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The Fourier Transform in Chemistry-NMR Part 3. Multiple-Pulse Experiments Kathryn R. Williams and Roy W. King University of Florida, Gainesville. FL 32611 The previous artides (1, 2) in this series an the Fourier transform in chemistry introduced the concepts of pulse FT-NMR, with examples limited to cases in which only one R F pulse was applied before data acquisition.' The ready availability of the Fourier transform technique has also led to the development of many experiments that use more than one pulse per acquired free induction decay (FID). These pulse sequences give information that is difficult or impossible to obtain by single-pulse techniques. The final two papers in this series will describe a few of the multitude of multiplepulse experiments that have been proposed in the literature, with emphasis an their application to common problems in chemistry. In some cases it is possible to understand the behavior of the nuclear spins by simple vector pictures, hut the explanations of many pulse sequences require quantum mechanical analysis. This level of complexity is beyond the intent of the present series. As with many other spectral techniques, it is often not necessary to comprehend the underlying theory fully in order to analyze the spectra, but, like any physical method, the utility of a tool increases with the user's understanding of it. This paper will provide the average chemist with an introduction to the information that can be gained from these powerful methods. Individuals who are freauentlv involved with molecular .~ structure determination wrll also want to runrult some of the many texts and publications on this ~ u b j r r tfor , example references 3-7, to cite just a few
rotate a t the Larmor frequency of the nuclei, so that the nuclear magnetic moments appear stationary. The rotating frame convention will be used throughout this work, but for simnlicitv . . the mimes will he omitted. The nuclei are first subjected to an R F pulse of sufficient length to cause M to rotate through 1809 to the -2 axis. Following the pulse there is a delay period, r, whose
length is varied as the pulse sequence is re. peated. This segment is the key to this and many multiple-pulse method*. In the inwrsion-recovery experiment eight or 10 ivalues are used, ranging from a small value up During the r interval to four or five times TI. the system returns to equilibrium by the spin-lattice relaxation process. Spin-spin relamtion (see below), which is involved
.~~~~
~~~~
~
3
Relaxation Tlme Measurement and Spin Echoes
TI by Inversion Recovery One of the oldest and simplest pulse sequences is the inuersion-recovery method for measurement of the spin-lattice relaxshown in Figure 1. At the ation time TI, start of the sequence the nuclei are at equilibriumin the fixed magnetic field Bo, with a small excess population of the nuclei in the Lower energy state. According to the classical description, the individual magnetic moment vectors Drecess about the Bn axis a t the Lormor . --~ ~ ~freouencv. For a oasitive moenetogyrie ratio the result is a net magnetization uector, M, in the same direction as Bo.As explained in a previous article (0, it is convenient to set up axes z' and y', which
, ~ ~ . . ~
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Figure 1. TI bythe inversion/recovery method. (a) Pulse sequence. (b) Vector description. (c)Plot of heights of transformed peaks as a hrnction of r. (Continued on page A94)
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only with components of the magnetization in the xy plane, is not a concern, because M lies along the z axis. As the individual magnetic moments gradually return to their favored orientation along the +r axis, the net mmetization vector shortens in the -z direcihn. Depending on rhc lengrh 0 1 the delay. M pasaea through rero and eventually recovers it* full original magnitude along the +z axis. T o determine the extent of relaxation, M must he converted into observable magnetization in the xy plane. This is done by applying a second pulse of half the length of the first to the + x axis; this 90, pulse rotates M to lie along they axis. If M is still negative before the 90' pulse, then themagnetization is rotated to the +y direction, hut, when relaxation is complete, the magnetization after the 90' pulse lies along the -y axis. If the transformed spectrum is phase-corrected to give a positive-going peak for a 90, pulse applied to M a t equilibrium, the intensities I, of the transformed peaks will vary with,, frommaximum negative for r = 0 to maximum positive for r = infinity (practically, four or five times TI). The intensities are related exponentially to TI by the equation:
I = I& - ~ e - " ~ ~ )
(1)
and a typical plot is shown in Figure Ic. The peakintensity iszero w h e n r / T ~= In (3, i.e., when r = 0.693T1.This feature issometimes used to discriminate against an unwanted resonance, e.g., a solvent peak whose T,is longer than those of the solute nuclei. The sample is subjected to a 180" pulse followed by a delay of 0.693 times the solvent TI. At this time the solvent magnetization is just osssine throueh " the zero ooint:. the samole nurlei, which have relaxed rnorerompletely, will give positive signal* when the 90" pulse is applied. Although the schematic pulse sequence shown in the figure is a useful pictorial derice, it may be represented more compactly as:
space interaction of two nuclear dipoles, which must he spatially close, but not necessarily bonded to each other. Carbon-13 nuclei in natural abundance must usually rely on the presence of nearby protons to Promote relaxation. This requirement is readily observed in ethyl benzoate, whose carboxyl and substituted ring carbons, which are most distant from protons, have the longest TI%.The remaining carbons demonstrate the importance of the other factor in relaxation: the correlation time, r,. For amall molecules in nonviscous liquids TI is inversely related to 7,. This means that, assuming the presence of the requisite protons, less mobile carbon groups relax more rapidly. In ethyl benzoate the para ring carbon has the shortest TI, which confirms that a principal motion of this molecule is rotation ofthe benzene ring aboutthe CI-CI axis, a process that results in minimal reorientation of the C4-H bond. Thus, the correlation time of the para carbon is long, and the T,is short. Relaxation studies, once restricted to chemical physics, are now routinely helping chemists learn ahout the motional characteristics of their molecules.
The Spin Echo Effect and T, As was mentioned in the first paper of this series, in addition to spin-lattice relaxation, xy magnetization may be lost by processes that donot affect the2 component. The rate constant for this loss is the recinrocal of the time constant of the FID, T;, ihe effective spin-spin relaxation time. 'I;may be broken down into a Bo inhomogeneity component (the major cause of line broadening in NMR) and the spin-spin relaxation time, Tz. The value of T2 is determined by the same factors that are responsible for TI, plus other processes such as spin and chemical exchange.
The spin echo pulse sequence shown in Figure 3 allows Tz to he measured independently of the BOinhomogeneity component. The initial 90, pulse turns the total magnetization vector to the -y axis. If the axes are rotating a t the exact Larmor frequency of the nuclei. the effect of Tn will he a eradual .. shortening o t M in the -;direction (no appearance of -3 mapetizatiml. However, because R - is not perfectly hrmmgeneour, the sample is actually made up of mirrusropicregionswithslightly different maynitudrs of I1 . Within any m e rerion the nuclei may he considered to experience the same Bo and have the same precession freouenev. .. i.e... thev. form a soin isochromnt. Some of the isnrhromata precess faster than the rotntinp: liame and more in the counterrlocku,~aedirectim; the fasteat group is labeled 1in the figure and the slightly slower one laheled 2. Similar isochromats, 3 and 4 precess slower than the frame and rotate clockwise. As a result of this disparity the spin isochromat vectors fan out in the zy plane during the delay, r, after the SO0 nulse. At the end of the first r delay a 180, pulse flips the spins about the x axis. The isochromats are still precessing in the same directions at the same rates, so, for example, the isochromat, 1 that moved fastest counterclockwise now has farthest to go to reach the +y axis. After a second r period of equal leneth all the isochromats refocus alone the " +y axis to give a maximum %ymagnetization. If the NMR signal is monitored during this 90,-r-l80,-r sequence, it dies away during the first r interval. Then it recovers to another maximum, the spin echo, when the isochromats are refocused after rr. Since the magnetization is now along the +y axis, the echo signal is inverted with respect to the first signal observed. (The method can ~~~~~~
.
