If the A and X nuclei are separate nuclear species, i.e. heteronuclear coupling, then normal refocusing occurs as in Fig. 4c and d. However, if the two nuclei are homonuclear coupled then echo modulation occurs. This is because the 180’ pulse affects both nuclei in this case. The 180” pulse has two different effects, it flips all isochromats into a mirror-image configuration (Fig. 4c) but it also interchanges the spin-states of the X nucleus, which interchanges the slow and fast components of the A doublet (Fig. 4c’). As a result of this latter reversal, the slow and fast components continue to diverge after the 180” pulse and although chemical shift and magnetic-field inhomogeneity effects are refocused at time 22, two echo components occur, each dephased from the y axis (Fig. 4d’). The phase angle between them becomes progressively larger with time. For a simple first-order AX system, the modulation rate between the components of the doublet is JHz. The phase of each component of the doublet deviates from that of a singlet by an angle 8 = 2lcJr radians. Thus, for a first-order spectrum refocusing when 27 = l/J, a doublet will be 180’ out of phase with respect to the phase of a singlet. The central component of a triplet, like a singlet, shows no phase modulation but the outer components have a phase deviation rate twice as fast as doublets. Thus for 27 = l/J a triplet appears to be in phase because the outer components have undergone a complete revolution. This simple treatment only applies for the case of first-order coupling.(g6*g7) In the general case of a molecule with several groups of coupled spins, very complex phase modulation occurs. Although a rapid sequence of multiple refocusing pulses suppresses echo modulation, the best method is the acquisition of the whole echo combined with the absolute value mode of display.“@ Fourier transformation of the whole echo eliminates the dispersion-mode components from the echo signal. The sine and cosine transforms become amplitude modulated absorbtion signals. This modulation is undesirable so the absolute-value-mode signal is calculated. The elimination of

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dispersion components also avoids interference effects between the various lines in a spin multiplet. The delay t between the 90” and 180“ pulses should therefore equal half the acquisition time, with data acquisition starting directly after the 180’ pulse. If this delay is to be lengthened, then multiple refocusing (CPMG) at a rate faster than the chemical shift difference separating the coupled nuclei must be added. However, the delay between the penultimate echo and the last refocusing pulse must be extended to equal half the acquisition time.

3.13. Generation of Multiple Quantum Coherence Two 90” pulses separated by a delay z will generate multiple quantum coherence in a spin-coupled system if the delay z = (2N+ 1)/(24 where N is an integer and J is the coupling constant.‘22*99) If the two 90” pulses have the same phase then only even orders of multiple quantum coherence are excited. If there is a 90” RF phase shift between them, then odd orders of multiple quantum coherence are generated. This method of generating multiple quantum coherence is dependent on the resonance offsets. Insertion of a 180” pulse at the centre of the delay produces offset independent generation of multiple quantum coherence, which is the basis of the INADEQUATE experiment discussed in Section 8.7.2. The offset dependent generation of homonuclear multiple quantum coherence by two 90” pulses is mainly a nuisance since it destroys observable single quantum magnetization in a manner which is extremely hard to predict for a spin-coupled system of more than two spins. The effect can be minimized by phase cycling.(39) The generation of heteronuclear multiple quantum coherence can be put to good use as a simple method for the calibration of the decoupler power,““) and since this is a method of destroying all observable magnetization from heteronuclear coupled spins, it may be used as the basis of a reliable method of quaternary carbon selection in 13C NMRo0’*102) (see Sections 8.3 and 8.8). The sequence is shown in Fig. 5. The broadband proton decoupling is optional and just serves to impart an NOE, which improves the sensitivity. The delay z is set to l/(25). When the flip angle of the proton pulse is adjusted to 90°, the magnetization from nuclei which have an appropriate heteronuclear coupling constant cannot be detected after this pulse. The single quantum magnetization has been converted into zero-quantum and double-quantum coherence. Although these nuclei may be long-range coupled, these coupling constants are so small as not to interfere with this process. When this sequence is used to calibrate the decoupler power, it is advisable to check that an RF phase shift does not generate a change in RF amplitude.

S

FIG. 5. Pulse sequence for the destruction of observable single quantum magnetization in a heteronuclear coupled system. t is set to 1/(2J). The decoupling is optional. The short delay (u 100 usec) is undesirable but maybt necessary to allow for the hardware changes in the decoupler power and modulation mode to take place. When the decoupler is being used as a transmitter, it may be desirable to use its full power to minimize off-resonant effects; however, it should be possible to use less power for broadband decoupling if a suitable modulation scheme is employed.

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3.14. Binomial Pulse Excitation

The excitation pattern generated by a series of pulses can be approximated by the Fourier transform of the pulse sequence. The transform oi a simple pair of pulses separated by a delay T is a cosine function with null points at l/(22) either side of the transmitter.(lo3) This can be used as a method for the suppression of unwanted signals such as intense solvent peaks.‘lo4) The slope of the excitation pattern (or first derivative) at the null is at a maximum and thus a signal of finite width must be imperfectly suppressed (see Section 6.10).

4. RESOLUTION

ENHANCEMENT

4.1. Resolution Enhancement by Spin-Echo Techniques This form of resolution enhancement relies upon differences in line-width. The intensity of the sharper resonance relative to that of the broader resonance increases as the time between the read pulse and the data acquisition increases. The use of echoes for resolution enhancement is inherently better than the simple process of delayed acquisition(30) or the process of digital resolution enhancement(rg) because neither of these latter methods can reliably distinguish between a single broad line and a group of closely spaced sharp lines. The use of echoes is superior to that of delayed acquisition for the additional reason that it removes the large frequency dependent phase shifts which are an inevitable result of delayed acquisition. (31)Digital resolution enhancement has been shown to be capable of producing completely artificial splitting of peaks.‘ro5) Examples of the use of echoes for the selective suppression of broad components in complex spectra have been presented.(lOG-‘Og) Th ese effects have been put to especially good use in biochemical systems, such as whole cell work.” lo-l 12) 4.2. Reduction of the Effective Sample Volume The idea behind this technique is that if one could use a very small NMR sample then the magnetic inhomogeneity across the sample would be negligible. However, if the actual volume of the sample is reduced by using a microcell, then the resolution is degraded because of problems with discontinuities in the magnetic susceptibility at the edge of the container. But the effective volume can be reduced by exciting only part of the sample. This can be achieved by frequency selective excitation in an imposed field gradient.” 13)This basic principle is used in spin-imaging(’ 14)and topical magnetic resonance,” 15, though here the field gradient is only applied during the selective excitation and not during the data-acquisition. This method could help to improve the resolution of magnets which are already extremely homogeneous. Very similar effects have been reported (lr6) during selective population transfer experiments (see Section 7.4) where the line-width in SPT difference experiments depends on the length of the selective proton 180” pulse and not on the magnetic homogeneity. The use of composite pulses has been demonstrated as a method of discriminating against signals from sample regions where there is a large deviation from an ideal 180” pulse.““) These have been named “depth” pulses, and while they were proposed for use with surface coils they could find application with normal NMR probes. They consist of a simple Carr-Purcell echo sequence with the use of the EXORCYCLE”‘) on the 180° pulse and essentially no delay between the pulses. Further discrimination can be obtained by using additional phase cycled 180° pulses. 4.3. Removal of Baseline Distortion FT NMR spectra are notoriously prone to baseline distortion, especially when large spectral widths and very short acquisition times are used, as for instance, in the study of quadrupolar nuclei. These artifacts, often caused by the transient response of the probe, or acoustic ringing, can be thought of as broad (artificial) signals and can thus also be removed with a spin-echo. An alternative method

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exists(11s.119) which takes into account the difference between these artifacts and real NMR signals. Authentic resonances and acoustic ringing differ in that signals from acoustic resonance depend only upon the phase of the read pulse, while the phase of authentic signals depends upon their Ti. The experiment is performed in two parts. Firstly, the signal from a conventional read pulse is obtained, then the signal from an inversion-recovery experiment, with a very short delay between the 180’ pulse and read pulse, is subtracted from the first signal. The real peaks in the second part of the experiment will be inverted but the artifacts from acoustic resonance behave as if they have an infinitely short Ti. The real peaks will add coherently while the artifacts cancel. The sequence is set out below: T-90”-ACQ( +)-T-180°-r-90°-ACQ(

- ).

It might be thought that z would need to be long enough for the acoustic ringing from the 180” pulse to die away, however, this time can be shortened considerably by alternating the phase of the 180” pulse through a cycle such as X, -X. This results in the cancellation of the acoustic ringing from the 180° pulse over a cycle of four transients. Since the sequence leaves the z-magnetization inverted, the preparation time T must be much longer than TI in order that the signals do not cancel along with the acoustic ringing. 5. FREQUENCY

SELECTIVE

PULSED

EXCITATION

5.1. Introduction For sensitivity reasons, the basic intention in modern FT NMR is to provide non-selective excitation. The opposite situation can arise where it is desirable to excite a single nucleus or spectral line without perturbing the rest of the spectrum. Selective pulses are best avoided, if possible, since they tend to be tedious to implement. The selectivity of a pulse depends on its length, with the important result that a 180° pulse is always more selective than a 90’ pulse with the same transmitter power. A measure of the selectivity of a pulse might be taken as the distance to the first null in its excitation pattern. The excitation pattern of a square pulse of duration r corresponds to its Fourier transform which is a sin x/x (or sine) function. This function has its first null at frequencies approximately l/r away from the carrier frequency. This is only an approximation, but is quite useful in practice. In order to achieve a selectivity of 1 Hz, a pulse length of about one second must be used. An alternative to selective excitation is selective suppression (discussed in Section 6). Selective suppression is most often used as a method of removing unwanted signals, such as those from solvents, but has been applied to the observation of a single proton-coupled carbon site in a complex molecule by a form of difference spectroscopy.(‘*‘) 5.2. Very Low Power Pulses The simplest method that has been used to excite a chosen resonanceozl) is to adjust the spectrometer frequency so as to place the chosen line exactly on-resonance. The RF power is set so low that only the selected resonance line is significantly affected. All other lines are so far from resonance that their excitation is negligible. This is usually only possible for spectra with well-resolved groups of sharp resonance lines. A major problem with this technique is that relaxation during the pulse cannot be neglected. However, this is normally the method used to generate the selective 180’ pulses in selective population transfer experiments. 5.3. Long Pulse Techniques An alternative technique (21,122)is to place any unwanted resonance on the null in the excitation pattern of the pulse. This allows the transmitter power to be increased and reduces the problem of relaxation during the selective pulse. This means adjusting the transmitter power so as to give a 90’ flip to the chosen line but a 360” flip to the unwanted resonance. The signal to be suppressed

Multipulse.NMR in liquids

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experiences an affective field in the rotating frame of Bdf = 4B,. If A is the distance (in frequency units) of the signal to be suppressed from the transmitter, then since A, B, and B,s form a right-angled triangle, the pulse width can be calculated to be ((15/16)‘/‘)/A or 0.97/A. The major application of this experiment is to suppress signals from the solvent. It has also been used to generate the selective 180° pulse for inversion transfer experiments, in crowded spectra of compounds which have broad linesoz3’ The problem with any of these long pulse techniques is that if they are used as a read pulse then they introduce all the problems of delayed acquisition (see Section 1). Although these problems disappear if the long pulse is used prior to a normal non-selective read pulse, the problem of relaxation during the pulse remains. 5.4. DANTE All the methods discussed so far, require that the spectrometer frequency be adjusted to bring the desired line (or lines) into resonance. A very elegant but remarkably simple technique for selective excitation has been producedoz4) in which the position of irradiation is also adjustable. Instead of a single 90“ pulse, a regular sequence of m pulses of small Rip angle a are applied such that = 90". pulses are by delays which the are free precess. The are set the inverse the separation the chosen line from carrier frequency The chosen then precesses during each these delays, the pulses a cumulative turning this component down align it the y of the frame. Resonance at other do not this exact The cumulative of the and the during the takes them from the axis, often small circular around the axis. No transverse magnetization excited. In this is side-band technique. the first is used. selectivity depends the total of the of pulses, can also increased by a higher (iz3) DANTE Alternating with for This pulse has been Tailored It has used to partial spectra an individual coupled carbon in a where several overlap. (iz5) is possible that the decoupled lines resolvable. The involves selectively a single during broad-band decoupling. The establishes an enhancement and the spectrum. decoupler is gated off the acquisition the protonmultiplet subspectrum. series of spectra may assembled for chemical shift If many subspectra are be obtained alternative technique two-dimensional heteronuclear would be expeditious. The sequence illustrates general disadvantage one-dimensional techniques are concerned reducing the content of spectra. In where only small fragment the molecule to be these techniques be faster the rival techniques. However, the general where information to be from the molecule, the techniques are superior. Two-dimensional are often to avoid loss of content which inherent in selective one-dimensional by moving data into dimension. In DANTE sequence train of 20-50 pulses normally used reasons of This means some attenuation the RF of the is necessary, pulse widths less than psec are implemented properly most spectrometers. very short are used are often in shape. there is interesting possibility generating pulses small flip as a of two pulses 180° of phase, that the nutation angle the difference the two widths. The “short” pulse then have better shape. improvements to basic sequence phase-cycling the in order differentiate signals opposite sides the carrier in quadrature This can achieved by the phase a positive (O”, 90”, 270“) for frequencies from carrier, but them in opposite direction 270°, 1800, for frequencies the other of the

