Selective polarization transfer using a single rf field

Transcription

1 Selective polarization transfer using a single rf field Eddy R. Rey Castellanos, Dominique P. Frueh, and Julien Wist Citation: J. Chem. Phys. 129, (2008); doi: / View online: View Table of Contents: Published by the American Institute of Physics. Additional information on J. Chem. Phys. Journal Homepage: Journal Information: Top downloads: Information for Authors:

2 THE JOURNAL OF CHEMICAL PHYSICS 129, Selective polarization transfer using a single rf field Eddy R. Rey Castellanos, 1 Dominique P. Frueh, 2 and Julien Wist 1,a 1 Departamento de Química, Universidad Nacional de Colombia, Bogotá D.C., Colombia 2 Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, Boston, Massachusetts 02115, USA Received 10 March 2008; accepted 14 May 2008; published online 1 July 2008 NMR is a popular and mature technique used in fields as diverse as chemistry, biology, or material science. One reason for this versatility lies in its ability to correlate the nuclei that are present in one molecule to another. This provides the researcher with correlation maps allowing for studies of the molecules at an atomic level. Selective experiments allow isolation of one such correlation to focus on spins of interest. This leads to a savings in precious experimental time by reducing the dimension of the experiment, which in turn may enable one to record more elaborate experiments that would otherwise not be amenable within reasonable acquisition times. Here, we present an alternative method to selectively transfer magnetization using a single rf field. This technique, which we call single field polarization transfer, allows to obtain longitudinal two-spin order of two scalar-coupled spins when only one of them is irradiated. The method is easy to implement and does not depend on stringent conditions, such as Hartmann Hahn matching for selective cross-polarization transfers or very long inversion pulses and identification of coupling satellites in selective population inversion experiments American Institute of Physics. DOI: / INTRODUCTION a Electronic mail: jwist@unal.edu.co. URL: The ability to correlate signals from different nuclear spins is one of the most powerful features of NMR. It provides structural, kinetic, and dynamics information on molecules at an atomic level. In solution state, scalar and dipolar couplings enable transfer of polarization between nuclear spins and information is obtained about the coupled spin pairs. In addition, transfer of polarization facilitates the observation of insensitive nuclei, 1 since their polarization is enhanced. In principle, all correlations for a given set of spin systems in a molecule e.g., 1 H, 13 C can be obtained from a single multidimensional experiment. However, such experiments can be time consuming and may still feature spectral overlap for complex samples. Selective experiments are an attractive alternative, because they enable to isolate a subset of signals from the spectra. They also allow to focus on a spin system of interest when performing in-depth investigations that would not have been compatible with nonselective methods due to long data collection times. 2 4 In effect, the use of selective experiments allows for a reduction in dimensionality 5 while still resolving overlaps. Furthermore, selective experiments allow for faster repetition rates during signal accumulation due to increased longitudinal relaxation of the selected spins, which is exacerbated by the reservoir of longitudinal magnetization provided by the nonexcited spins. 6 8 This provides a further reduction in the experimental time. Polarization transfers, mediated by dipolar or scalar couplings, can be achieved with or without the presence of a continuous radio frequency rf field. For example, a selective experiment can be obtained by using a selective excitation or inversion pulse in a pulse sequence e.g., in an insensitive nuclei enhanced by polarization transfer INEPT scheme An alternative method is to make the transfer effective only for a particular spin pair by spin locking both nuclei with rf fields at the appropriate frequencies, as in cross-polarization 2,3,12 CP experiments. CP experiments are extremely selective, 13 but require information about the chemical shifts of both nuclei involved, as well as the associated scalar coupling constant. Thus, they cannot be used to identify correlated nuclei. In addition, CP transfers rely on fulfilling the Hartmann Hahn condition for both nuclei. This is difficult to achieve at different frequencies using phase modulated rf fields, so that such selective transfers