r
~
~
~
-
~
~
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equilibration delay-180,-r-90,-acquisition The sequence may be divided into three periods: preparation (the equilibration delay and the 180' pulse), evolution (the 7 delay), and detection (the 90Dpulse and the data acquisition). These periods are easy to pick out in this simple sequence and will he important when analyzing the more involved pulse sequences to he presented later. The utility of this experiment is demon-
Figure 2. Carbon-13 T, values (seconds) for ethyl benzoate in CDCi3. not dwgassed. strated by the results of a study (Fig. 2) of the carbons of ethyl benzoate. (The assignment of the resonances in this molecule will be discussed in later sections.) As was described in aprevioue article (I),for diomagnetie systems the most important mechanism for TIrelaxation is the direct through-
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Figure 3. The spin-wchoexperiment. (a) Pulse sequence (Can-Purcell version). (b) NMR signal showing r,, etc. (c)Vector description. "echoes" at the end of r2,
be modified to refocus the isochromats in the -y direction by applying the 180° pulse to they axis.) After the period shown as r s in the figure, the FID again decays to a minimum, because of the same & inhomogeneity effects as before. A second 180-r seauence results in an echo a t the end of n along the -3 axis. The amplitude is reduced by ?; relaxation and alro t,y any rpsidual spin-lactice effects in the system. The rime constant for the decrease in the magnitude since the effects of the echois the "true" Tx, have been eliminated of Bo inhomogeneity . hy the refocusing process. Modifications of the spin echo method can also counteract experimental difficulties such as pulse imperfections and molecular diffusion, which complicate T2measurements (5,pp 8-10,s). In Figure 3b the NMR signal is shown throughout the entire sequence, hut in practice the receiver is activated only a t the times of the echo appearance (i.e., after r z , T ~ etc.). , In the customary abbreviated form the echo sequence is:
Decoupler On 1~
~
equilibration delay-90~-~-180~~-aquisition Again the three periods corresponding $ preparation (equilibration delay and 90, ~ u l s e ) ,evolution (the r-180,-i segment), and detection are evident in the pulse sequence. The evolution and detection periods are repeated when successive echoes are acquired. The key to echo formation is the division of the evolution period into two equal parts. Whatever happens to the spins during the first r interval is negated (except for true Tneffects) hv the 180" ~ u l s and e the Since T Iand T?are usually equal in mobile liquids, T. is not commonly measur?d in such systems. However, the spin echo pulse sequence is very important because it is an essential component of many multiplepulse experiments. Although the sequence was originally designed to refocus effects of Bo inhomogeneity, it is equally applicable to spin divergence caused by chemical shift effects. I t is often necessary to observe one effect (e.g., spin coupling) without interference from other sources of divergence. Inclusion of suitable refocusing pulse(s) as part of the sequence allows the undesirable effects to he removed.
The Attached Proton Test With a small modification, the spin echo sequence can provide some very useful structural information. The simplest example, shown in Figure 4, is the Attached Proton Test, APT, which allow the chemist to determine whether each carbon in a molecule has an odd or even number of protons attached to it. The basic apinecho sequence is s ~ ~ l i to e dthe carbons, whereas the modifieklon lies in the use of gated decoupling of the hydrogens during the second r interval. The effect of spin coupling of the hydrogens to the carbons is not the same in the second r period compared to the first, and this change produces some interesting results. Figure 4b shows the behavior of the earbon spin of a CH group. Because the effects of Bo inhomogeneity and chemical shift are refocused, only the precession caused by spin coupling is presented in the vector description. The net magnetization vector, which is rotated to the -y axis by the
Figure 4. The artached proton teat (APT). (a) Bask p~lsesequence. lb) Vector dascr ption fora Crl gro-P IC) R O S U I ~ ~ V B C I Oimmediately TS prim to lBO0 pulse lor CH, CH2,snoCH,gro~psandquaternanlcarDonsir =