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carrier. This phase modulation of the pulses in a DANTE sequence also reduces the number of side-bands, since the pulse repetition rate becomes four times higher which leads to four times the sideband spacing. This can be an advantage in crowded spectra where the presence of more than one maximum in the excitation spectrum may be a problem. For example, the four phase cycle used above restricts the higher side-bands to (1+4M) where M is an integer. This leads to an excitation pattern with maxima not at. . . , - 3f, - 2f, - f, f, 2f, 3f, . . . etc. as in a conventional DANTE experiment but at . . . , -3f,f,5f...etc. Selective excitation by the DANTE sequence has been combined with single frequency offresonance decoupling during data acquisition as a method of multiplicity determination in complex spectra.(‘27*‘2*) The method has little to commend it. 5.5. Tailored Excitation Undoubtedly, the most elegant and versatile method for performing selective excitation is the concept of Fourier-synthesised or Tailored-Excitation. (12’) Unfortunately, it is also the most complex in practice. The basic principle is that the excitation pattern needed for a particular application is chosen. The computer in the spectrometer then Fourier transforms this pattern and uses it to modulate the amplitude or pulse-width of a sequence of RF pulses. Tailored-Excitation has recently been reviewed.” 30) 6. SELECTIVE SUPPRESSION 6.1. Introduction In biological or biochemical investigations, it is often necessary to study the NMR spectra of solutes in aqueous solution. The high dynamic range of these solutions causes instrumental problems. However, the appropriate hardware and software necessary for direct acquisition of proton spectra of solutes at millimolar concentration in aqueous solution (55 M H,O) is becoming increasingly common in modern NMR spectrometers. Nevertheless, it is often convenient to circumvent the problems inherent in direct acquisition. This might result in a saving in time for data-collection, by the use of pulses with larger flip angles. The major disadvantage of suppression techniques is that they are often sensitive to a whole collection of small instrumental imperfections. Painstaking optimization of a variety of experimental parameters, such as fine adjustment of pulse lengths, phase shifts, RF amplitude and transmitter frequency is necessary to counteract these defects and achieve an acceptable level of suppression. These sequences may require complete relaxation of the water signal. This means preparation periods of ca. 10sec will have to be inserted between adjacent transients. Thus, direct acquisition may turn out to be faster in the long run, especially if the time taken to optimize the suppression technique is included. Basically, there are only two methods of selective suppression. One can aim not to excite a particular signal, or to arrange that its magnetization is extremely small when the read pulse is applied. Steady state methods are also useful, however, they cannot eliminate a solvent resonance; they merely reduce it. The measurement of proton spectra in aqueous solution has been re~ewed.‘131.‘32’

6.2. Steady-State Method One of the simplest methods of solvent suppression is to optimize the data acquisition for the solute, not the solvent. When the solute is a macromolecule, differences in Tl and T2 between the solute and the solvent may be exploited by increasing the repetition rate of the experiment.(‘*) This has formed the basis of a steady-state technique, o33) which uses 90“ pulses repeated as fast as is consistent with the desired resolution (i.e. solute line-width). Four (or more) dummy acquisitions should be used before the start of data sampling.

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6.3. Presaturation Presaturation of the solvent signal with a long (and therefore selective) pulse at the solvent resonance frequency (or frequencies) prior to data acquisitiono3”136) is one of the most convenient methods of solvent suppression. Suppression ratios in excess of 1000: 1 can be obtained. These experiments often employ a presaturation pulse of 0.1-l set with low RF power. Turning the presaturation pulse off slowly helps to minimize the residual solvent signal.036’ The aim here is to turn the decoupler off in an adiabatic manner. The addition of a homogeneity spoiling pulse before data acquisition also helps. Separate phase-cycling of both the presaturation and the observe pulse in a 16 transient cycle is also desirable.t136) An important advantage of the presaturation technique is that it does not introduce any large frequency dependent phase shifts across the spectrum. This is especially important when broad lines (> 50 Hz) appear in the spectrum since the combination of broad lines and large frequency dependent phase-shifts often gives rise to baseline distortion (see Section 2.3). Another advantage is that suppression may be applied at more than one position by time-sharing the presaturation amongst the various frequencies. Problems appear when homodecoupling experiments are attempted in conjunction with presaturation.03’) The decoupler can excite an appreciable solvent signal during the data acquisition if the decoupler frequency must be situated close to the chemical shift of the solvent. The major disadvantage of presaturation as a method of solvent suppression is that transfer of saturation may occur from the solvent to the exchangeable protons. 03*~13g)This effect may be caused by either chemical exchange or cross relaxation. Exchangeable resonances will have their signals reduced if either their chemical exchange rate or cross-relaxation rate with the solvent is comparable with their spin-lattice relaxation rate in the absence of exchange or cross-relaxation. A method to overcome these problems has been suggested, (14’) which allows an extrapolation to be made of the peak intensity in the absence of solvent saturation. The technique is basically the repetition of the solvent suppression experiment with presaturation pulses of differing lengths. The extent of cross-saturation is reduced as the length of the presaturation pulse is reduced. A difficulty with this method is that if the presaturation pulse is applied for a short time it is then no longer selective. 6.4. Irradiation During Acquisition A very simple method of solvent suppression is to use a normal homonuclear decoupler to continuously irradiate the solvent signal(141~142)Thi s method has the advantage of no added delays in the sequence. High decoupler powers may be necessary to continuously saturate the water resonance in the time-shared mode.(141) The alternative to time-shared irradiation, which is to introduce a CW signal during acquisition,‘142) would almost certainly overload the receiver and produce distortion. The major problems with this method are that signals near to that of the solvent experience Bloch-Seigert shifts and off-resonance decoupling effects. Saturation transfer effects also appear. 6.5. WEFT One of the earliest methods of solvent suppression is the so-called WEFT technique(143) (Water Eliminated FT). In its simplest form this utilizes differences in Ti between the solute and the solvent. The inversion-recovery technique for measuring T, forms the basis of this method. Provided that the solute nuclei relax faster than those of the solvent, it is possible to choose a value of r such that the 90” read pulse is applied at the instant the solvent magnetization passes through zero. In situations of time-averaging, it is essential that the preparation time T > 5TlC,,where TIC,)stands for the Tl of the solvent. This can greatly reduce the efficiency of the experiment with regard to signal/noise enhancement. Increased efficiency can be achieved by performing the experiment under steady-state conditions.” 33) A homospoil pulse (HSP) is added to minimize any transverse magnetization. The sequence becomes: (T-180°-HSP-r-90’),.

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The steady state condition obeys the equation: exp (r/Ti(,))+exp (- T/T(,)) = 2 where Ti,,, stands for the ‘& of the solvent. Thus the time r can be calculated for any appropriate preparation time. A prerequisite for the successful application of this technique is a precise determination of Tics). For aqueous solutions, the principal area of solvent suppression, a Tr measurement requires at most 15 min. The steady state is reached when there is a dynamic balance between the effect of the pulse and the relaxation. Therefore, dummy pulses should be applied before data acquisition. Various authors have also explored this technique.044~‘45) WEFT has several disadvantages. Firstly, the relative intensities of the resonances may be significantly distorted by the use of WEFT, since partially relaxed spectra are being recorded. Secondly, the intensities of exchangeable resonances will again be distorted by the presence of cross-relaxation and chemical-exchange effects. Thirdly, the technique is not amenable to relaxation time measurements; and lastly, good temperature control and spectrometer stability is necessary to preserve the null condition and maintain the initial suppression ratio throughout the data collection. 6.6. Selective WEFT An important modificationo24’ of WEFT is to apply the 180’ inversion pulse selectively to the solvent resonance, followed by the normal delay and non-selective read pulse. A homospoil pulse may again be used to improve the repetition rate of the experiment. Although this experiment bears a superficial resemblance to WEFT, it is not dependent on the differential relaxation behaviour between the solvent and solute. Hence it is applicable when the Tl value of the solvent and solute are equal. This technique has been successfully applied in conjunction with NOE measurements.(‘46r It is not necessary to make the selective pulse exactly 180’ .(147)It is possible to shorten the delay z by adjusting the amplitude and duration of the nulling pulse to correspond to a nutation angle 0 in the range 90°-180”. For any desired z the nutation angle 0 is given by: cos 8 = 1 -exp (z/T,). Since the choice of the duration of the nulling pulse is limited only by the separation of the resonances of interest from the solvent, it can be made arbitrarily short (< 10msec) when observing resonances > 100 Hz away from the solvent. Since the delay F could also be shortened by appropriate choice of the nulling pulse flip angle, it should be possible to avoid the complications due to cross-relaxation and saturation transfer that plague so many methods of solvent suppression. In the suppression methods discussed so far, the aim is to disperse the solvent magnetization symmetrically so that no signal is observed. Presaturation disperses the solvent magnetization evenly over the surface of a sphere. WEFT disperses the magnetization in the xy plane. There is an alternative to these approaches, namely to attempt to concentrate the solvent magnetization along the +z axis. This can be achieved by selectively exciting the solvent magnetization and then returning it to the + z axis by further pulses and/or delays. For example, a selective pulse of arbitrary flip angle followed by a non-selective pulse with opposite RF phase but equal flip angle (’24)leaves the solvent with negligible transverse magnetization but the rest of the spectrum with full transverse components. 6.7. Long Pulse Methods Long pulse techniques also excite the solvent magnetization and then return it to the + z axis. They rotate the solvent magnetization in a cone about a highly tilted effective RF field, (see Section 5.3). This is achieved by placing the solvent resonance near the edge of the spectral width and reducing the transmitter power. Thus, if the solvent lies in the centre of the area of interest (e.g. proton NMR spectra in aqueous solution) the two separate experiments are required to measure the complete spectrum. The reduction in the transmitter power leads to large phase changes across the spectrum, which in conjunction with broad lines (> 50 Hz) gives rise to baseline roll.

331

Multipulse NMR in liquids -T

-0.6~ co.4

7 -c

FIG. 6. Redfield 2-l-4 composite pulse. 6.8. Redjield 2-l-4

The long pulse technique has been extended to produce the “Redfield 2-l-4” pulse,‘148) which is composed of a long pulse in which the third and eighth tenth of the pulse are phase-shifted by 180’ relative to the rest of the pulse, as shown in Fig. 6. The idea behind this composite pulse is that if two waveforms are added together in the proper magnitude and phase, it should be possible to produce a broad null by arranging to have the slopes of their Fourier transforms equal and opposite at the null. One of these waveforms is the usual sine function excitation, the other is a cosine function. A cosine was chosen for ease of implementation, because two narrow pulses spaced l/(22) apart will have a Fourier transform, which is approximately a cosine function, with a first null at the same position as a long pulse of length r. Thus the 2-l-4 pulse might be thought of as a long pulse of RF power B, (sine function excitation), minus two short pulses of twice the RF power (cosine excitation). A better null in the excitation pattern has been achieved by independently varying the length of the “4” section, This has been called the “Redfield 2-l-X” or “Magic-knob” sequence.(149) The Rcdfield 2-l-4 sequence achieves a suppression ratio of about 300 : 1. 6.9. Time-shared Redjield 2-l-4

This could be thought of as a combination of the phase modulated DANTE sequence (see Section 5.4) with a Redfield 2-l-4 pulse. (149*1so)It consists of a series of ten hard pulses separated by the appropriate delays, as shown in Fig. 7. The phases of the third and eighth pulses are inverted by 180’ relative to the other pulses. The delays separating the pulses make the overall length of the pulse train approximately the same as that in a simple Redfield 2-l-4 pulse. Analogous to the “Magic-knob” modification, the delays following pulses four to seven can be optimized by independently varying

a

a

FIG. 7. Time-shared Redfield 2-l-4

a

b

b

b

b

a

a

sequence. The length of the b delays can lx varied independently of the a delays to provide better suppression.

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their length. The time shared Redfield 2-l-4 sequence produces a suppression ratio of 500-1000 : 1. The time-shared sequence has the advantage that the total flip angle can be controlled independently of the overall spacing without having to change the RF level. This is especially desirable for experiments that require both 90” and 180” pulses. 6.10. Binomial Pulse Sequences

These sequences apply non-selective pulses separated by a delay r which is chosen so that r = l/(26) where A is the frequency separation of the signal to be suppressed from the transmitter position. This results in a cosine excitation function. These sequences can also easily be adjusted to give 1805 pulses. The phase of the pulses can be alternated to provide sine excitation (which moves the null position of the sequence to be coincident with the transmitter frequency). In either case the delay is chosen to be ca. 1 msec. The number of pulses and their widths are chosen as rows in Pascal’s triangle. These sequences are currently the most promising methods of solvent suppression, since they give high suppression ratios of above 1000 : 1, without saturation transfer from the solvent to solute. Their major disadvantage is that they generate a 180’ phase discontinuity at the position of suppression, and thus, would be unsuitable if a broad solute peak extends to either side of the solvent. There are also problems of unequal excitation across the spectral width. The simplest sequence (also mentioned in Section 3.14) would be 1,1°04) where the comma indicates the delay. A vector diagram of the magnetization in the yz plane during excitation by the 1,l sequence is shown in Fig. 8. The magnetization at the transmitter frequency is represented by a thick arrow, while the magnetization at l/(22) from the carrier is represented by a thin arrow. Before the first pulse, all the magnetization lies along the +z axis. The first pulse flips all the magnetization by 4Y. In the interval r, the magnetization at the transmitter frequency remains stationary whereas that at l/(27) from the transmitter precesses by 180’ in the xy plane. The second 45” pulse brings the magnetization at the transmitter frequency down to the y axis while returning that at l/(22) back to the +z axis. The principle is very like that of DANTE (see Section 5.4). The number of pulses in the sequence can be expanded to produce the 1,2,1;051-‘53) 1,3,3,1°54) or 1,4,6,4,1 etc. These sequences provide excitation with increasingly broad nulls in the excitation pattern. Phase inversion yields 1, - lo51) (also known as “Jump and Return”); l,-2,l or 1 -3 3 - 1.(15’) The 1,2,1 sequence transforms to give a cosine-squared function which again has a null in ;he same place, but now the first derivative is also zero at the null points. Thus, it has a much broader null which should result in better suppression. In general, a sequence based on the nth series of binomial coefficients will generate an excitation pattern of the form cos” (or sin”) and has n - 1 higher derivatives simultaneously zero at the null points. (ls4) However, there is a problem with increasing the length of the sequence. The longer the sequence, the greater the frequency dependent phase correction that has to be applied to the final spectrum. Therefore, there is a greater likelihood of baseline undulation. In theory, sine excitation is preferable to cosine excitation since the transmitter is placed in the centre of the spectrum in the former case. Thus, sine excitation should be less sensitive to off-resonance

FIG. 8. Vector diagrams to explain the 1,l suppression sequence. The magnetization at the carrier frequency is represented by a thick arrow, while that at l/(2 r ) from the carrier frequency is shown as a thin arrow, in the yz plane of the rotating frame. Prior to the first pulse, all the magnetization lies along the + z axis. The first pulse flips all the magnetization by 45”. During the interval r, the magnetization at the carrier frequency remains stationary whereas that at 1/(2r) from the carrier frequency precesses by 180° in the xy plane. The second 4Y pulse brings the magnetization at the carrier along the +y axis and returns that at l/(27) from the carrier back to the +.z axis.