do not allow for the simultaneous selection of various spin pairs. For the same reason, selective CP is not a good candidate for homonuclear selective transfers of magnetization. We present here an alternative technique to selectively transfer magnetization from a given spin, with selectivity comparable to CP transfers. The method, referred to as single field polarization transfer SFPT, only employs a single rf field and, thus, does not suffer from Hartmann Hahn limitations. In contrast to CP, no a priori knowledge of the spin system is required. The method is simple to implement, easy to optimize, and is expected to find immediate applications in conventional selective experiments. HETERONUCLEAR POLARIZATION TRANSFER Here, we briefly present an analytical procedure to predict the transfer of magnetization that occurs within a coupled spin pair IS when only the I spin is irradiated with a weak rf field. We consider coherent interactions in an isotropic solution, neglecting stochastic processes relaxation. Thus, only evolution under scalar couplings and the isotropic /2008/129 1 /014504/9/$ , American Institute of Physics

3 Rey Castellanos, Frueh, and Wist J. Chem. Phys. 129, FIG. 1. Creation of longitudinal two-spin order under a single low power rf field calculated using Eq. 3 applied to the SQC I x. Solid, dashed, and dotted lines represent the longitudinal two-spin order 2I z S z, the inphase doublet I x, and the antiphase doublet 2I y S z. components of the chemical shifts is considered. In addition, we account for the presence of an on-resonance continuous wave cw rf field with a frequency 1. For spins 1 2 in the Hilbert space, this Hamiltonian can be written in the rotating frame RF as V t + =Tr U 1 W t U V, where U =exp ih represents the propagator of evolution. In order to obtain an analytical solution and gain insights, the Hamiltonian is diagonalized: 3 H RF = 1 I I x +2 J IS I z S z 1 H D = M 1 H RF M, where the matrix representation of the transformation M is = 2 JIS 1 0 J IS J IS J IS. The evolution of the density matrix is described by the solution of the Liouville von Neumann equation t+ =U 1 t U, and the transfer of magnetization from an operator W to an operator V is s 0 c s 0 c 0 M = 0, 5 0 c 0 s c 0 s 0 where c=cos /2, s=sin /2, and the diagonal form of the Hamiltonian is H D = J 2 I z S z. 6 FIG. 2. Numerical simulations of the expectation value 2I z S z at optimum duration 5050 s J=140 Hz as a function of the offset. The solid line represents the offset profile of a rectangular rf field of 70 Hz, while the dashed and dotted lines represent the profile of trapezoidal- and Gaussian-shaped rf fields of the same durations. In the last two cases, the magnitude of the rf field was corrected according to the integral ratio of the shaped envelope with respect to the squared-shape envelope. The gray curve represents the offset profile of a CP transfer of duration rf =1/J using perfectly synchronized spin-lock fields and with 1 J.

4 Single field polarization transfer NMR J. Chem. Phys. 129, FIG. 3. Numerical simulations of the expectation value 2I z S z as a function of the transfer duration rf for different rf-mismatch ratio J/2 1. The extra bold line represents the buildup of the dipolar order when the ratio was 0.43, while the bold, solid, dashed, and dotted lines stand for ratios of 0.71, 1 no mismatch, 1.29, and The transfer of magnetization was not found to be critically dependent on the matching condition. However, the duration for a maximum transfer varies with the mismatch: the transfer time is shorter when 1 J/2 and longer when 1 J/2. Thus, in this frame, the evolution under scalar couplings, chemical shifts, and the rf field amounts simply to an evolution under a scaled scalar coupling. The density operator in this frame is obtained with = M 1 M. 7 Transfer from transverse magnetization We now consider the evolution of a two-spin system I,S, for which a single quantum coherence SQC on spin I has been created. In the interaction frame, the SQC I x becomes FIG. 4. Numerical simulations of the expectation value 2I z S z as a function of the transfer duration rf for different rf-mismatch ratio J/2 1. The contours represent the normalized transfer yield = 4 1 J/ J 2 cos eff t exp Rt as a function of both the duration of the transfer and the mismatch ratio, for a spin system a without relaxation and b that relaxes with T 1 =T 2 =400 ms. The optimum transfer yield=1 occurs when the rf-field strength is 70 Hz in a and 87.5 Hz in b. The increments between each contour are 0.1 top and 0.05 bottom and the bold lines represent conditions where no transfer is achieved.