initial 9OX0pulse, is the resultant of two vectors of equal length, corresponding to the equalnumber of carbons coupled to protons of n and p spin. During the first i interval one vector rotates ahead of the frame (counterclockwise) a t 512 revolutions per second ( d radls), while the other rotates in the clockwise direction a t the same rate. The deeoupler is gated on a t the same time as the 180" pulse, producing rapid inversion of the oroton snin. This removes the J-coudina A d causis bath vectors to move at the ;am; rate, i.e., a t the precession frequency determined by their chemical shift. This means that the vectors are projected onto the midline between them. The length and direction or'the resultant vector determrnes the amplitude of the observed peak and whether it is ~ositiveUI negatiw. For a CH wstem the resultant, priorio the 180° pulsi, is given by:
M = Mocos (8) = Mo cos ( d r )
(2)
where Mo is the initial length of the spin vector just after the 90' pulse, 8 is the angle
through which one vector has moved in the timer, and J i s the one-bond C-H coupling constant in hertz. This equation neglects relaxation effects, because r is usually much shorter than either T2 or TI. Following the 180" pulse the second r delay is included to make sure that chemical shift and Bo inhomogeneities are refocused. Then the reeeiver is activated, and the FID is acquired. Equation 2 shows that the peak height i.e., the peak height varies cyclically with i; is modulated by the r delay. (Thisconcept is also essential to the understanding of twodimensional spectroscopy, which will be discussed in the fourth paper in this series.) In the APT experiment iis set equal to l / J c - ~ because this value produces the most notable effects in the spectrum. The vector resultwta for the carbon magnet~mt~on lust hefure the 180' pulse are shown in F w r e 4r fur CH. CH,. CH and auaternarv rarhon groups.(~h&ead;r may &fy thebalues of 9 and M for him- or herself.) The essential feature is the opposite direction of the vec-
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inftrumentotion tor for a CH or CH3 group compared to that of a CH2 or quaternary carbon. A practical example of the use of the APT sequence is shown in Figure 5. The sample came from a bottle laheled "l-octanol", hut in the APT spectrum the direction of the peak a t 68.1 ppm for the hydroxylated carbon is opposite to that of the majority of the remaining peaks, which presumably correspond to CH2 carbons. In addition, the sign of the C-OH resonance is opposite to that of the CDCL solvent, which must exhibit the same behavior as a quaternary group. (The sign of the solvent peak is a useful check in APT work.) Obviously the hydroxylated carhon hears only one hydrogen, and the sample is not aprimary alcohol. To add insult to injury, 15 sample peaks are identified by the computer instead of eight, indicating that the bottle labeled "l-octan01" actually contains a mixture of secondary alcohols. Although the number of hydrogens bonded to each carhon can in principle he obtained from a coupled spectrum, the APT method allows much information to he ohtained from a decoupled spectrum, eliminating the problem of overlapping multiplets, and retaining the intensity enhancement resulting from the nuclear Overhauser effect.
Polarization Transfer Another important group of multiplepulse experiments includes the polarization transfer methods for sensitivity enhancement. A nucleus such as % or I5N suffers from poor sensitivity because of its low natural abundance and also because of its small magnetogyric ratio, y, which, for a given Bo, determines the energy difference between the two spin states (AE = yhBal2n). According to the Boltzmonn distrrbution, the ratio of the population of the lower state to that of the upper state is exp(AE1kT). A small AE results in a small excess population, or magnetic polarization, and a small
signal intensity. For nuclear spin states, AE is much less than kT at room temperature, and the exponential may he expanded in a power series to give, for n total nuclei, n(l AEI2kT) and n(l AEf2kT) as the populations of the upper and lower levels. This means that the population differences, compared to a zero energy reference level (i.e., the energy in the absence of any Bo field), are directly proportional to AE and the magnetogryic ratio. Since the magnetogyric ratio of the proton is very nearly four times that of carbon-13, the population differences are in the same proportion. If some of the polarization of the proton can be transferred by some means to the less sensitive nucleus, then the signal of the latter will he enhanced. One pathway for polarization transfer is the nuclear Overhauser effect (NOE), which operates via t h e same through-space dipolar interaction that is mostly responsible for spin-lattice relaxation in lJC-H svstems (1). In contrast. Dolarirntion transfer pulse sequences have been developed toarhieve the desired resulr solely via spin coupling effects.