Multipulse NMR in liquids

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effects of the finite B, field. Sequences with even numbers of pulses would also be predicted to be superior. Since even if the pulses are nonideal, or their ratio is incorrect, then the symmetry of the sequence ensures that there is still a null, albeit less flat. In practice, attenuation of the RF field strength has been recommended(‘55) in order to improve the shape of the pulses. The choice of which of these sequences is best in practice is probably highly dependent upon instrumental defects, and may even be solute dependent because of problems with multiple-quantum and echo effects. A discussion of the theoretical aspects of these sequences, and their practical implementation has been presented.‘132) 6.11. Miscellaneous Other techniques which have been used for solvent-suppression include the DEFT (Driven Equilibrium Fourier Transform) technique which is discussed in detail in Section 7.2. The suppression ratio obtained was rather low, typically 100: 1.(‘56*157) Spin-echo spectra have also been used for solvent suppression (lo’) while measuring spectra of small molecules contained in cellular systems such as human erythrocytes suspended in D,O or H,O at high magnetic field strengths (9.4T). Under these conditions, the residual HDO (or H,O) signal has an abnormally short T2 (0.1 set or less). 7. SENSITIVITY

ENHANCEMENT

7.1. Introduction Pulse sequences which are designed to improve the sensitivity of an NMR experiment must do so selectively, i.e. one resonance (or type of resonance) is enhanced while others are either reduced or suppressed. Thus, the sequences which are discussed in this section might find application in selective suppression, multiplicity selection or spectral editing. 7.2. DEFT One of the first techniques for signal enhancement(‘58) was used to effect a rapid restoration of the equilibrium magnetization during a study of the spin-relaxation time of 12’Xe. This technique was later proposed as a general method of signal enhancement especially for 13C studies”5g) and named the DEFT (Driven Equilibrium Fourier Transform) technique. The DEFT sequence is set out below: ( T-90°-ACQ-1

80°-r-90’),

where 7 stands for the minimum usable acquisition time. The first two pulses constitute a normal spin-echo sequence, with data being acquired in the delay between the 90° and 180’ pulses. At a time equal to twice the acquisition time a partial reversal of the dephasing of the magnetization in the xy plane occurs. The final 90” pulse applied at the peak of the echo restores the refocused magnetizaion to the z axis ready for the next sequence. In the case where T1 = T, optimum sensitivity would be achieved where T= 47. Since in practice Tl > T, > T? the sensitivity gain from this sequence is rather 10w.(‘~~) DEFT is of little practical value because refocusing also occurs in the steadystate(78s7g)response to a regular sequence of pulses repeated at an interval 7 <: T,. This enhances the sensitivity by an amount comparable to DEFT. DEFT has been used as a method of solvent suppression but does not achieve particularly high suppression ratios.” 56*157) 7.3. Steady-State Techniques It is well known that in the pulsed FT experiment there is a conflict between the conditions for maximum sensitivity and those for maximum resolution. Thus, a simple method for sensitivity enhancement presents itself, which is to sacrifice resolution. The highest sensitivity is attained when the pulses are repeated at a rate equal to the inverse of the desired resolution. Thus, if one were prepared to accept observed line-widths one hundred times broader than their natural width a gain

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in sensitivity of a factor of ten might be made. (16r) This increased line-width may be caused by deliberate reduction of the acquisition time or by the study of very sharp lines in an inhomogeneous magnetic field. The problem with rapid pulsing is that it leads to phase and intensity variations across the spectrum. (78)These variations are a periodic function of offset across the transformed spectrum with a relatively high frequency l/~r Hz where r,, is the total time between the pulses. They are caused by Hahn or steady-state echoes. The maximum signal intensity is obtained at an offset of (2n + 1)/(2T,) where n is an integer. To paraphrase this, the maximum steady state magnetization occurs midway between two of the sidebands created by the repetitive pulsing. Conversely, the minimum intensity occurs if the signal happens to sit directly on top of one of the sidebands. Thus, if the position of the signal to be enhanced is known, the spectrometer frequency can be adjusted to maximize the steady state component of its magnetization in the xy plane. Of course, this is not possible while searching for a signal of unknown position, so some method has to be found to avoid the minimum signal. The best method of achieving this is to move the sidebands, either by changing the transmitter frequency or by varying the delay between transients in a block-wise manner so that a variety of different steady-states are used. The first of these methods has been called the Quadriga FT technique.(16’) It involves the acquisition of the FID, four separate times with different spectrometer frequencies each time. The frequencies are given by the equation: 0, = ma -n/(4r,) where n = 0, 1,2 and 3, rp is the total time between pulses, WE is the basic offset and w, is one of the four different offsets which are actually used. These must all remain on the same side of the resonance to be detected, which constitutes a minor problem if the position of the signal is not known. The four separate decays are Fourier transformed and then added together after displacing the origin of each spectrum so that the desired signals are superimposable. The technique has been applied to an impressive array of slowly relaxing nuclei with poor NMR receptivity, such as 57Fe 062~163) '09A (164)183~(165)89y_(166),,d 103Rh(l67)of course, all these single line spectra are obtained with is very low digital resolution because that is the essence of the technique. The addition of a random delay between adjacent transients in one-pulse NMR suppresses the formation of echoes. This removes the offset-dependence of the signal intensity that occurs when the time between pulses is less than T,. It also removes any gain in sensitivity from the steady state. An alternative technique which retains this gain is that of the scrambled steady stateJ7’) This involves the periodic change of a random delay between transients. This delay is kept constant within a batch of about 64 transients. This allows the sensitivity gains from each steady state echo to build up, but the final average suppresses the echoes. A minor problem with these steady state echo techniques is that the time between pulses of the same phase has to be of the order of T, in order to generate these echoes. Thus, if the normal artifact suppression by CYCLOPS phase cycling is desired, then the acquisition time will have to be reduced by a further factor of four. 7.4. Heteronuclear Selective Population Transfer Selective Population Inversion (SPI) and Selective Population Transfer (SPT) are the FT analogies of the INDORo68,‘69) experiments used in CW NMR. The two acronyms SPI and SPT tend to be used interchangeably in the literature, probably because complete population inversion is the experiment which is normally attempted, but is not always achieved in practice. The convention adopted here is to refer to the experiment as SPT, while referring to the 180’ pulse used in the experiment as a SPI pulse. The technique was originally introduced in its homonuclear form,t”‘) but has found greater application in its heteronuclear version. 071-173) This involves a CW decoupler pulse of low power yB,/2n = 0.1-l Hz which is applied selectively to a heteronuclear transition (usually a satellite signal) for a time r equal to a selective 180’ pulse prior to normal broadband excitation by a non-selective read pulse. Provided that r is chosen to be less than the shortest Tl of any of the connected

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FIG. 9. Energy levels and relative populations, in units of B&CT, for an AX spin coupled system of one proton and one nitrogen.

heteronuclear transitions, the decoupler pulse causes inversion of the corresponding energy level populations. In a hereronuclear AX system, the excess populations are proportional to yA and yx. Substantial increases in sensitivity are expected when irradiating the nucleus having the higher magnetogyric ratio (usually protons). A slight disadvantage of the technique is that it requires a knowledge of the position of the satellites in the proton spectrum, though this can be estimated from an approximate value of the coupling constant. A more important disadvantage is that since only one transition is normally excited, only one resonance is enhanced at a time. While this has obvious applications in the area of spectral assignment, it is inconvenient as a general method for sensitivity enhancement. In order to visualize the cause of these gains in sensitivity, Fig. 9 sets out the energy levels, populations and single quantum transitions for an AX system of 15N and ‘H. It is easier to understand the effect of a selective population inversion if we add yu/2 and y~j2 to all the populations and substitute yu/y~ = 10 as shown in Fig. 10a. The intensity of a transition is related to the difference

(b)

FIG. 10. (a) Effect of a selective population inversion on the population of the energy levels of an AX system of one proton and one nitrogen. (b) Comparison of the intensities in the resultant spectra.

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in population. Figure lob now clearly demonstrates the effect of a selective population inversion. Thus, the spectra display an enhnacement y&N (ca. 10). Normal decoupled spectra show an Overhauser enhancement which, at its maximum value reaches 1+ (Y&N)/2 (ca. - 4).(174)Protoncoupled spectra may be obtained with almost this enhancement by allowing the Overhauser effect to build up during a delay of 55lOI’, while the protons are irradiated. The decoupler is then gated off during the acquisition. The effects of spin coupling reappear immediately. The time constant for the decay of the Overhauser enhancement is close to Tr. Thus, their effects can be separated. The Overhauser enhancement is much smaller for nuclei without an attached proton. Published valueso75’ for 15N in pyridine show the NOE = 0.6 with Ti = 85 sec. In this case, substantial enhancements per transient should be obtained with SPT. A further advantage of the method is that the repetition rate of the experiment depends on the proton Ti. Since these are often shorter than those of other spin l/2 nuclei, there can also be a considerable gain in time. This has been demonstrated in some 15N SPT experiments on pyrrole and 2-fluoropyridine where truly dramatic results were achieved.“‘@ The spectra are normally obtained in a proton-coupled form, but do not display the normal intensity distribution for the components of the multiplets. Doublets appear as + 1, - 1, triplets + 1, 0, - 1, and quartets + 1, + 1, - 1, - 1. In molecules with degenerate proton transitions such as an AX, spin system, extremely large intensity gains may be obtained. The largest gains are predicted for the outermost lines of a multiplet. An especially impressive demonstration of this feature of the study of degenerate spin systems has been given by some 29Si SPT experiments.(178~179’ Extremely useful gains in sensitivity have also been made in the study of quaternary carbons.(180*181) The results of SPT may be conveniently displayed in the form of the difference between the normal and SPT spectra. This eliminates all lines not affected by the SPI pulse. (ra2) The same experiment with a slightly better timing scheme has been used to observe hidden lines in i3C spectra.‘183’Although the sensitivity gains in SPT experiments are greatest when the irradiated nucleus has higher magnetogyric ratio than the observed nucleus, the experiment can be carried out in reverse. In highly degenerate systems, sensitivity gains can still be obtained. This has been demonstrated in SPT experiments on methyl isocyanide where 13C was observed whilst 14N nuclei were irradiated.oE4) The ratio yl4N/yl3c is only 0.3 but application of a selective 180” pulse to a nitrogen transition leads to intensity changes of up to 50 %. The application of the SPT technique has an inherent difficulty, if it must be applied to closely spaced lines. A very long 180’ pulse (which is more selective) must be used to avoid perturbing any close lying transitions. However, the longer the 180“ pulse, the greater the likelihood of relaxation during the pulse. In order to avoid this problem, the alternative technique of continuously irradiating the satellite lines has been proposed. (1*5,186)The idea that this is in fact better than a SPI pulse, has been refuted on the grounds of both experimental resultsoE4’ and computer simulations.“87’ There have been other studies of intensity variations in experiments involving continuous irradiation.088~1 90)A summary of some of the applications of SPT is presented in the next paragraph. In this connection, it may be worth noting that the acronym SPT has also been used for Soft Pulse Transfer experiments,““’ which is another name for saturation transfer experiments. The SPT experiment has also been called GASP for GAted Spin tickling. u’~) Neither usage will be adopted here. Sensitivity gains have been reported in experiments involving SPT from 19F to 15N in 2-fluorocoupling constants,“93*194’ to determine pyridine. (19’) SPT has been used to assign carbon-proton the magnitude and relative signs of coupling constantso95-201’ and to detect partially resolved heteronuclear coupling.(202) Resolution enhancement by SPT has been demonstrated.” 16)This occurs because the selective pulse affects only the ‘H spins in a particular slice of the sample. Hence, magnetization is transferred only to those nuclei in the same slice. As discussed in Section 4.2, this is a method of resolution enhancement by restricting the effective size of the sample. A method for analyzing relaxation data obtained by introducing a delay after the SPI pulse has been presented!203’ A procedure for selectively inverting transitions of both the A and the X nucleus successively, in order to retain the SPT enhancement in decoupled spectra, has been demonstrated. This has been proposed as a time-saving method of Tl measurement for nuclei with negative magnetogyric ratios.(204’

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However, there is a much more convenient method for insuring that the various components of a multiplet do not interfere destructively (‘05) which is based on refocusing and is discussed in Section 7.5. SPT combined with selective proton decoupling has been demonstrated,‘206) as has a method of using completely proton decoupled SPT spectra as a technique for selective r3C-lH chemical shift correlation.(207) 7.5. INEPT The INEPT (Insensitive Nuclei Enhanced by Polarization 7ransfer) pulse sequence(205) is an elegant method for achieving a J-selective population inversion. It belongs to a small, but important, class of one-dimensional experiments which can be thought of as being derived from two-dimensional NMR. The two-dimensional precursor of this experiment is the heteronuclear chemical shift correlation experiment.(208) A modification of INEPT was also one of the first methods to demonstrate the utility of multiplicity selection (or spectral editing) in proton-decoupled 13C NMR spectra.(209) The pulse sequence is set out in Fig. 11. In order to understand how the sequence works it is convenient to consider an AX system of one proton (Z-spin) and one carbon (S-spin). In Fig. 12 the

FIG. 11. INEPT pulse sequence. r/2 is set to 1/(4J). In this, and subsequent, diagrams the phase of all 180” pulses is of no practical importance, apart from the necessity of inverting the receiver reference phase if the phase of a 180° pulse is changed by 90”. All 180” pulses should be phase-cycled through all four RF phases. To eliminate undesired contributions from the native S-spin magnetization, the 90° I-spin transfer pulse is alternately applied along the +y and -y axis, combined with inversion of the receiver referencephase. The delays are labelled r/2 to emphasize that the delays in this sequence are half those in DEPT. (a)

z

h

Y

x

(d)

1

FIG. 12. Vector diagrams to explain the behaviour of the I-spin magnetization during the INEPT pulse sequence.. After an initial 900 pulse (a) the two vectors precess for a period r and acquire a relative phase angle of 900 (b). A 1800pulse about the x-axis flips them into mirror-image positions (c), while a simultaneous 1800pulse on the S-spin interchanges the spin-state labels (d). Further precession for a period z leaves the vectors opposed along the x axes (e). A !W pulse about the y axis aligns them along the .z axes (f). The magnetization represented by the a vector now has inverted spin populations. .JPNpLRs 16:3,4-J

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TI

3

’

2

sequence. t1/2 is set to

~~ varies with the multiplicity

vectors CIand /3.The first proton 90° pulse tips the magnetization (Figure 12a). During the delay 1/(4JcH) vectors 0:and /I a relative vectors continue diverge. At the time of the echo, the two have acquired relative phase angle of 180“ (Fig. 12e). At this the third proton pulse (which is phase-shifted rotates the magnetization vectors

difference Thus, INEPT requires

Section 7.4 on SPT. The refocus the chemical protons. position of the carbon satellites

spectra was originally proposed spectra of sequence is shown in Fig. decouple containing multiplets at non-equilibrium states, various components precess to a position related to both J and the multiplicity applied simultaneously nucleus and the observed nucleus, to minimize off-resonance effects. This sequence

in the first description dipeptide.” 13. Basically,

against the angle 0 =

zJ7,.