5 Rey Castellanos, Frueh, and Wist J. Chem. Phys. 129, FIG. 5. Numerical simulations of the expectation value 2I z S z as a function of the carrier offset. The durations of the transfer were set to rf dotted, 3 rf dashed, 5 rf solid, and 7 rf bold, with rf =5050 s. I x = M 1 I x M = cos 2I x S z + sin 2I z S z, where =cos 1 J/ eff and eff = J 2. The longitudinal two-spin order 2I z S z becomes 2I z S z = M 1 2I z S z M = sin 2I x S z + cos 2I z S z. Furthermore the antiphase I-SQC 2I y S z becomes 2I y S z = M 1 2I y S z M = I y. In the special case where 1 =J/2, we find that I x and 2I z S z become 2 I x = 2 2I xs z +2I z S z, 8 2 2I z S z = 2 2I xs z +2I z S z. 9 The evolution of =I x is calculated using the Liouville von Neumann equation t + = U 1 t + cos 2I x S z + sin 2I z S z U t The second term of I x remains invariant, since it commutes with the Hamiltonian of Eq. 6, while the first term of I x oscillates at a frequency eff. Comparison of Eqs indicates that a state 2I z S z is obtained from I x after a period 1/ eff. The result in the RF, at time t+, is obtained by t + = M t + M In the case that 1 =J/2, longitudinal two-spin order is created periodically at rf =n/ 2J, as shown in Fig. 1. This dipolar order can be converted into antiphase SQC 2I z S y by a /2-pulse and subsequently refocused into S x, as routinely done in refocused-inept sequences. Alternatively, 2I x S z has a maximum at rf =1/ 2 eff = 2/ 4J and may be converted into 2I z S x with /2-pulses applied to both the I and S spins. This may become advantageous in the presence of relaxation, in spite of the lower magnetization yield 70% theoretical versus 100% for 2I z S z at rf =1/ eff. Note that there is already a substantial amount of longitudinal two-spin order present at this value of rf. Thus, by only applying a /2-pulse on the S spin, a mixture of S-SQC and IS-multiple quantum coherence MQC can be obtained. This can then be used for encoding with the S-spin frequency in indirect experiments. This is not the focus of the current work and will be discussed elsewhere. Since only one nucleus of the pair is irradiated, it is not necessary to know a priori the frequency of the second nucleus, in contrast to CP experiments. In fact, the magnetization from the irradiated spin flows toward all coupled spins, unlike what happens in CP transfers where only the two irradiated spins lead to a transfer. In general, the scalar couplings have very different magnitudes e.g., 2 J HH 1 J CH, so that the transfer duration can be adjusted to optimize for a given transfer. Alternatively, the duration can be chosen as a compromise in order to see many transfers. This is formally identical to what is observed for a nonselective INEPT and will not be further developed here. Note that relaxation optimized transfers 14,15 resulted in the application of a rf field to a single nucleus of a spin pair, in analogy to what we present here. However, these experiments were not designed for selective transfers, but rather to demonstrate how relaxation losses can be minimized during transfers. TRANSFER FROM LONGITUDINAL MAGNETIZATION The effect of a low-amplitude CW rf field on a longitudinal magnetization is now investigated. In this case, the initial state is given by I z = M 1 I z M = S z. 12 This system was found to evolve into the antiphase SQC 2I x S z with a maximum at rf =1/ eff. Thus, applying a rf field on resonance for the Zeeman order of a coupled spin pair leads to a polarization transfer, irrespective of which of the Zeeman order I z or S z is irradiated. As a consequence, the signal of the spin pair that is the most isolated can be used