+
Selective Polarization Transfer Conceptually the simplest experiment of this type is selective polarizqtion tramfer (SPT). The pulse pattern for two repetitions is given in Figure 6, which also shows an energy level diagram for the C-H system. Each level is represented by a dashed line corresponding to the energy in the absence of spin-spin coupling and s solid line showing the effect of a positive coupling constant, which is exaggerated for clarity. The 180° proton pulse must induce a selectiue inversion of only one of the proton resonances. Recalling that a very short, high) a broad power RF pulse (-10 ~ s produces hand of frequencies centered at the spectrometer frequency (I),this means that a rather long, low-power pulse (tenths of seconds) is needed. Also shown in the figure are the differences (AHand Ad of the spin populations of the four levels relative to the populations that would exist in the hypothetical zero-
energy level. I t is useful to normalize the differences to units of Aa which is onefourth as large as AH. Figure 6c shows the population differences when the nuclei are at equilibrium in the Bo field. A 180" pulse at the frequency of the HI transition results in an inversion of the spin populations of the protons bonded to carbons in the n state. The population differences for the 180° proton pulse are shown in Figure 6d. The population differences of both of the 0 carbon levels do not change, hut the population in the Bunc state has increased by 8 X Ac (from -3 x Ac to +5 X Ac), while that of the awe state has decreased by the same amount. Because the signal intensity is proportional to the population excess in the lower level, this means that the Cz carhon resonance increases in intensity. The C1 resonance is now observed as an emission (negative) peak because the population of the a& level exceeds that of the nHnc level by 6 X Ac. The enhancement factors and ahsorptionlemission patterns for carbons bonded to more than one hydrogen are available in the literature (5, pp 37-43). As a means of increasine sensitivitv the poiarizatwn transfer method ha- several advanmaen over the nuclear O\,erhnuser effert. Because the transfer occurs as a result uf spin-spin coupling, the degree of signal enhancement does not have the strict relaxation requirements associated with the NOE. A less obvious advantage arises because the transfer of polarization depends on the inversion of magnetization of the proton. The waiting time between pulses is determined by the time required for the proton spin population to return to equilihrium. Because proton TI'Sare usually much shorter than those of 13C or I5N, S P T thus allows a more rapid pulse repetition rate. The S P T experiment can also be useful in the assignment of resonances in complicated spectra and for the determination of relative signs of coupling constants (5, pp 4 P 50). However, the method suffers from experimental problems because it is often difficult to determine the proper frequency of the 180° proton pulse. The HI and Hp reso-
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Figwe 5. APT resdm fw "l&mI". The sign ot me unpromnated CDCI. triplet (77 ppm) Is me same as lhat of the meWene carbons. The opposite sign of the hydroxyleted carbonat 68 ppm (same sign as me memy1 peakat 14 ppm) Indicateathat the alcohol cannot be prlmary. The presence of fifteen resolvablesamplepeaks shows that thls material is anually a m i m e of secondary alcohols.
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nances shown in Figure 6h correspond to the very weak satellite peaks produced by coupling of the protons to the honded 13C's (only 1.1% of total carbon in anaturalahundance sample). The utility of S P T is also limited by the obvious disadvantage that only one multiplet a t a time can he polarized.
"INEPT" By using a more sophisticated pulse sequence it is possible to produce polarization transfer simultaneously for all mutliplets in the molecule. In the S P T experiment the 180° pulse selectively inverts the net magnetization vector of one component of the proton doublet. The result is called antiphase magnetization, because the doublet vectors are a t 180' with respect to each other.%The same effect can be produced by using the INEPT (Insensitive Nuclei Enhanced by Polarization Transfer) family of sequences, the simplest of which is shown in Figure 7. The initial 90, preparation pulse nonselectiuely rotates the vectors for all of the proton resonances to the -y axis. The figure shows the behavior of the two components of a proton resonance split by one carbon-13. During the first r internal the vectors rotate in the xy plane as a result of chemical shift and spiu-spin coupling. However, only the precession due to spin coupling must he considered, because, as in the APT experiment, the ~-180'-r segment refocuses dispersion of the spin vectors arising from chemical shift differences. One essential feature of the experiment is the length of the r delay, which is made equal to 11 (UGH). This means that a t the end of the first r interval the two vectors have rotated 90° apart from one another, shown as + and -4V from the -y axis in the figure. The protons are then subjected to a 180, pulse, which assures that chemical shift effecta are refocused. However, because of the second important part of the sequence, the usual spin echo a t the +y axis is not observed. Simultaneous with the proton 180, pulse, a 180; pulse applied to the carbons causes the labels of the spin states of the protons to be reversed. Those that were formerly bonded to carbons in the u spin state now find themselves coupled to 'C's with 0 spins, and