Multipulse NMR in liquids 90~

180 ~

90~

901

J80 ~

339 90~

180 ~

~-I II I-P HJ VI HR__] q? --ff

-U

"-ff

DecoupLe

180 ~

900

180 ~

901

180*

901

FIG. 15. PREP pulse sequence: "c1 and ~2 are set as in refocused INEPT. been called refocused INEPT. 1211) It may be useful to employ composite 180 ~ pulses, especially during the z2 interval. The delay zl/2 is always set to 1/(4J) while the value of t2 varies with multiplicity. Ir doublets are to be decoupled, then %q should also be set to 1/(4J) while for triplets 1"2/2should be set to 1/(8J). Figure 14 shows a graph of the enhancement factor against the precession time for various multiplicity values. From Fig. 14, ir is apparent that to observe all the signals in the spectrum irrespective of their multiplicity, a 1"2/2 delay of 1/(6J) is appropriate. However, an important effect is observed ir the ~zq delay is set to 3/(8J), when triplets appear negative while both doublets and quartets appear as positive peaks in the final spectrum. In practice, phase cycling is used to suppress any contribution from the magnetization which does not arise from polarization transfer. Ir is also used to minimize problems with inaccurate phaseshifting and miscalibration of the 90 ~ and 180 ~ flip angles. Since seven pulses are used in the refocused INEPT sequence quite extensive phase cycling could be envisioned (in principle up to a 1024 transient cycle, as five of the pulses could be independently cycled though all four RF phases, while the other two can only have their phases inverted, making 45 x 2 x 2). However, a cycle of between 32 and 128 steps is often adequate. An alternative method has been proposed for obtaining decoupled INEPT spectra, which has been named PREP (Population Redistribution for Enhancement with Proton decoupling). (z12) The sequence is set out in Fig. 15 and involves a sequence of population transfers involving both the observed and decoupled nuclei. This technique will probably be of limited practical value because of its complexity and also because the sequence takes longer than refocused INEPT. The only major improvement to the refocused INEPT sequence is concerned with the observation of proton coupled spectra with the natural multiplet patterns known from conventional NMR spectra (whose intensities ate given by the binomial coefficients or Pascals' triangles). This has been called INEPT+J 213) The sequence is shown in Fig. 16. The improvement in the sequence being the addition of the final 90~ decoupler pulse. This also reduces the phase distortions resulting from variations in the coupling constants. This phase-shifted 90 ~ pulse is often referred to a s a "purging" pulse. The vector model is unsuitable for an explanation of purging pulses. The interested reader is referred elsewhere.(13,213) The same sequence has also been suggested a s a form of spectral editing and named SEPT, (214) although INEPT + seems to be a preferable name. INEPT has been applied to sensitivity enhancement in a variety of nuclei: 13C,(215-11s) 14N(219) 15N,(21~176 11B,(222) 1~ and 1~ and 119Sn,(224)although some of these examples are mete demonstrations while others ate real applications. INEPT has also been applied to the indirect detection of deuterium double quantum transitions. (215) Polarization transfer from nuclei other than protons has also been demonstrated, examples include 13C{2H},(226) 57Fe{31P}, 103Rh{31e} ' 183W{31p} (227)

340

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ie0*

sil

FIG. 16. INEPT+

pulse sequence: 2, and ~~ are set as in refocused INEPT.

One of important factors considering any pulse sequence its length, T2 relaxation normally ignored the discussion the sequence. importance of point has demonstrated by failure of INEPT to any enhancement the ’ NMR spectra tRNA, a of MW (211)There to be contributing factors. both the and the have quite T2 values secondly the Tl values actually shorter those of protons. INEPT probably a useful sequence refocused INEPT INEPT+. Sensitivity is often in the of proton-coupled INEPT is remarkably insensitive to errors in the parameters. Most importantly, INEPT is a very short sequence. 7.6. DEPT An important variant of INEPT has been demonstrated which has been entitled Distortionless Enhancement by Polarization Transfer (DEPT). (22s)The sequence is set out in Fig. 17. Although the sequence does provide less distortion it is not distortionless as implied by its However, DEPT have the over the sequence that is less to the variations in coupling constants. DEPT is suited to task of editing than INEPT. DEPT produces the mutliplet patterns the spectra not decoupled. it suffers a major The time for the is three longer than basic INEPT This disadvantage been demonstrated a comparison INEPT and which shows INEPT provides significantly better enhancement for with broad (229) DEPT a generalization the related sequence (Exclusive Transfer)(230) and been further to form UPT sequence Polarization Transfer.‘231) use of for multiplet experiments is in Section

I

FIG

DEPT pulse

z is

to l/(24.

341

Multipulse NMR in liquids

9

G

Decouple

FIG. 18. SINEPT pulse sequence: z, is set to l/(25), 7z is set as in refocused INEPT.

7.7. SINEPT

SINEPT is an exact one-dimensional replica of the original two-dimensional heternuclear chemical shift correlation experiment. It provides a method for performing polarization transfer experiments on spectrometers which are not equipped with 90” phase shifting capabilities in the decoupler channe1.(232) The pulse sequence is set out in Fig. 18. A 180’ i3C pulse may be used at the start of each alternate transient to suppress the native ’ % magnetization. It differs from INEPT (See Section 7.5) in that it omits the two 180“ refocusing pulses applied to both the decouple and observe channels at the midpoint of the ‘F~ interval in INEPT to make the polarization transfer process independent of the decoupler position. Thus, the polarization transfer process shows a sine function dependency of the frequency separation between the position of the decoupler and the individual proton chemical shifts. Because of the broad extrema for the sine function, this may not be too serious in practice. Two SINEPT experiments must be performed with the decoupler position differing by J/2, to insure that all proton bearing carbon sites in a large molecule may be observed with intensities of at least 70 % of those which would be observed with INEPT. SINEPT should be easier to perform than SPT for general sensitivity enhancement but SPT would be preferable for assignment purposes. 7.8. SESET

SEmiSelective Excitation for polarization Transfer (SESET) (233) has been demonstrated as a method for sensitivity enhancement. Like SPT (see Section 7.4) or SINEPT (Section 7.7) it requires no form of RF phase shift. It is closely related to SPT but involves the use of a pulse of carefully chosen amplitude and flip angle. Semi-selective excitation is taken to mean that the pulse affects not just a single line but a whole multiplet. For example, the i3C satellites in a proton spectrum. The semi-selective pulse would be centred between them. Selective excitation by the DANTE sequence (see Section 5.4) has been advocated. The purpose of carefully selecting the pulse power and length is to tip the magnetization associated with the two satellites A’ and A” in opposite directions in the rotating frame. A normal non-selective pulse hips all the magnetization in the same direction. A selective pulse is designed to flip the magnetization of one specific line only. If the magnetization was in equilibrium, this semi-selective (X) pulse would Ihp one satellite (A) to the +x axis and the other satellite (A”) to the -x axis. After the semi-selective excitation, the two magnetization vectors lie 180’ apart in the xy plane. During a carefully chosen delay the magnetization vectors rotate by 90’ in the xy plane, to lie along the +y and -y axis. This delay has the same effect as the 90” phase-shift of the last proton pulse in INEPT. Thus, precession in the xy plane is used to avoid the necessity of a phase shift. The application of a non-selective 90” proton pulse then rotates the vectors to the +z and -z axis which corresponds to a selective population inversion. The subsequent 90” read pulse permits detection of enhanced antiphase proton-coupled spectra. Appropriate refocusing may be added to obtain proton decoupled spectra. Notwithstanding the undeniable elegance of the spin-physics associated with the semi-selective

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pulse, the sequence will probably be of limited use, since it is no easier to perform than SPT and probably a lot harder than SINEPT. It has been extended to form the basis of SESETACR(234) (SEmi Selective Excitation for polarization Transfer and Assignment of Carbon Resonances) which is analogous to DSPT experiments (see Section 9.3). 7.9. J-Cross Polarization Sensitivity enhancement by cross polarization is commonly used in the observation of i3C NMR spectra of solids. (235)Cross polarization can also be used in the study of liquids. In this case, it is the spin-spin coupling (not the dipolar coupling) which is responsible for the coherent magnetization exchange at a frequency comparable with the coupling constant: this technique is thus referred to as J-cross polarization (JCP). A related JCP experiment was first considered by Hartmann and Hahn,‘236) who developed the theory and determined ‘J mu in hypophosphorous acid by observation of the proton magnetization in a proton-phosphorus cross polarization experiment. The sequence can be described as follows. Initially, the protons are flipped 90” from the z to the y axis and then spin-locked along this axis by a 90’ phase-shifted RF field of strength Biu. Simultaneously, an RF field Bit is applied for a time known as the “contact-time”. The RF field strengths are balanced so that the respective nutation rates are identical i.e. yHBIH = y&c. When the matching is exact, (which is known as the Hartmann-Hahn (H-H) condition), the two nuclei will exchange polarization periodically keeping the total polarization constant. The resultant spectra can be obtained either proton coupled or decoupled. The technique has the same advantages as SPT or INEPT in that the pulse repetition rate is governed by T,(H) and the intensity enhancement is determined by the ratio of the magnetogyric ratios. However, it has the severe disadvantage that the accuracy of matching the H-H condition is far more important for liquids than solids. For liquids, the mismatch of the RF power must be less than the coupling constant. This may be hard to maintain over the whole sample unless a single coil is used for both observation and decoupling. Another problem is that the decoupler power, on an NMR spectrometer designed for the study of liquids, will usually be far less than that of the observe channel, Another method of expressing the H-H condition is to realize that the 90” pulse width must be equal for both nuclei. This is usually far from true. For example, on a 10mm probe on a commercial spectrometer, the 90” pulse width for carbon will usually be betweeen lo-20 usec while the 90” pulse width for the proton decoupler will often be of the order of 30-50 usec. For the experiment to work, the two 90° pulse widths will have to be equal to better than 1 usec. The easiest solution would be to attenuate the observe power. However, this leads to problems with unequal excitation across the spectral width. Despite all these problems, sensitivity enhancement by JCP has been demonstrated for 13~

(237)

15~(238)

and

29Si (239)

Various modifications to the basic experiment have been proposed. If proton-coupled spectra are desired, the relative phases of the multiplet lines will vary with the contact-time. This can be overcome by adding a 90” purging pulse to either the observed or decoupled nucleus at the end of the contact-time. This modification has been called Phase Corrected J-Cross Polarization (PCJCP).(240) The undesirable sensitivity of JCP experiments to mismatch in the H-H condition can be reduced by using a refocusing technique called RJCP (Refocused JCP). (241)The pulse sequence involves briefly turning off both RF fields during the spin-locking for a time equal to a 90’ pulse. The difficulty of obtaining the H-H condition can be circumvented by simultaneously varying the amplitudes of the two RF fields in opposite directions, so that at some instant a cross-over and match is achieved. When this occurs there is an adiabatic transfer of magnetization and the technique has thus been called AJCP.(242) Adiabatic Demagnetization in the Rotating Frame (ADRF) and subsequent Adiabatic Remagnetization (ARRF) have also been used. (243)These are actually methods of performing a selective population inversion, and have been analyzed theoretically!244) The problem with sensitivity enhancement by any form of JCP is the practical one of implementation. Despite the elegant modifications designed to reduce the undesirable sensitivity to the mismatch of the H-H condition these sequences are unlikely to be of any practical value. The major

Multipulse NMR in liquids

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use of cross polarization in liquids is as a method of checking the H-H condition before cross polarization experiments on solids are undertaken. Thus, it is the sensitivity to mismatch which is being employed. Experiments such as AJCP, ADRF and ARRF involve the use of “shaped” pulses which are not normally available on commercial spectrometers. Probably the most interesting use of cross polarization is its ability to provide information on the distribution of molecular motion. For instance, it has been used in a study of the gelation of deoxyhaemoglobin S molecules. The normal “C-{ ‘H} experiment detects only the isotropically mobile haemoglobin molecules with rotational correlation times less than 1 usec, whereas cross polarization experiments induce signals only from the motionally restricted molecules. Thus, the fraction of haemoglobin in the polymer phase can be determined.(245) 8. MULTIPLICITY