6 Single field polarization transfer NMR J. Chem. Phys. 129, FIG. 6. Effects of rf inhomogeneities. Top, the curves represent the magnetization transferred as a function of the transfer duration when the rf-field homogeneities are assumed to follow Gaussian distributions. Bottom, the corresponding Gaussian distributions of rf-field amplitudes with standard deviations chosen so that the resulting FWHM are of a 0.1, b 0.15, c 0.2, d 0.25, e 0.3, and f 0.5. The integral of each distribution is set to unity. for the selection, in complete analogy with selective INEPT transfers where the selective -pulse or /2-pulse can be applied either on I or S. OFFSET EFFECTS AND SENSITIVITY TO rf MISMATCH The Hamiltonian of Eq. 1 is valid only in the case that the rf field is set exactly on resonance, i.e., in the center of the doublet. If this is not true, an additional term I z describing the offset of the rf field enters the Hamiltonian. The effect of this offset on the polarization transfer is studied using numerical simulations. 16,17 In Fig. 2, the expectation value 2I z S z at optimum rf-field duration rf =1/ 2J is plotted against the offset. As expected, the maximum transfer is found when the rf field is set on resonance. Off resonance, the transfer efficiency rapidly deteriorates, with the first zero amplitude at 75 Hz. At 125 Hz, 50% of the magnetization is transferred, while after 200 Hz only 10% of the signal can be detected. The best profile i.e., with minimal off-resonance effects is achieved when using a Gaussian-shaped rf field. As will be shown in the next section, selectivity can be improved by using longer rf-field irradiation times. However, relaxation and rf-field inhomogeneities lead to losses in the transfer yield. Note that the maximum magnetization transferred in Fig. 2 is slightly less than 100%, in contrast to Fig. 1, since relaxation is accounted for in these numerical simulations. 16 For the sake of comparison, a numerical offset profile for CP transfer is also shown. When the applied rf fields do not match the condition 1 =J/2 Fig. 3 a reduction in the transfer yield is observed. However, even a strong mismatch see J/2 1 =0.43 allows a transfer with 80% efficiency, showing that the method is relatively robust with respect to this condition. In addition to this reduction in intensity, the mismatch leads to a shift in the optimal transfer time. As a result, a rf field of amplitude higher than J/2 results in a faster transfer rate. This may be exploited for fast relaxing systems, where minimizing relaxation losses with a shorter transfer time compensates for losses due to the mismatch. For instance, the optimum rf strength to transfer magnetization from a proton to a carbon nucleus assuming a scalar coupling constant of J=140 Hz is increased from 70 to 87.5 Hz when relaxation time constants of T 1 =T 2 =400 ms are considered for both spins Fig. 4 b.