vice versa. This means that the rotation directions of the vectors are also switched; the countereloekwise-rotating vector becomes the cloekwise-rotating one, ete. Instead of meeting on the +y axis a t the end of the second 1 / ( W interval, the vectors arrive 180° out of phase along the and -x axes. The 90; pulse on the protons rotates the antiphase vectors to the 2 axis, and the polarization transfer to the coualed carbons is produced. The immediate 90, carbon pulse rotates the carbon magnetization to the -y axis, and the FID is obtained in the usual manner. In the INEPT sequence the refocusing of the rotation due to spin coupling is prevented hv the aoolicatian of simultaneous 180° .. pulses to hr.lh coupled nuclei. The same effect ir pmdured whenever the r-180'-i segment is used in sequences involving homonuclear coupled systems (e.g., a pair of coupled protons), heeause the 180° pulse affects all the nuclei nonseleetively. The spin echo sequence removes the rotation due to chemical shift, hut the exchange of labels means that spin coupling effects are
h~ ........... a. ~" ,. % ~
+A,-A,=+3A,
+AH-Ac=+3Ac
+AH+A,=+~A,
-AH+AC=3AC
fldc
Normal
b
c
After 180' Pulse d
Figure 6. Selective polariration transfer. (a) Pulse sequence lw two FiD accumulations. (b) Energy level diagram tor a C H system showing selective irradiation of the H, bansillon. (c) Population differencesfor equilibrium magnetiratlon. (d) Population differencesaner appilcation of the selective 180' pulse.
+
Figure 7. The INEPT experiment. (a)Pulsa sequence. (b) Vectw desaiption 01me proton spin system. not refocused and persist in the spectrum. This result is used in many multiple-pulse methods ta separate chemical shift- and spin coupling-induced precessions.
Spectral Editing The APT pulse sequence provides some
limited information about the number of hydrogens honded to the carbons in a molecule. Spectral editingtakes this prccessone step further by producing "edited" spectra, each of which contains only the peaks from carbons with a single proton multiplicity. (Continued on page A98)
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Although the INEPTsequence can he modified for this purpose, the most common spectral editing methods belong to the DEPT (Distortionless Enhancement hy Polarization Transfer) family. As the name implies, DEPT experiments make use of polarization transfer, hut this group of pulse sequences also involves the generation and manipulation of multiple quantum coherences (MQC's). Quantum mechanical analysis is necessary for complete understanding of the meaning and consequences of MQC, and therefore the pulse sequences will be described only briefly here. Considerable simplification of the mathematics is made possible by the use of the product operator formalism, and the reader is encouraged to consult sources such as refs 5, 6, and 7,
whieh offer an introduction to its use. A coherence exists between two energy states wheu the involved spins have a definite phase relationship. In this context it helps to refer to the description of CWNMR, as presented in the first paper in this series, hut the concept applies to the pulse method as well. At equilibrium the nuclei are randomly distributed about the axis of the BOfield, hut, when the applied R F frequency meets the resonance condition, the vectors come into phase with the 8, field. They then precess as a group (i.e., coherently), and the rotating group of vectors induces a signal in the receiver coil (cf. ref I, Figure 4). In the pulse experiment the duration of the BI field is only a few microseconds, hut spin rouping is established and persists until z e f f e c t a randomize the vectors about Bo,or until a subsequent B,pulse is applied. Because the nuclei also change their spin states when the pulse is applied, a
coherence is sometimes defined a s a "trausition" between the two energy states. However, although a transition is necessary to produce a coherence, the coherence itself continues after the transition is complete. For a single spin there are only two levels, corresponding to the a and 0 spin states, with magnetic quantum numbers, ml, equal to +I12 and -112 respectively (+I12 state lower in energy if the magnetogyric ratio is positive). These form a single-quantum coherence ( I ~ m l = l 1) a t the Larmor frequency. With two spin-112 nuclei it is necessary to consider the total magnetic quantum number, MI, which is the sum of the ml values for each nucleus. In this ease there are four energy levels (cf. Figure 6b) with MI values of +1 (am), 0 (a@and pa), and -1 (BP). Four single-quantum coherences ( n a l 08, na/@a, olBlBB, BalBB) connect states in whieh only one spin changes. In addition, it is possible to have multiple-quantum coherenees, which connect levels with both spins flipped. If they both change in the same direction, the AM,is *2 (aa/88), resulting in a double-quantum coherence. A zero-quantum coherence exists if the connected states involve an up flip of one nucleus simultaneous with a down flip of the other nucleus (a81Bn). According to the selection rules for nuclear magnetic resonance, only single-quantum coherences can he detected, and MQC's cannot be generated hy a single RF pulse from a system a t equilibrium. However, in a pulse sequence a singlequantum coherence already exists at the time wheu the second (or later) pulse is applied. Often at least some of the nuclei can
Figure 8. The DEPT pulse sequence
e Unedited
11
Figure 9. M P T results for ethyl benzoate. (aHc):CH.. CH2,and CH subspectra. (d) Subspacuum of all pratonatedcarbons. (e) Unedited spectrum. 16 FID's were accumulated for each 0 value.