SELECTION

8.1. Introduction Multiplicity selection may be performed by introducing delays which are related to the reciprocal of an appropriate coupling constant. These experiments are, therefore, also J-selective. Pulse sequences have been proposed (246)which are designed to achieve J-selective excitation. These will also perform multiplicity selection. In general, multiplicity selection experiments require the presence of a limited and predictable set of coupling constants. This is their major drawback. 8.2. Homonuclear J-Modulation Echo-modulation has been employed in a variety of ways to simplify the interpretation of overlapping homonuclear coupling, by altering the phase of a selected signal (or signals) in the final spectrum. The best example of this has been in the proton spectra of proteins.(247) The suitable editing of complicated spectra is often of crucial importance in the study of biomolecules.(248) The simplest technique, which has been called Spin-Echo Difference Spectroscopy (SEDS), involves the acquisition of spin-echo spectra with and without multiple refocusing. A rapid sequence of multiple refocusing pulses suppresses J-modulation. The difference spectroscopy is not strictly necessary but serves to allow for differential T, relaxation. Since the phase of the observed signal will depend on whether it has even or odd multiplicity the difference between these two experiments may be used to explore the multiplicity of the various resonances. This process is explained in more detail in Section 8.3. The technique has been used to study the tryptophan residues in the proton spectra of lysozyme(248~249) and in carbon spectra for the examination of overlapping signals showing carbon-carbon coupling.(250) In the latter example there was no need to use difference spectroscopy. A related technique (251) designed to remove many of the signals from overlapping proton multiplets, sums the results obtained in spin-echo experiments with different delay times. Since the signals from most multiplets are cosinusoidally modulated as a function of the delay time in the spin-echo sequence, summing the results for a variety of delay times causes these signals to vanish. The resulting spectra only contain singlets and the centre lines of odd multiplets, such as triplets. This has been applied to the simplification of the aromatic region of the proton spectrum of the enzyme RNase. In practice complete averaging for different J-values is impeded by an insufficient number of delay values used in the averaging process, and also because of relaxation effects. This experiment can be improved by the addition of a 90’(Y) purging pulse. The purging pulse. is inserted immediately before acquisition in every ,alternate transient. The only phase cycling necessary is a simple phase alternation of the 90” preparation pulse with alternate addition and subtraction of the incoming signals. 8.3. Heteronuclear J-Modulation Multiplet selection by J-modulation has been applied to heteronuclear spin systems.(35,z53-255) This technique is another example of a one-dimensional experiment which could be thought of as

344

C. J. TURNER (a) I

Decouple

Decouple A

(b)

I

Decouple

3

i

Decouple

FIG. 19. Basic echo sequences for heteronuclear multiplicity selection. z is set to l/J for an even/odd subspectrum. 7 is set to l/(24 for selection of nuclei without an attached proton, see text for details. (a) gated decoupler method; (b) spin llip method.

NMR. In this case the precursor would be heteronuclear twodimensional J-spectroscopy. The one-dimensional technique breaks down the broad-band decoupled spectrum into simpler partial spectra based on the multiplicities that would be observed in the proton coupled spectrum. The attraction of this type of experiment is that a broadband decoupled spectrum is observed which minimizes problems of spectral overlap. An added advantage is that the sensitivity of the experiment is higher than that of a proton-coupled spectrum since the broadband decoupled resonances (which are acquired) often decay much slower than the proton-coupled signals. The technique has found a major application in the simplification of “C spectra. The key to the technique is the phase-modulation observed on carbon-13 spin-echoes due to C-H coupling. This modulation is normally introduced by gating the decoupler but can also be introduced by a 180’ proton pulse synchronized with the 180’ carbon pulse. (‘w These methods are referred to as the gated-decoupler and proton flip techniques, by analogy with heteronuclear two-dimensional J-spectroscopy. (l) Both methods are shown to Fig. 19. The proton-flip method uses delays which are half as long as the gated decoupler method and thus would be the preferred method for the study of spectra with broad lines. A similar effect can be achieved without generating spin-echoes, (discussed in Section 2.3), since it is the delay that does the work, the function of the echo is merely to minimize the phase change across the spectrum which is a by-product of the delay. For the sake of brevity, only the spin-echo method in its gated-decoupler version is discussed here. The assignment procedure can be broken down into three steps. The first of these is easy, the discrimination of carbon signals on the basis of an even or odd number of attached protons. In its simplest form, this involves interrupting the decoupling for about 6.9msec (assuming an average value for ‘Jcn of 145 Hz). In which case the phase of the methyl and methine carbon signals is inverted with respect to that of the methylene and quaternary carbons. Thus, the spectrum can be sorted into an even and an odd subspectrum. Although, the first step in the assignment procedure is straightforward, it is the next two steps which present practical difficulties; i.e. distinguishing between quaternary and CH, sites within the even being derived from two-dimensional

Multipulse NMR in liquids

345

3’

FIG. 20. Variation of the decoupled signal intensities in the basic echo sequence for heteronuclear multiplicity selection against the angle 8 = nJ7.

subspectrum and between CH and CH, sites within the odd subspectrum. Consider the even case first. A second spin-echo experiment may be performed with 7 = l/(25) so that all proton bearing sites give a null signal, while quaternary signals retain close to their full itensity. In practice, there is rather poor cancellation for CH sites both because the timing condition is quite critical and also because of the variation in the magnitude of ‘Jcu. The discrimination between CH and CH, sites within the even subspectrum presents an even more difficult problem. Difference spectroscopy has been suggested.‘z54*255)The subtraction of the subspectrum obtained with 7 = 2/(U) from the corresponding spectrum obtained with 7 = 3/(U) discriminates between CH and CH, sites. However, difference spectroscopy is always unattractive (although it may sometimes be unavoidable), because of the loss of signal/noise and also because of instrumental instability which leads to incomplete cancellation of unwanted signals. A modification has been suggested(256) which separates quaternary and CH sites in a single experiment. The technique makes use of the inevitable difference in the magnitude of the one-bond coupling constants. The idea behind this is that the condition for nulling CH sites is much more critical than that for CH, or CH, sites as is shown in Fig. 20. This sensitivity may be put to good advantage. If ‘Jc- for sp2 hybridization is taken as 165Hz then the optimum 7 value would be l/25 = 3 msec while for sp3 hybridization the corresponding values would be Jcn = 125 Hz and 7 = 4msec. An average value is used. This still gives negligible signals for CH, groups (4 %) and CH, groups (1%) but leaves appreciable signals for CH groups (21%) as indicated by the dashed lines in Fig. 20. Thus, in a single experiment, quaternary sites are recognized as positive signals of full intensity, while CH sites are recognized by lines of reduced intensity, positive for sp3 and negative for sp’. Combined with the first experiment to determine whether the number of attached protons is even or odd, this identifies all four types of multiplicity. A general problem involved in 90°-7-180” spin-echo experiments is that a substantial preparation period of about ST, must be allowed for relaxation. For non-protonated carbons this can be a considerable length of time. An improvement to the basic technique has been introduced which is concerned with this problem of sensitivity optimization in spin-echo experiments.‘257) This sequence, which has been dubbed the Attached Proton Test (APT) is shown in Fig. 21. It involves the use of a double echo in order that the first pulse in the sequence may be set to the “Ernst Angle”!258) It is well known that sensitivity can be better optimized using pulses with small flip angles repeated frequently rather than 90° pulses repeated at a slower rate. (‘a) The second delay in the sequence is used only to reinvert the z magnetization. It need not equal 7i but may be set equal to the receiver dead time in order to mitigate instrumental problems such as pulse breakthrough and acoustic ringing. The same sensitivity advantage could be attained in the basic two pulse sequence by increasing the length of the first pulse to (180“-the Ernst angle). In practice, both APT and the basic sequence benefit from phase cycling. The RF phase of each 180’ pulse should be independently cycled through all four phases for JPNn3.S 16:3/4-J*

C. J. TURNER

346 I

Decouple

Decouple

FIG 21. APT sequence. For multiplicity selection, only rL need be varied. r2 is set as small as possible, equal to the receiver dead time (lOOpsec-1 msec). z1 is set as in the basic sequence of Fig. 19.

FIG. 22. Structural

200

I.60

160

140

120

formula

100

usually

of azadirachtin.

80

60

40

20

I

0

Ppm

FIG. 23. Proton

decoupled

75 MHz r3C spectrum of azadirachtin containing CDCI, signal appears at 77 ppm.

some minor impurities.

The solvent

347

Multipulse NMR in liquids

each of the receiver reference phases leading to a 16 transient cycle for the basic sequence, and a 64 transient cycle for the double echo technique. The use of these sequences for multiplicity selection is demonstrated here by some spectra of azadirachtin,‘376) whose structure is shown in Fig. 22 and proton decoupled 13C spectrum is shown in Fig. 23. Azadirachtin is the most important insect antifeedant known. Despite almost 25 years effort it cannot be crystallized. The proposed structure contains many unprecedented structural moieties. NMR spectroscopy remains one of the most powerful methods of structural elucidation for this type of molecule. Figure 24 shows the results of two APT multiplicity experiments. In the top subspectrum, all 12 quaternary carbon are recognized as positive peaks. Some of the CH carbons can be detected at the high frequency end of the spectrum as small negative peaks. This subspectrum was acquired for the same length of time as the bottom even/odd subspectrum. Notice that these spectra do not unambiguously separate all the multiplicities. This is generally the case with APT. The experiment is helpful but not conclusive. There is no clear nomenclature for this experiment. ‘The basic sequence has been named GASPE for GAted SPin-Echo(254) but this invites confusion with the acronym GASP, which has been used as an alternative description of the SPT experiment. It has been called SEFT,‘255) but SEFT was originally an experiment (like DEFT) proposed for sensitivity enhancement which did not really work. It has also been called JMSE (25g)for J-Modulated Spin-Echo, however this also seems a little inappropriate since it is not the spin-echo but the choice of the delay which controls the experiment. Perhaps the use of the name APT should be extended to include both the basic and the double echo sequence. Several authors have suggested refinements to these basic techniques.‘260-262) All of these refinements have some value but none of them greatly enhance the technique. The basic sequence has recently been used to determine the multiplicity of deuteriums attached to carbon.(263,264)

L

200

1,

I.

1,

I.

1.

180

160

140

120

loo

1.

80

I.

60

I.

40

I

20

.,

0

Ppm FIG. 24. Example of APT multiplicity selection experiments on the 75 MHz “C spectrum of azadirachtin. Top, quaternary carbon selection. The negative signals with reduced intensities at the high frequency end of the spectrum arise from CH groups. Bottom, even/odd subspectrum.

C. J. TURNER

348 8.4. INEPT

The refocused INEPT technique was one of the first one-dimensional techniques to be demonstrated as a method of determining proton multiplicity in i3C NMR spectra. (20g,265)It operates on analogous principles to the spin-echo techniques discussed in Section 8.3. The principle behind the INEPT experiment is discussed in Section 7.5. Multiplicity selection by refocused INEPT requires two experiments. One to sort the resonances into those having an even or odd number of attached protons (i.e. CH and CH, vs CH, sites) and another to select only CH doublets. Quaternary sites are, of course, normally suppressed by the polarization transfer technique. By comparison of Fig. 12 and 20, it is apparent that CH and CH, sites are more easily differentiated by INEPT than by use of APT. The refocused INEPT sequence has been extended to provide other methods of editing proton coupled spectra. w~**~‘) The first of these techniques has been mentioned before and has been called INEPT+.(*13) The sequence is shown in Fig. 16. If spectra are obtained with opposite phases for the last proton pulse are subtracted then doublets and quartets are cancelled but triplets (which appear as + l,O, - 1 multiplets) are enhanced. (‘w The second of these methods is to lengthen the last proton pulse so that it becomes a 180” pulse, which again provides a method of enhancing or suppressing signals from CH, groups.(267) 8.5. J-Scaling J-scaling(268~z6g) has been proposed as an alternative to SFORD in order to provide a method by which all heteronuclear coupling constants can be uniformly reduced so that the resultant residual splittings are predetermined and insensitive to frequency offset. Ideally, the reduction would be such that the splitting is just resolvable which necessitates a scaling factor in the region of 0.02405. The experiment has not been popular in practice. The first method to be demonstrated is shown in Fig. 25. In this method, the proton decoupler is switched off for a small part (ta) of a delay (tt,) following a 90” observe pulse. At the end of the interval t,, the carbon magnetization is sampled with complete proton decoupling. Multiple refocusing with repeated sampling of the carbon magnetization has been suggested to improve the sensitivity of the

I

(a)

I I

b--

t,

I

(b)

I

I I

_; 1800 -

I Coherent

S

FIG. 25. Pulse sequence for J-scaling. Notice that this experiment requires interleaving of pulses with acquisition.

Multipulse NMR in liquids

349

S

FIG.