7 Rey Castellanos, Frueh, and Wist J. Chem. Phys. 129, FIG. 7. a Refocused-INEPT pulse sequence Ref. 19 used for reference, b T-SFPT, and c L-SFPT blocks are used instead of the INEPT in a for selective experiments. Narrow solid rectangles and broad open rectangles indicate /2 and pulses, respectively. The carrier frequency during the selective transfer of length rf must be set on resonance with the spin to be selected. 1 = y, y, rec = x, x, and 2 = x, x. The phase cycle ensures that no 13 C native magnetization contributes to the spectrum. 13 C decoupling during detection is achieved by using the WALTZ-16 scheme with an amplitude of 3050 Hz. Selectivity In general, the bandwidth of a pulse depends on its duration and amplitude, and increasing the duration of the rf field while reducing its amplitude increases the selectivity. In SFPT transfer the amplitude is somewhat restricted by the matching condition. The effect of the duration of the rf field on the offset profile was investigated in Fig. 5. Although increasing the duration shifts the first region with no transfer toward the on-resonance frequency, strong wiggles remain that spread over a ppm at 400 MHz. In addition, in practice, longer transfer durations result in the attenuation of the observed signal due to relaxation phenomena and rf-field inhomogeneities. Numerical simulations using trapezoidal or Gaussian-shaped envelopes showed that although it is possible to attenuate the wiggles, this is accompanied by a reduction in the transferred intensity. Thus, further investigations are required for the design of highly selective experiments. Additional simulations were used to investigate the effect of a rf mismatch i.e., 1 J/2 on the offset profile of the transfer pulse. At constant transfer duration, the selectivity is almost not affected by the mismatch but the attenuation of the observed signal becomes important as seen in Fig. 4. In contrast, when the duration of the transfer is chosen to compensate for the mismatch, the selectivity of the transfer is modified: the shorter the transfer, the wider the profile. rf inhomogeneities In general, rf pulses are affected by rf-field inhomogeneity, which may be an impediment to efficient SFPT transfer. We conducted simulations to investigate how these alter the transfer yield. The ensemble average over several Gaussian distributions of rf amplitudes, each with a different standard deviation, was evaluated. The results are shown in Fig. 6; for FIG C spectra of menthol, a using INEPT, b d using transverse SFPT, and e using longitudinal SFPT. The spectra 32k complex points were recorded on a Bruker Avance 400 MHz with 16 scans using the standard INEPT, T-SFPT, and L-SFPT pulse sequences. All the experiments were recorded using a broadband double resonance probe at 298 K. Nonselective excitations of protons and carbons were achieved using 22 and 27 khz rectangular pulses, respectively. During SFPT experiments, the 1 H carrier frequency was set on resonance with the proton signal at b and e 3.42, c 1.57, and d 2.21 ppm. The duration rf was set to 1/J 2=5050 s and the rf amplitude to 70 Hz. Each experiment was recorded using the same parameters.

8 Single field polarization transfer NMR J. Chem. Phys. 129, FIG. 9. Comparison between SPI and SFPT experiments. a 13 C 1 H spectrum. b d SFPT black and SPI gray experiments. b 5, c 25, and d 50 ms inversion pulses 100, 20, and 10 Hz were applied on resonance with the downfield satellite for SPI. Transfer pulses of the same lengths were used for SFPT, in which the centerline of the doublet was irradiated. With the exception of b, the amplitude was chosen so that eff J. The SPI experiments were performed as proposed by Sarkar and Bax Ref. 21 ; antiphase 13 C SQC was allowed to refocus prior to decoupling on the proton channel and the 13 C native magnetization was eliminated by applying a 90 pulse on 13 C followed by a pulsed-field gradient. e Region of the 1 H spectra highlighting the frequencies irradiated gray areas in SPI side bands and SFPT center band experiments. Note that the 13 C satellites are not observable, and it is thus difficult to identify the frequency for the selective inversion in SPI experiments. typical transfer times approximately 5 ms, even the most extreme situations only lead to a deterioration of less than 5%. If the inhomogeneities produce rf-field mismatch within 10% full width at half maximum of 0.2, the transfer yield remains higher than 70% even after 100 ms. Thus, even very selective transfers are achievable in the presence of rf inhomogeneity. The effects of rf inhomogeneity may be addressed by using an amplitude and phase modulated rf field during the transfer, as proposed in recent related work. 18 EXPERIMENTS Selective heteronuclear transfer Our method is demonstrated on a sample of 0.1M unlabeled menthol. To investigate the transfer efficiency, the experiment is compared to the refocused-inept experiment, 19 which allows detection of in-phase SQC on spin S 13 C originating from spin I 1 H. The comparison is done by replacing the INEPT scheme, in brackets in Fig. 7 a, with one of the SFPT transfer schemes Figs. 7 b and 7 c. This was done for a spin I with both transverse T-SFPT, Fig. 7 b and longitudinal L-SFPT, Fig. 7 c magnetizations. First, the INEPT transfer time was optimized for the selected spin pair in order to obtain a reference for the associated transfer. The corresponding scalar coupling was measured on a 13 C detected spectrum without proton decoupling. Next, the duration of the T-SFPT and L-SFPT was set according to rf =1/ 2J. Finally, the amplitude of the rf field was optimized to provide a maximum transfer. In the T-SFPT experiment, special care was taken to correct for the dephasing of the SQC prior to the transfer, which results from a change in power level between the hard /2-pulse and the lowamplitude rf field. The spectra obtained for menthol using INEPT and the SFPT sequences are displayed in Fig. 8. As expected, only the selected signal, carbon 3 b and e, 1 c, and 8 e of menthol, is observed in spectra corresponding to both FIG. 10. Experimental diamonds and simulated solid line buildup of the transfer as a function of the rf-field duration rf. The calculated curves were obtained using a rf-field strength of 90 Hz, which corresponds to the experimental value for the selected spin system.