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become involved in mnltiple-quantum coherence~.Even though the MQC's cannot be detected, the spins involved undergo precessional effects during the evolution period. After the evolution stage another suitable pulse can convert part of the MQC's back to detectable single-quantum coherences. All this may seem very complicated (and it is), but the important concept is that in the DEPT sequence different types of coherence~are generated, depending on the hydrogen multiplicity af the carbon, and are subseauentlv converted back to detectable signals. 1n DEPT pulse sequence (Fig. 8) the choice of the detected signals is achieved by altering the tip angle, 8,of the third proton pulse and also by applying this pulse alternately along the +y and -y axes. In one modification of this experiment the spectra are acquired with tip angles of 45, 90, and 135'. Linear comhinations (5,p 60) of these spectra are then used to generate the edited versions. Onlv, a sin& value for the I3C-H ,, roupling constant, J, can be used in an experiment, whereas the actual couplings in a molecule often span quite a wide range. In practice a compromise value of J is used, which is usually adequate for multiplicity assignments, although it may not provide perfect cancellation of all unwanted peeks. The CH, CHz, and CHI edited spectra of ethyl benzoate are shown in Figure 9, along with the edited spectrum for all protonated carbons and the unedited I3Cspect~um.The absence of peaks a t 166 and 130 ppm in any of the edited spectra clearly shows that these are from quaternary carbons, which from their chemical shifts can be assigned to the ester carbonyl and the substituted ring carbon, respectively. The assignments of the other aromatic peaks are less obvious, except for the 132-ppm peak, whose lower intensity shows that it belongs to the para carbon. The remaining peaks will be assigned by means of two-dimensional NMR spectroscopy, which will be the topic of the last article in this series.
tee
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Literature Cned 1. King, R. W.: Williams. K. R. J. Chem Educ. A213. 2. King, R. W.: Williams, K. R. J. Cham. Edur.
1983.66, 198'3.66,
s. Kessler, H: dehrke. M.; Griesin&r. C. Annew. Chem. l n f . E d .Engi. 1988,27.490-6R6. 7. Emst, R.R.: Bodenhausen, G.: Woksun, A. Plincipies of Nudeor Mogndic Reaanoncs in One and Tuo Dimznsions; Oxford University: Oxford, 1987. 8. Farrar. T. c.;B ~ c k e r E. , D.Pulse and Fourier Transform N M R ; Academic: New York. 1971:Chapter 2.
' A glossary of NMR tenns used in the four papers of this aeries appears in the next article (page AIDO). Phrases defined in Me glossary are italicized at their first appearance In the text. ZThe usages of the word "phase" can be a source of much confusion. The terms in-phaseand antiphase refer here to the relative directions of the magnetic vectors. The same words are also used to describe the peak patterns produced by this effect. An ifhohase aoublet has both m k s poimine me same way. whereas an anfiphasedoublet nas one peak posit ve and the other nsgat ve. These convent ons must not oe cOnt.sed woth lne phase correction, or phasing, of a spectrum to produce pure abscxption (or dispersion)mode signais. In many multiple-pulse experiments in-phase absorption,antiphase absorption, in-phase dlsperdon. and antiphase dispersion peaks are all passible!
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