26. Pulse sequence for &scaling. This experiment does not require synchronization of the decoupler pulses with acquisition.

experiment. This is then repeated for a number of different values of ts keeping the ratio t&b (which controls the scaling factor) constant. This is basically a tilted projection of a two-dimensional heteronuclear J-spectrum and, apart from the savings in processing time, makes little sense since one-dimensional presentation does not impart any sensitivity advantage, while the information content of the two-dimensional spectrum is actually reduced. This technique requires the interleaving of pulses with the acquisition of data. Another alternative(272) is to apply 180” pulses to the decoupler not exactly at the midpoint between ADC sampling points, but displaced by a small interval with alternation of the direction of this displacement. However, this approach has been criticised as leading to non-uniform scaling.‘271) A better method(270*271)is shown in Fig. 26. There is no need of synchronization of pulses with data acquisition in this method. A series of phase-alternated decoupler pulses are applied, of appropriate flip angle (a) and spacing (7). It is possible to scale the heteronuclear couplings arbitrarily by appropriate selection of 7 and 0: (usually above 180”). However, despite the fact that sensitivity of this method is much better, it does suffer from the disadvantage that the proton chemical shifts are simultaneously scaled with the heteronuclear spin-spin couplings, so that complex splitting patterns may appear exactly as in SFORD. A set of practical guidelines for J-scaling has been published.‘27’) 8.6. Masked Projection of 2-D Data This is a rather sophisticated technique which combines two-dimensional data acquisition with one-dimensional data-processing and display. (273)It produces two subspectra, one containing singlets and triplets, and the other containing doublets and quartets. Despite the fact that the technique operates in the time domain, it is most easily visualized as a frequency domain masking of a two-dimensional heteronuclear J-spectrum. A suitable mask for doublets would be a symmetrical pair of Lorentzian lines separated by the appropriate coupling constant. This corresponds, in the time domain, to a masking function which is the Fourier transform of this, i.e. an exponentially decaying cosine wave. However in the gated decoupler 2-D J-experiment, the multiplet components only diverge for half the evolution time and consequently all splittings are halved in the F, dimension. Thus, the separation of the lines in the frequency domain mask should also be halved. The only extra data processing which is necessary is to alternate the signs of the incoming half-echoes after multiplication by an exponentially decaying term corresponding to the line-width. The sign alternation can be done after acquisition if the half-echoes are stored separately. The sensitivity of the experiment can be dramatically improved by decreasing the number of transients which are collected for each Ti increment, in proportion to the exponentially decaying term i.e. the line-width. This avoids the necessity of any exponential multiplication. In order to select

350

C. J. TURNER

singlets and triplets, the signals are added without sign alternation. Both subspectra can be generated from the same data. The same experiment has been applied to the simplification of homonuclear coupled spectra.(274) Despite the fact that the experiment has not been popular in practice, it is clear that masked projection of two-dimensional data is a general technique which might be convenient when the capacity for data-storage is limited. The frequency selectivity in the F, dimension may be adjusted at will, opening up the possibility of discrimination based on differences in J-values for signals of the same multiplicity. In chemical shift correlation spectroscopy, it might be possible to mask the two-dimensional data according to a specific proton in order to obtain a partial 13C spectrum. In general, time-domain masking of the data with several different masks permits the breakdown of the spectrum into several components without the need for repetition of the experiment. 8.7. Generation of Multiple Quantum Coherence 8.7.1. General Features. Elegant methods of multiplicity selection have been proposed which utilize the selective generation of multiple quantum coherence. These techniques include INADEQUATE, DEPT and SEMUT. This review uses a simple vector model to explain experiments involving single quantum magnetization. However, to attempt to explain experiments involving multiple quantum coherence by this vector model risks oversimplification. A more rigorous explanation involves the use of either the density matrix or the product operator formalism. For such an explanation the interested reader is referred to references (1, 13, 22, 213, 275). What follows here is a description of how the experiments are performed but which avoids analysis of why they work. The first of these methods is a technique designed to selectively detect singlets in proton spectra of molecules of biochemical interest which contain only doublets and singlets.(276) It involves the use of the sequence below : The delay 7 is set to l/(45). The singlet magnetization remains unaffected by the sequence, but the phase-shifted 45” pulse applied at the top of the echo converts doublets into multiple quantum coherence which is not directly observable. Any spurious single quantum magnetization that is generated by the last pulse can be cancelled by phase alternation. Unfortunately, in the general case of complex spin-spin coupling, this technique fails to select only singlets. 8.7.2. INADEQUATE. This technique is designed to selectively detect doublets while suppressing singlets.‘276*277)This has found a major application in the study of carbon-carbon coupling constants which may be difficult to detect because of strong parent signals from the isolated 13C spins.‘262) Problems such as poor lineshape of these intense signals, spinning sidebands, spurious modulation (e.g., from incomplete decoupling) and impurities may hinder this work. Despite all these difficulties 13C-‘3C couplings as small as 1.8 Hz have been measured by direct acquisition from 13C satellites in natural abundance 13C spectra.(27s) However, it is generally easier to circumvent the problems inherent in direct acquisition, though it should be noted that this will usually decrease the sensitivity. The pulse sequence used for the suppression of singlets is shown in Fig. 27a. This has been called the INADEQUATE experiment and has recently been reviewed. (279)The basis of the method is that only coupled spins can generate multiple quantum coherence. The special phase properties of double quantum coherence are then employed to suppress any residual parent signals. The condition for maximum generation of double quantum coherence (280)is that the delay 7 = (2n + 1)/(4Jcc). The optimum suppression is obtained by phase cycling in a 128-step cycle. Good suppression of the parent signals may be hard with the inaccuracy and instability of analogue phase-shifters used in some older spectrometers. Better results are to be expected with the more modern approach of digital phase-shifting at an intermediate frequency. The timing interval 7 must be specially adjusted in situations where the adjacent carbons form a strongly coupled AB spin system. (281)Problems can also arisiwhen ‘Jcc changes dramatically, as it does when the formal hybridization of the coupled spins changes. (282)For instance, this problem can make the linkage of an aliphatic sidechain to an aromatic ring hard to detect.

Multipulse NMR in liquids

351

(a)

(b)

FIG. 27. (d) Uncompensated INADEQUATE pulse sequence. (b) Compensated INADEQUATE sequence. Extensive phase cycling is used in both methods, se-eRefs. (1) and (284). The nomenclature used in this diagram is explained in Section 3.3.

The signal-to-noise ratio of the basic INADEQUATE experiment has been improved@a3) by transferring proton polarization to the carbon spins just before the double quantum experiment, using the INEPT sequence (described in Section 7.5). The INEPT version permits a higher repetition rate resulting in a sensitivity gain of 2-3. This could well be an important gain, because of the very low intrinsic sensitivity of the INADEQUATE experiment, however it has not proved popular in practice. The use of self-compensating 180’ pulses in the basic sequence has been recommended,‘z79) as a remedy to the severe sensitivity problems that exist if the coupled nuclei are far apart from each other in the spectrum. However, it is not advisable to try to remove this offset problem simply by compensating the excitation sequence whilst leaving the read pulse unmodified. Thus, the basic INADEQUATE sequence has been improved by the introduction of composite pulses at each step in the sequence. (377)The idea here is to construct the sequence as symmetrically as possible so that phase error terms cancel out. So the compensated excitation sequence becomes: 180°(x)-1800( - X)-900(X) -Z/22700(X)-1800(-X)-SO’(X) -r/2900(X) with a read cluster of 180’(Y)-180°( - Y)-90”(Y)-270’=( - Y)-1800(Y)-90°( - Y)-90’(X). There is a clear similarity of structure between the compensated excitation sequence and the compensated read cluster, which accounts for their ability to cancel each others phase errors. If the delays in the excitation sequence were omitted, the two sequences would become identical, except for the phase shift of the pulses in the read cluster. The uncompensated and compensated forms of the INADEQUATE pulse sequences are compared in Fig. 27. The superiority of the compensated sequence was demonstrated with a sample of propanoic acid (total shift range 17Oppm), where no

352

C. J. TURNER

FIG. 28. Symmetrical excitation/detection sequence for multiple quantum filtering. r/2 is set to l/(24. t, should be the shortest practical delay. The phase-cycling scheme is discussed in reference 252.

detectable signals were obtained with the basic sequence, but signals with a signal/noise of 13 : 1 were obtained with the compensated sequence under the same experimental conditions. An important use of the INADEQUATE sequence is as the basis of a two-dimensional experiment where the 13C double quantum frequencies are used for assignment purposes by identifying adjacent carbons in an unambiguous manner.@5-28s) 8.7.3. Uniform Excitation of Multiple Quantum Coherence. Despite the success of the INADEQUATE technique, no general scheme is yet known for the uniform excitation of multiple quantum transitions in complex spin systems. The efficiency of excitation depends on the magnitude of the relevant coupling constants, which usually show a substantial variation throughout the spin system leading to strong intensity anomalies. Averaging of INADEQUATE experiments with different z values (to compensate for variation in the magnitude of spin coupling) is, unfortunately, not feasible since the experiment produces a vanishing average. Thus, the basic idea of uniform excitation is to modify the experiment to remove this problem. w*) This can be achieved by the symmetrical excitation/detection sequence shown in Fig. 28. In practice, complete averaging is impeded by an insufficient number of z values and because of relaxation effects. Some antiphase magnetization may remain and distorted multiplets may appear. These undesirable features can be removed with a purging pulse (an additional 900(Y) pulse) inserted immediately before aquisition. Applied in all experiments it restores the natural multiplet patterns, while its application in every alternate experiment improves the suppression of antiphase magnetization. These ideas have led to the production of p-spin filters. These differ from a conventional p-quantum filter which responds to systems with at least p-coupled spins. It would be quite desirable to be able to select systems with exactly p-spins. This is what a p-spin filter is designed to do. Unfortunately, the p-spin filters that have been demonstrated are far from perfect, but no doubt these techniques will improve in the future. 8.7.4. DEPT.

The DEPT sequence has been demonstrated as a method of multiplicity selection.‘22s,229) DEPT is a generalization of EPT, a sequence designed to select only doublets.(230) DEPT itself, has been further generalized to form UPT. (*‘l) For the sake of brevity, only DEPT will be considered here. The pulse sequence is set out in Fig. 17. DEPT does not use a variable delay to achieve multiplicity selection, but rather the flip angle 0 is varied in order to achieve a separation of carbon signals according to their proton multiplicities. Compared to either INEPT or any of the basic echo techniques (all of which use variable delays), spectral editing into three separate subspectra, CH, CH, and CH,, by the DEPT technique is less sensitive to variations in the J-couplings within the spectrum. Three DEPT spectra must be measured with tI1 = 45’, & = 90’ and f& = 135’. The CH, CH, and CH, subspectra are generated by the combinations co,-z(e, and

+xe,)i, c(l/2)(e, -xe,)i [(l/2)(0, +xe,)+,i

respectively. The parameters x, y and z are determined empirically by minimization of cross-talk between the subspectra. Their theoretical values are 1.00, 0.71 and 0.00 respectively. The use of difference spectroscopy to achieve the multiplicity selection is probably the major disadvantage of the

353

Multipulse NMR in liquids

CH2

CH3

150

130

110

90

70

50

30

1

IO

wm FIG. 29. Example of DEPT multiplicity selection of the 75 MHz 13Cspectrum of azadirachtin for the selection of CH, CH, and CH, subspectra. The spectrometer employed for this work uses analogue phase-shifting. The artifacts in the subspectra probably arise from the known inaccuracies in the phase-shifting, since an RF phase shift of !W generated a 10 y0change in the RF amplitude for the decoupler.

technique, and for this reason the three separate experiments are best interleaved in order to minimize problems of imperfect subtraction. Of course, sequences which utilize polarization transfer cannot be used to select quaternary resonances if the large one bond coupling constant is used to generate the polarization transfer. Figure 29 shows the result of some DEPT experiments on azadirachtin. The total time for the data acquisition was the same as the total time spent on the APT experiments. Notice that these experiments again do not totally define the carbon multiplicities in azadirachtin since there is no quaternary carbon subspectrum. There might be accidental coincidence of a quaternary carbon with one of the other multiplicities. Figure 30 demonstrates the superiority of DEPT over refocused INEPT. Cholesterol was chosen in this case because it has a much more limited set of coupling constants than azadirachtin. Thus, cross-talk in the spectra arising from an improper choice of delay are more vividly demonstated. The array of spectra shown are the CH subspectra, since cross-talk between subspectra progresses downward in multiplicity. The CH subspectrum being the worst. Notice that refocused INEPT shows large errors if the delays are selected incorrectly. These spectra are usually obtained with broadband proton decoupling. For proton coupled spectra, the natural multiplet patterns known from conventional spectra are obtained, but for this application the basic sequence has been improved (‘i3) to yield the DEPT+, (Fig. 31) and DEPT++ (Fig. 32) sequences. Further improvements in the basic DEPT sequence by introducing composite pulses at each step in the sequence have been suggested. (284)Other proposed modifications include the introduction of a purging 90”-r-180”-r-90’ sandwich to reduce cross-talk between the subspectra.(*s9) This sequence for Subspectral Editing using a Multiple quantum Trap, known as 8.7.5. SEMUT. SEMUTool) is set out in Fig. 33. For the special case where 0 = 0” and 180’ the same sequence has

n.

rl

._.

FIG. 30. Comparison of the delays in the sequences. The employed for this work uses in these spectra are probably

I

A

JJd&&&&_,

J,I

I

3,

A”

A

“‘A.

J=llO

,

J =I20

J=l30

A

1.

i

1’;

,

A

1

)

J_j:

1

1

_I

L

1.

4

J=llO

J=l20

J= 130

J =I40

---

_ ,.

___,_

.“__

_---

-

cross-talk in the 50 MHz CH subspectrum of cholesterol by (a) DEPT and (b) refocused INEPT. The stacks of spectra were obtained by varying the delay values used are expressed in terms of the appropriate coupling constant ‘Jew, since the delays differ between the two sequences, The spectrometer digital phase-shifting at an intermediate frequency. The change in RF amplitude with RF phase-shifting was unmeasurably small (_ 1%). The artifacts due to cross-talk between groups of differing multiplicity. Notice that refocused INEPT is only efficient when the delays are set accurately, while DEPT is remarkably tolerant to the inevitable missetting of these delays.

I

,L

J=140

’

cl

Multipulse NMR in liquids

355

FIG. 31. DEPT+ pulse sequence. The last 180” I pulse (dotted) is applied only every alternate transient. ‘Lis set to

l/(25).

FIG. 32. DEPT+ + pulse sequence: z is set to

l/(25).