9 Rey Castellanos, Frueh, and Wist J. Chem. Phys. 129, FIG. 11. Experimental diamonds and simulated solid line offset profiles, using a transfer duration of 5050 s. The calculated curves were obtained using a rf-field strength of 90 Hz. T-SFPT b d and L-SFPT e schemes. Note also that the signal intensities are equal for the three experiments. This demonstrates that, for small molecules i.e., with slow transverse relaxation, the SFPT transfer is as efficient as the IN- EPT transfer. An alternative way to obtain selective spectra relies on the selective inversion of a single transition of the I-spin resulting in longitudinal two-spin order, which can then be converted into S-coherences. This method, referred to as selective population inversion SPI, requires a selective inversion of one component of the I spin multiplet. Thus, while SFPT transfer may be considered as operating on decoupled spectra of spin I, SPI in effect uses nondecoupled spectra. Consequently, SPI is subject to increased spectral crowding leading to an increase in pulse lengths, which are typically ranging from 25 to about 100 ms. For comparison, the results obtained with menthol above used 5 ms SFPT transfer. In studies of natural low abundance nuclei e.g., when transferring polarization from 1 Hto 13 C, the spectrum of the I spin contains resonances for both I nuclei attached to magnetically inactive S spins and satellite resonances originating from the active S spins. It may be extremely difficult to identify the S spin satellites, which may overlap with another and lead to simultaneous SPI conversions see Ref. 21, for example, thus obfuscating the correlations. In addition, the satellites may overlap with the central resonances of other I spins, which can lead to SFPT transfers since these are also effective for long pulses. A comparison of SFPT and SPI for various lengths of rf pulses is shown in Fig. 9. Itcan be seen that the selective inversion of the downfield satellite of proton 4 in SPI also leads to the selective inversion of the upfield satellite of proton 1, even when the irradiation field is made extremely selective 10 Hz. In contrast, the irradiation at the center of the doublet of proton 4 results in a clean spectrum for long pulses. Note that for short pulses, SFPT transfer still allows for unambiguous identification of the correlation since the off-resonance transfer of H 1 to C 1 results in a small signal in antiphase with respect to the C 3 signal, unlike SPI which leads to two strong signals of the same phase. Buildup and offset profile To validate our theoretical predictions, buildup of transferred magnetization was recorded using an heteronuclear single quantum correlation HSQC -like sequence 24,25 where the first INEPT block was replaced by the T-SFPT block of Fig. 7 b. The initial duration of the rf field 2 ms was incremented by 1 ms between each experiment. The experimental parameters were those described in the caption of Fig. 8. The intensity of the selected signal was then plotted against the duration of the rf field and shown to correlate with the simulated buildup Fig. 10. The experiments were recorded for the signal selected in Figs. 8 b and 8 e carbon 3 of menthol. The experimental offset profile of the T-SFPT transfer was obtained by shifting the proton carrier frequency between experiments and by plotting the selected signal intensity as a function of the offset. Forty points were measured using an increment of 20 Hz. Figure 11 shows