Decouple

FIG. 33. SEMUT pulse sequence: 5 is set to 1/(2J).

been applied to the separation of a proton-decoupled carbon spectrum into two separate subspectra containing CH,/CH and CH,/C resonances. (2go)The sequence has also been used with the special case 0 = 900 as a method of selecting only quaternary carbon resonances~102~2g1~2g2) and as a method of calibrating the proton decoupler power. (loo) However the potential of the flip angle dependence for the proton 8 pulse is much richer than that realized for these special cases. The reason for this is that the transfer of magnetization to unobservable multiple quantum coherence differs according to the proton multiplicity and is governed by the magnitude of the 8 lIip angle. SEMUT has the same low dependence as DEPT on the spread in J-coupling constants. It has the advantage of allowing a complete separation into individual subspectra for all types of carbon resonances, including quatemaries. The technique is suitable for spectrometers not equipped with a proton phase shifter as opposed to DEPT. Four spectra with O1 = O”, & = 60°, ~9~= 120° and

356

C. J. TURNER 180”

90: Decouple

TI

9

9Q By r2 Y

T

T3

Decouple

FIG. 34. SEMUT GL pulse sequence. See text for details of the values of zl, rz and r+

e4 = 180’ are acquired. These four acquired spectra A, B, C and D (respectively) are combined by sums and differences into four intermediary spectra (X, Y, U and V respectively) as follows: X=A+B

Y=A-B

U=C+D

V=C-D.

This allows a partial editing into even and odd multiplicities. The final separation into CH,, CH,, CH and C subspectra is achieved using the combinations of X, Y, U and V spectra indicated below: C=U-X

CH=V-Y

CH,=X-U

CH,=Y-V.

Theoretical considerations dictate that the best overall signal/noise in the final four subspectra is obtained by acquiring twice as many transients for the C and D spectra as for the A and B spectra. The advantages of SEMUT over DEPT include the following: (a) SEMUT uses fewer pulses than DEPT and thus is less prone to pulse imperfections, (b) SEMUT is a shorter sequence, suggesting that for larger molecules with short proton and carbon relaxation times SEMUT may be more advantageous than DEPT, and lastly (c) the SEMUT sequence allows subspectral editing of all carbon sites and thus does not necessitate other sequences or techniques for the detection of quaternary carbon resonances. On the other hand, SEMUT does not benefit from the sensitivity gain of polarization transfer that is inherent in the DEPT or INEPT techniques, however this gain for carbon spectra is only a factor of 4/3 over the usual NOE intensity gain available in SEMUT. The SEMUT sequence has been improved to yield the SEMUT GL sequence which is shown in Fig. 34. This sequence requires 90’ phase shifts of the decoupler pulses. The introduction of the 90°-r,/2-180’~r,/2-90’ purging sandwich reduces problems associated with adjusting the various 0 pulse flip angles so that they are symmetrical about the 0 = 90” pulse. The introduction of the 180“ phase shift of the first (or the second) 90” pulse in SEMUT GL removes the need for 0 flip angles to be greater than 90°. Therefore the four experiments required for subspectral editing using SEMUT GL become: A[O“, +X] B[O”, -X] C[W, +X] and D[W, -X] where the arguments in brackets indicate the 0 flip angle and the phase of the 90” pulse, respectively. The A, B, C and D spectra are acquired and combined exactly as in SEMUT. A further modification is that the various z delays need not be identical. This modification is also valid for the ordinary SEMUT sequence. The general expression for cross-talk form a CH, group to the CH, subspectrum (m < n) is given by : K,,{sin

(7c.J~~)sin (nJr,)}“{cos (rr.Ir,)cos (xJr,)cos

(rrJ~~)}“-~

where K,, is the binomial coefficient. Compared with the cross-talk in SEMUT (or DEPT) an additional factor of cos (RJzJ-~) has been introduced. This introduces another degree of freedom in choosing the various r delays. In order to suppress cross-talk over a wide range of J values it is necessary to minimize the product of three cosine factors. This problem has been analysed in a

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different context.(293) Thus, for a set of 7 values equal to 3.79,2.87 and 2.30msec, the product of the three cosine factors has a maximum residual amplitude for all J cross-talk signals which will be less than cu. 4% within the range 125 < J < 225 Hz. This procedure is most suitable for unknown compounds. However, when the coupling constant range is known to be smaller, a judicious choice of these delays allows an even more efficient suppression of cross-talk. For instance, when 125 < J < 190 Hz the corresponding 7 values are 3.86,3.17 and 2.70 msec. Further improvements are possible by incrementing the value of z2 in successive experiments and summing the resultant FIDS. The value of the SEMUT GL experiment has been convincingly demonstrated with an example of 13C spectral editing on a mixture of brucine and 2-bromothiazole which has a spread of coupling constants from cu. 125 to 192Hz, which shows virtually no cross-talk. The ordinary SEMUT sequence, with a single z value corresponding to J = 145 Hz would give cu. 25 % cross-talk from the CH carbons of 2-bromothiazole into the quaternary subspectrum. 8.8. Comparison of Spectral Editing Techniques A plethora of one-dimensional techniques have been suggested for enhanced selection of quaternary carbons.(2g4-303) This is not a trivial task since half the central component of a CH, triplet (the antisymmetric component(304) may behave just the same as a quaternary site.‘305)However, the effect is unpredictable since it disappears if the CH, protons are sufficiently non-equivalent. This means that the effect is less likely to appear with high field spectrometers. For instance, Noise Off-Resonance Decoupling (NORD) combined with spin-echo acquisition(2g*~300) may well be a useful method for quaternary carbon selection, but would only be unequivocal for aromatic carbons and thus, little better than APT with a l/(W) delay. The only reliable method for enhanced selection of quatemary carbons is the generation of heteronuclear multiple quantum coherence either with the simple sequence shown in Fig. 5, discussed in Section 2.12, or SEMUT with 0 set to 90“, or a sequence modified from SEMUT GL.@*‘) The problem with one-dimensional spectral editing techniques when applied to selection of CH, CH, or CH, sites is the inevitable variation in the magnitude of the associated coupling constant. For example, ‘Jcu can vary from about 125 Hz for sp3 hybridization, up to about 225 Hz for the case of sp hybridization. So far the only technique that has been demonstrated to accommodate this huge range is SEMUT GL. Many of the authors who have advocated multiplicity selection by these one-dimensional techniques have criticized Single Frequency Off-Resonance Decoupling (SFORD).‘306) While there undoubtably are problems with SFORD, many of which are associated with the RF inhomogeneity of the decoupler coil, (307)these problems have been overemphasized. Since the use of SFORD requires no knowledge of the heteronuclear coupling constant, it is a rather general technique for multiplicity determination. Furthermore, the use of SFORD may permit conclusions to be drawn not only from the multiplicities of the signals but also from the variation in the magnitude of the splittings across the spectrum.(61*308)The SFORD experiment then becomes a primitive form of heteronuclear chemical shift correlation. Even the appearance of complex patterns in SFORD spectra can be put to good use.(‘O’) The practical use of SFORD to the spectral assignment of a reasonably complex molecule, brucine (CZ3HZ6N204), shows that the use of SFORD need not be restricted to trivial applications.(309) Most of the techniques for heteronuclear multiplicity determination offer a better sensitivity than a heteronuclear two-dimensional J-spectrum, but they lack its generality, convenience and ease of operation, particularly in its gated decoupler version. Spectral assignment often requires the measurement of coupling constants. Thus, multiplicity selection is only a first step in the assignment procedure. For instance it is often necessary to distinguish between groups with the same multiplicity. The two-dimensional J-spectrum is, as yet, unrivalled in its ability to disentangle proton coupled spectra. This is the method we have chosen to unravel the 13C spectrum of azadirachtin. The sensitivity of the technique can be improved (at the cost of some generality) by the use of semi-selective two-dimensional J-spectroscopy.(310) The disadvantages of two-dimensional spectroscopy are associated with the line-shape and .l*mms

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dynamic range of the signals, since absolute-value displays must often be used. These problems prevent accurate integration of two-dimensional NMR spectra. However none of the one-dimensional editing techniques has been demonstrated to be superior under conditions of high dynamic range, especially when it is necessary for assignment purposes to measure the coupling constants. 9. CONNECTIVITY 9.1. General Features This section is concerned with pulse sequences which may be used to demonstrate spin-spin coupling between two resonances. This is sometimes called coherent magnetization transfer as are most of the experiments discussed in the previous two sections. Incoherent magnetization transfer is reviewed elsewhere.074,323) The experiments to be discussed here could be classified as chemical shift correlation experiments, indirect detection experiments, or selective detection of satellite spectra (isotope filtration). These experiments could also be achieved by decoupling or multiple resonance. This is such a vast topic that it cannot be covered here. It has been extensively reviewed elsewhere.(310-317) Recently, considerable attention has been focused on the interpretation of offresonance decoupled spectra.‘317-322) The value of many multiple resonance experiments can be enhanced by use of difference spectroscopy(323) in either its heteronuclear(32”327) or homonuclear(32s-331) version. Heteronuclear decoupling difference spectroscopy has been called AISEFT for Abundant Isotope Signal Elimination.‘325) This experiment, in its CW form, was originally named the “isotope filter”, which seems a preferable description of the technique. Section 9.8. discusses pulse sequences designed to achieve this. Many difference spectra are marred by artifacts arising from the lack of reproducibility and poor long term stability of the spectrometer. These problems can be reduced by numerical transformations which allow correction for such factors as resolution degradation, changes in sample spinning speed, etc.‘332,333)Nu merical methods have also been applied to the removal of BlochSeigert shifts in homonuclear decoupling difference spectra.‘334) 9.2. Homonuclear Selective Population Transfer Homonuclear SPTo70,335*336)d’ff I ers significantly from heteronuclear SPT (see Section 7.4). In the homonuclear case, both the number and intensity of the observed resonance depend on the flip angle of the read pulse.‘337-340) A small llip angle (20°-30’) detects responses only for those transitions having an energy level in common with the perturbed transition. Whereas a 90” flip also produces responses from those transitions which have an indirect relationship. These effects have been demonstrated for both weakly(341s342)and strongly(343) coupled spin systems. Probably because of these flip-angle effects, homonuclear SPT has not proved very popular. In fact, since the same sequence is commonly used for homonuclear NOE difference experiments, methods have been developed in order to suppress SPT effects in NOE difference spectra.(344) Homonuclear SPT has been applied to the investigation of i3C-“C coupling in i3C spectra,(345) and to the study of the connectivity of amide and alpha-protons in biological materials in aqueous solution.(346) There are a few other published examples.‘323*347) The same sequence can be used to investigate saturation transfer between resonances which undergo chemical exchange. This has recently been reviewed.(323) 9.3. Double Selective Population Transfer Homonuclear or heteronuclear coupling can be investigated with enhanced sensitivity by heteronuclear Double Selective Population Transfer (DSPT). 34* In this technique, two heteronuclear SPI pulses are simultaneously applied to the X and the Y satellites in the proton spectrum prior to the observation of either the X or the Y nucleus by means of a nonselective read pulse. The resulting SPT leads to a convenient method for determination of the sign and magnitude of the X-Y coupling from the enhanced satellites in the X or Y spectrum. If X equals Y then homonuclear coupling may be

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Presaturatian

FIG. 35. SLAP pulse sequence. r1 and r2 are set as in refocused INEPT.

observed. The spectra may be proton-decoupled by introducing a delay to allow the components of the multiplet to refocus (see Section 7.5). Since a non-selective read pulse is applied to a coupled homonuclear spin system at a nonequilibrium state, the flip-angle effect must be considered in order to correctly interpret the intensities of the individual transitions.(377m340) In a spin system, such as, 13C-‘3C-1H no effects of population transfer will be observed if 90” read pulses are employed after inverting the two outermost satellite lines in the proton spectrum. The optimum flip angle is either 45’ or 13Y’, the only difference being a reversal in phase for the polarized satellite spectra. Since DSPT would normally be used to observe spectra from an isotopically dilute nucleus in the form of satellites surrounding an intense parent signal, various methods have been proposed to suppress the parent signal. Probably the best method would be to combine presaturation of the parent signal with alternation of the flip angle of the read pulse between 45” and 13Y while simultaneously inverting the receiver reference phase. DSPT has also been used for sign determination of a one bond r5N-’ 5N spin coupling constant.‘34g) 9.4. Sign-Labelled Polarization Transfer SLAP which stands for SignLAbeled Polarization transfer provides a method for the determination of the signs of 13C-i3C couplings. (350)It does not require selective pulses (unlike DSPT, see Section 9.3) and is only weakly dependent on the magnitudes of the couplings. The sequence is basically that of refocussed INEPT, preceded by a series of 13C presaturation pulses. However, the two 90” proton pulses are in phase in this sequence. The sequence is shown in Fig. 35. The initial 90” proton pulse creates transverse proton magnetization. During the first delay ri the two carbon-proton couplings J CIHl and JCZH~lead to a dephasing of the four proton multiplet components, while the proton chemical shifts are refocused. The time rr is selected such that the dephasing with respect to both couplings is near 180’. A pair of simultaneous proton and carbon 90” pulses then creates carbon zeroand double-quantum coherence. The delay r2 is needed to rephase the heteronuclear couplings before the decoupler is turned on. Finally a 90’ pulse generates carbon magnetization components of C, and/or C, antiphase with respect to the other carbon spin. The polarity of the “C antiphase magnetization, which forms the initial state for the observed precession, is labelled with the sign of the product of the two carbon-proton couplings and forms the clue to the sign determination of the r3C-13C coupling constant. The latter determines the evolution of the carbon doublet during observation. From the sequence of doublet components with positive and negative intensities in the resulting spectrum, it is possible to deduce the sign of the product of all three involved couplings. Thus, the determination of the sign of the 13C-‘3C (one-bond or many-bond) coupling requires a knowledge of the signs of the couplings of the two carbon spins to a proton directly bonded to one of the carbons. Of course, the signs of the ‘J CH are known to be invariably positive but the signs of longer range C-H couplings must be determined separately. 9.5. Selective Excitation Transfer This is superficially related to heteronuclear SPT. However it differs significantly in that the selective excitation of the nucleus to be observed occurs before the 180° pulse to the other nuclei. This