the comparison between the experimental and simulated profiles. CONCLUSIONS We have shown that transfer of polarization from a source spin to a given target spin is possible using a single on-resonance rf field applied to the center of the doublet of the source spin. Since no prior knowledge of the target spin frequency is needed, the technique can be used to identify this correlation. Because the magnetization from the irradiated spin flows toward all coupled spins, the SFPT sequence may be used in principle to determine heteronuclear multiple bound correlation HMBC -like connectivity networks. We demonstrated that the transfer efficiency is not critically sensitive to rf mismatch and that the sensitivity of the experiment is identical to the one obtained with an optimized IN- EPT transfer. Further investigations are required to improve the selectivity and to account for relaxation processes and rf-field inhomogeneities. Since the technique only needs an approximate knowledge of the scalar coupling between the two spins, it can readily be applied to characterize chemical compounds. Out-and-back experiments can be designed to

10 Single field polarization transfer NMR J. Chem. Phys. 129, select for a spin in the detected dimension, which can further be correlated to other scalar- or dipolar-coupled spins. The simplicity and robustness of the technique suggest a number of applications in more elaborated experiments, such as selective total correlation spectroscopy TOCSY, ISSI- TOCSY, or nuclear overhauser spectroscopy NOESY experiments. The method thus allows to obtain detailed information on target spin systems de novo. This may prove particularly useful for metabolomics studies, for identification of a given compound, or for analyses of biosynthetic pathways, when investigating metabolism of selectively labeled moieties. ACKNOWLEDGMENTS J.W. acknowledges Professor Geoffrey Bodenhausen for valuable information and Dr. Damien Jeannerat for academic discussions. The authors also thank Professor Eliseo Avella and Professor Ricardo Fierro for technical help with NMR spectrometers. 1 G. A. Morris and R. Freeman, J. Am. Chem. Soc. 101, P. Pelupessy and E. Chiarparin, Concepts Magn. Reson. 12, E. Chiarparin, P. Pelupessy, and G. Bodenhausen, Mol. Phys. 95, T. R. Eykyn, D. Früh, and G. Bodenhausen, J. Magn. Reson. 138, H. Kessler, H. Oschkinat, and C. Griesinger, J. Magn. Reson , P. Schanda, E. Kupce, and B. Brutscher, J. Biomol. NMR 33, M. Gal, P. Schanda, B. Brutscher, and L. Frydman, J. Am. Hem. Soc. 129, E. Kupce and R. Freeman, Magn. Reson. Chem. 45, A. Bax, J. Magn. Reson , J. Stelten and D. Leibfritz, Magn. Reson. Chem. 33, T. Parella, Magn. Reson. Chem. 34, P. Pelupessy, E. Chiarparin, and G. Bodenhausen, J. Magn. Reson. 138, F. Ferrage, T. R. Eykyn, and G. Bodenhausen, ChemPhysChem 5, N. Khaneja, L. Burkhard, and S. J. Glaser, Proc. Natl. Acad. Sci. U.S.A. 100, N. Khaneja, T. Reiss, B. Luy, and S. J. Glaser, J. Magn. Reson. 162, P. Allard, M. Helgstrand, and T. Härd, J. Magn. Reson. 134, Copyright INRIA ENPC., URL: 18 N. Khaneja, R. Brockett, and S. J. Glaser, Phys. Rev. A 63, O. W. Sorensen and R. R. Ernst, J. Magn. Reson , K. G. R. Pachler and P. L. Wessels, J. Magn. Reson , S. K. Sarkar and A. Bax, J. Magn. Reson , R. Pachter and P. L. Wessels, J. Magn. Reson , S. A. Linde and H. J. Jakobsen, J. Am. Chem. Soc. 98, G. Bodenhausen and D. J. Ruben, Chem. Phys. Lett. 69, L. E. Kay, P. Keifer, and T. Saarinen, J. Am. Chem. Soc. 114,