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C.J. TURNER

causes excitations as well as populations to be rearranged before detection.‘351~352)The results cannot be explained in terms of population transfers alone, since this technique is, in essence, a method of generating multiple quantum coherence. 9.6. Spin-Echo Double Resonance The method of spin-echo difference spectroscopy (see Section 8.2) can be extended by applying decoupling during the evolution of the echo. (353) The application of homonuclear decoupling throughout the defocusing and refocusing period causes the multiplicity of the coupled resonances (and thus the phase of the detected echo) to be changed. This is an elegant method of detecting decoupling, while avoiding Bloch-Seigert shifts, since the decoupler is switched off during the data acquisition. Difference spectroscopy is used to display the result. The difference being between on- and off-resonance irradiation. This sequence has an intriguing aspect. If decoupling during the evolution of the echo causes the multiplicity to change, then the phase-modulation of the observed signal will be appropriate to the multiplicity when decoupled, and not that which is actually observed in the tinal spectrum. For instance, if a triplet is irradiated(354) and becomes a doublet while the echo evolves, it will acquire the phase appropriate to a doublet; but it actually appears as a triplet. This is because the spin-spin coupling reappears as soon as the decoupler is turned off. The converse of this technique, i.e. decoupling only during data acquisition can be used as a method for the accurate measurement of unresolved coupling in large molecules.‘355) This involves the measurement of an array of spectra with varying times for the evolution of the echo. If an unresolved doublet is converted (by decoupling) into a singlet during the acquisition of the FID, then the intensity of the observed singlet will pass through zero when the echo evolution time equals l/(25). 9.7. Chemical Shift Correlation

The use of frequency selective spin-echoes has been demonstrated as a method of mapping homonuclear spin coupling in complex spectra. (356)The method involves an array of experiments. Its principle advantage is that unlike the double Fourier transformation technique introduced by Jeener,“) this method does not require extensive data storage. The technique employs the simple spin-echo sequence but the 180” pulse is made semi-selective. A semi-selective pulse is taken to be sufficiently intense to invert all the component lines of a given multiplet, without significantly affecting the nearest chemically shifted neighbour. This means the RF power will be of the order of J Hz. A series of experiments is performed with the frequency of the 180’ pulse incremented in small steps across the chemical shift range of interest. These signals are subtracted from an off-resonance experiment with the frequency of the 180’ pulse set far from all the resonances, so that neither refocusing nor spin-inversion occurs. Fourier transformation produces a stack of difference spectra which closely resembles a two-dimensional Jeener spectrum and can be interpreted as such. The experiment differs from the Jeener two-dimensional method in two respects. Firstly, only one spectrum need be stored in the computer memory at one time. Once this has been plotted out, the same storage space may be used for the next spectrum. Secondly, the digital resolution can be maximized, since there is no restriction on how low a frequency range may be studied, and thus, problems with aliasing are avoided. Analogous techniques have been used in heteronuclear ‘H-i3C chemical shift correlation experiments by employing single frequency low power decoupling during the dephasing period of the echo.(357)However, complex phenomena occur (358)at very low decoupler powers. For the best results, the decoupler power should again be J Hz, roughly 125-225 Hz for these nuclei. Broadband decoupled heteronuclear SPT experiments have also been suggested for heteronuclear chemical shift correlation experiments,‘207) as have INEPT experiments with selective proton decoupling during the evolution of the second echo,‘359) and SESET(233) which is a DANTE-driven selective population transfer experiment discussed in Section 7.8. Selective DEPT experiments have also been advocated.(360) In the latter case, selectivity is achieved by use of a selective 180’ proton pulse, which is applied to one component of the 13C satellites in the proton spectrum.

Multipulse NMR in liquids

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Heteronuclear chemical-shift correlation experiments can be used to extract a subspectrum derived from one or two chosen proton sites while suppressing all other overlapping resonances.(361) Of course in simple situations, straightforward frequency selective pulse excitation (see Section 5) can be employed when the proton multiplet is well resolved from other resonances and has been properly assigned. However, it is equally likely that the chosen proton is entangled in a thicket of unwanted resonances. Thus, it is difficult to apply selective excitation or double resonance techniques because of the overlap of many resonances in the region to be irradiated. Selective excitation of the chosen proton by polarization transfer from an adjacent carbon site may provide a solution to this problem. This is an extension of the INEPT experiment described in Section 7.5 and 8.4. Only protons directly bound to the chosen carbon site are significantly affected since the polarization transfer is chosen to operate on a large value of Ja. Selective excitation of the chosen carbon is likely to be far easier than that of the proton because of the wider chemical shift range for carbon. The procedure involves seven steps: (a) (b) (c) (d) (e) (f) (g)

Presaturation of all proton resonances and establishment of a nuclear Overhauser enhancement. Selective excitation of a single (decoupled) 13C resonance. Free precession of the proton-coupled 13C vectors for a fixed period TV. Polarization transfer to the attached proton(s) by a 90” carbon pulse applied along they axis. Conversion to transverse proton magnetization by means of a 90° proton pulse. Free precession of the two proton vectors for a fixed period TV. Acquisition of this proton signal with broadband decoupling of the 13C line.

This last step may not be as difficult as might be thought at first sight since the carbon signal is on resonance and thus relatively easy to decouple with a simple form of modulation. There is an unavoidable penalty in sensitivity in this experiment since only 1% of the molecules contain the required 13C. The experiment would also be quite time consuming if subspectra from many different proton sites are to be investigated. Simple heteronuclear correlation experiments can also be performed by studying changes in the intensity of satellites in the proton spectrum caused by heteronuclear spin-echoes.(362) The principle here is that echoes can be modulated by a heteronuclear coupling if 180“ pulses are simultaneously applied to both nuclei. (363)These indirect detection experiments can have much better sensitivity than direct observation, since the sensitivity is that of protons multiplied by the natural abundance of the heteronucleus. However, problems often arise from the intense parent peaks. When the natural abundance of the heteronucleus is reasonable (about 10 %) and the heteronuclear coupling is large, e.g . lggHg, the satellites are well resolved from other resonances. Proton spectra may then be acquired while stepping through the frequency range of the heteronucleus with pulses of suitable selectivity. If the frequency of the heteronuclear pulse matches that of the chemical shift of the heteronucleus then the satellites in the proton spectrum will become inverted if the delay z in the echo sequence is set to (364.365) l/GJJ). The most obvious application of any of these sequences would be to generate a correlation for only a few well separated resonances. Of course, in simple situations this might just as well be accomplished by selective heteronuclear decoupling. (317)Judged solely on their merit these methods might offer a significant saving in the time for data-acquisition, over the well established techniques involving double Fourier transformation. (I) However, the non-selective two-dimensional techniques could still be more expeditious since they are probably easier to implement than any experiment involving selective pulses, as these require tedious calibration of the RF power at various amplitudes in order to achieve the desired selectivity. Two-dimensional heteronuclear chemical shift correlation experiments (in various forms) are clearly of exceptional utility.(3*2g3*366*367) In part this is because the technique of using two separate dimensions lends itself so well to the production of a map relating the two shift ranges. 9.8. Isotope Filtration 9.8.1. Basic Echo Techniques. The heteronuclear spin-echo technique can also be used to uncover satellites of low intensity by a form of difference spectroscopy in which the strong parent signals are

C. J. TURNER

362

(al

f

(b)

,

(c)

,

FIG. 36. Vector diagrams to explain isotope filtration by spin-echo difference spectroscopy. (a) Three proton magnetization vectors, representing the strong parent (p) and the fast (a) and slow (8) satellites, are aligned along the +y axis by a 90° pulse. (b) They precess for a time T until G(and /3 lie antiparallel (c). In the first sequence (a), (b), (c), (d), (e), the 180’ proton pulse flips the vectors to mirror-image positions (d). No pulseis applied to the carbon-13nuclei.(e) At time 2r all three vectors are aligned along the -y axis. In the second sequence (a), (b), (c), (d’), (e’), the introduction of a carbon 1809pulse at time 5 interchanges the spin-state labels (d’), with the result that OL and ,3 vectors become aligned along the +y axis at time 2r, whereas the p vector is returned to the -y axis. Subtraction of the responses from the two different sequences suppresses the strong parent but reinforces the satellites a and /?.

cancelled. This is another form of SEDS (see Sections 8.2. and 8.3). The most elegant implementation of this technique is set out be10w:‘~~‘) Proton Carbon

90”(X)-z-180’(X)-Z-Acquisition 90°(X)900( f X).

The delay z is set to 1/(2Jc~) so that the proton vectors in question build up a relative phase difference of 180” in this interval. The two 90” pulses applied to the heteronucleus act together to give a 180” or 0’ pulse in alternate experiments. This combination should work better in practice than the simpler method of applying a 180’ pulse in alternate experiments.(365) The evolution of the proton magnetization vectors is set out in Fig. 36. Figure 36a shows three proton magnetization vectors, representing the intense parent (P) and the (a) and (/?) satellites which are initially aligned along the +y axis. In Fig. 36b they precess for a time z until CIand /? lie antiparallel in the xy plane (Fig. 36c). In the first sequence the 180° proton pulse flips the vectors to mirror-image positions (Fig. 36d). At the time 22 all three vectors are aligned along the -y axis. In the second sequence a, b, c, d’, e’; the introduction of the “C 180’ pulse interchanges the c1and p spin state labels (Fig. 36d’) with the result that the CIand B vectors become aligned along the +y axis at time 22, whereas the P vector is still returned to the -y axis. Subtraction of the responses from the two different sequences suppresses the strong parent signal but reinforces the satellites GIand B. The major problem with these particular detection experiments comes from these intense parent signals, since they and the weak satellites must be reliably and reproducably digitized if the subtraction process is to produce high suppression ratios. The simple form of this technique has been applied to the observation of 13C(365)and 15N(369,370) satellites. to avoid the problem of accurate 9.8.2. Inverse Polarization Transfer. It is often convenient cancellation. The simplest method of doing so, is a direct application of the INEPT technique with the role of the two nuclear species reversed. c3~s)A vector diagram of the inverse polarization scheme is shown in Fig. 37. Here, attention is focused on the time evolution of the ’ 3C spins. For simplicity consider the case of a CH group. The z delay is set to 1/(4Jc~) so that the two 13C vectors (labelled CIand 8) precess during T to give a relative phase angle of 90” (Fig. 37~). The 180o 13C pulse refocuses the effect of the chemical shifts but the 180“ proton pulse causes the two vectors to continue to diverge until they are aligned along the + and -x axes (Fig. 37d). The 90”(Y) pulse converts these to + and -z magnetization (Fig. 37e). This corresponds to a disturbance of the spin state populations. Since the proton

363

Multipulse NMR in liquids

@

aD@

Protons

FIG. 37. Vector diagram for isotope filtration by inverse polarization transfer. (a) Two carbon-13 magnetization vectors labelled a (fast) and fi (slow) are aligned along the +y axis of the carbon rotating frame by an initial 90” pulse. (b) They process for a time T until they make an angle of 90’ with respect to each other. (c) Simultaneous proton and carbon 180” pulses interchange the a and j spin state labels and flip the magnetization vectors into mirror-image positions. (d) Further precession for a period r leaves a and j? opposed along the x axes. (e) A 90° carbon pulse about the +y axis turns the vectors into the z direction, /I representing equilibrium populations but a corresponding to a population inversion. (f) The proton magnetization is initially zero due to a presaturation sequence. (g) Because. of the population disturbance the proton magnetization acquires longitudinal magnetization from the carbon-13, labelled U (up) and D (down). (h) A final 90’ pulse on the protons creates transverse magnetization along the y axes. In every second pulse sequence the a and /I vectors are reversed by inverting the phase of the initial 90” pulse in (a) but since the last proton pulse is also reversed, the vectors D and U remain as shown in (h). Any residual parent is inverted and hence cancelled at the end of every second sequence.

transitions share the same energy levels, they are also affected (Fig. 37g). A subsequent proton read pulse excites satellite responses; one positive and the other inverted (Fig. 37h). Phase alternation of the first 90” carbon pulse and the last proton 90’ pulse insures that the satellite signals reinforce after two transients, but that the parent signals cancel. The parent signals can also be attenuated by presaturation, with a train of 90” pulses separated by intervals of a few msec. This not only eliminates the majority of the signals not generated by magnetization transfer, but also induces an NOE which improves the sensitivity. If CH, and CH, groups are also present, a slightly shorter setting for r is used which gives a near optimum for three cases (see Section 7.5). Inverse DEPT has also been demonstrated.‘371) 9.7. DOUBTFUL The INADEQUATE experiment (see Section 8.7.2) can be used to investigate connectivity in proton spectra, by selecting only a particular AB or AX spin system in a complex overlapping spectrum. All other signals are suppressed. (372)The sequence is set out below: 900(X)-z-1800(Y)-~-900(X)-t,-900(~)-ACQUIRE(+/-). As usual, the phases of the read pulse 0 and the receiver reference phase are cycled in opposite directions so that only signals derived from double quantum coherence are acquired. The spectra obtained with different values oft, are added together. The purpose of this is that the evolution of the double quantum coherence present during t, imparts an amplitude modulation to the detected magnetization with a characteristic frequency. For a pair of spins, this is determined solely by their chemical shift offsets from the transmitter. (373)By placing the transmitter at the mean shift position for AB or AX, this double quantum frequency is zero for the spins of interest. By varying t,, the oscillatory signals from other spins with nonzero double quantum frequencies tend to cancel while the desired signals add coherently. The experiment is carried out by incrementing the transmitter position until it matches the mean shift of the pair of resonances which are to be detected. It has been applied to the problem of establishing the ‘H NMR assignments and connectivities of cytosines in a 14 base pair fragment of double stranded DNA. (374)An extension of this experiment has been described which uses the creation of triple-quantum coherence as the criterion for multiplet selection.(375)

364

C. J. TURNER

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Multipulse NMR in liquids 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114: 115. 116. 117. 118. 119.

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Multipulse NMR in liquids 181. 182. 183. 184. 185. 186. 187. 188. 189. 190. 191. 192. 193. 194. 195. 196. 197. 198. 199. 200. 201. 202. 203. 204. 205. 206. 207. 208. 209. 210. 211. 212. 213. 214. 215. 216. 217. 218. 219. 220. 221. 222. 223. 224. 225. 226. 227. 228. 229. 230. 231. 232. 233. 234. 235. 236. 237. 238. 239. 240. 241. 242.

367

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