Two-Dimensional Nuclear Magnetic Resonance: Exploiting Spin

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2D NMR: Exploiting Spin Echoes to Maximize Information Content by Suppression of Diagonal Peaks in Homonuclear Experiments Abhishek Banerjee, and Narayanan Chandrakumar J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp512511h • Publication Date (Web): 22 Dec 2014 Downloaded from http://pubs.acs.org on January 12, 2015

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The Journal of Physical Chemistry

2D NMR: Exploiting Spin Echoes to Maximize Information Content by Suppression of Diagonal Peaks in Homonuclear Experiments Abhishek Banerjee and Narayanan Chandrakumar* MRI-MRS Centre, Department of Chemistry, Indian Institute of Technology Madras, Chennai – 600036, Tamil Nadu, India AUTHOR INFORMATION Corresponding Author *[email protected]; +91-44-22574920

ACS Paragon Plus Environment

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ABSTRACT

Two-dimensional Nuclear Magnetic Resonance (2D NMR) correlation spectra help visualize inter- or intra- molecular spin connectivity through space, or through bonds. This is accomplished by magnetization transfer between interacting (‘connected’) spins located at different sites in molecules. In homonuclear 2D experiments, cross peaks which demonstrate spin connectivity and result from magnetization transfer between sites are unfortunately invariably accompanied by other peaks that result from magnetization that has not undergone any transfer, viz., diagonal peaks. The latter can often mask close lying cross peaks. We report here the general principles that constitute a design strategy for diagonal suppression, relying on echo formation. Next, a novel experiment that effects diagonal suppression in high resolution mode is demonstrated. Pure phase capability is also introduced. Examples from both 2D exchange and high resolution 2D correlation spectroscopy are included, and the proposed method is compared with other established as well as recent attempts to accomplish diagonal suppression.

KEYWORDS Spin echoes; 2D NMR; homonuclear correlation spectroscopy and exchange spectroscopy; diagonal and cross peaks; diagonal suppression; pure phase 2D correlation spectra


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INTRODUCTION 2D NMR correlation experiments1,2 are vital in modern NMR practice, because they help visualize spin connectivity through space or through bonds, by effecting and/or tracking magnetization transfer between different sites in molecules during a ‘mixing’ (or ‘transfer’) period. Magnetization transfer seldom goes to completion, however, and the residual untransferred magnetization is also detected in homonuclear experiments. Such magnetization components constitute diagonal peaks: their precession frequency is unchanged during the evolution and detection periods, since there has been no transfer of magnetization between different sites during the mixing period that intervenes. Diagonal peaks generally do not offer any new information beyond the standard 1D spectrum, but on the other hand can pose problems in the identification of close lying cross peaks, which they could often mask. It has therefore always been of interest to generate diagonal suppressed homonuclear 2D spectra. In particular, diagonal suppressed variants3,4 of two important experiments for scalar coupled spin systems, viz., correlation spectroscopy (COSY)2 and spin echo correlation spectroscopy (SECSY)5 have been developed, relying on recording two sets of data, one being the normal correlation dataset, while the second is a “diagonal only” dataset. Clearly, this approach inevitably results in a significant loss of measurement sensitivity, since half the experiment time is used in acquiring no cross peak information at all. A recent alternative strategy also loses sensitivity by invoking a slice selective approach6. In the present work, we point out that working with spin echoes (as in SECSY) affords a unique opportunity to suppress diagonal peaks even in scalar coupled spin systems, while acquiring cross peaks in every scan from the entire sample. Because cross peaks are acquired during the entire measurement time, this leads to improved sensitivity despite the ‘duplication’ of the cross peak pattern in the resulting rectangular array of cross peaks.


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A spin echo7 is generated by employing a refocusing resonant r.f. pulse to effectively reverse the time evolution of transverse magnetization when it is governed by spin interactions which are linear in spin operators. An echo results from transverse magnetization rephased to its initial state (except possibly for a trivial reversal of sign, depending on the relative phase of the refocusing r.f. pulse) at a fixed point of time after the refocusing pulse equaling the preceding evolution time: which is generally the time between the initial preparation pulse and the refocusing pulse. Since phases of rf magnetic fields and of spin magnetization correspond to directions in the Zeeman interaction frame (the so-called rotating frame), rephased transverse magnetization at the time of the echo maximum is, in other words, back in alignment along its initial direction in the rotating frame (or opposite this direction). Crucial to echo formation – whether for spin echoes or for stimulated echoes7 – is the constancy of the precession frequency of the spin magnetization in the time durations before and after the refocusing pulse or pulse block. As we show below, echo formation constitutes the vital key to diagonal peak suppression. In this report we propose two novel schemes to suppress diagonal peaks, respectively in 2D exchange spectroscopy8 and in high resolution 2D correlation spectra. THEORY AND PULSE SEQUENCE In a 2D exchange experiment8, cross peaks contain sufficient information for extraction of the exchange parameters. Typically, slow exchange occurs primarily during a mixing time that is considerably longer than the maximum evolution time, equal halves of which occur both before and after mixing in the echo mode. During the mixing time the spin magnetization is parked longitudinally, so that slow exchange can still be registered, competing against T1 rather than against T2, which is generally shorter even in solution state. The pulse sequence for diagonal suppressed EXSY in spin echo mode is shown in Figure 1.


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Figure 1. Pulse sequence for 2D diagonal suppressed exchange spectroscopy (DISSEXSY). τm is the mixing time. If scalar couplings are present in the system, the last pulse needs to be phase alternated, keeping the receiver phase fixed: thus leading to a four-step phase cycle. The last 90° pulse could be replaced by a 180° pulse (on/off in alternate scans) with fixed receiver phase. In the situation typical of two-site exchange without any spin couplings, transformation of the spin magnetization starting from equilibrium longitudinal magnetization, right upto the end of the second half of the evolution time (t1/2) may be modeled as follows, taking chemical shifts into account, with both the second and third 90° pulses having the same phase:

°

1 I z → I x  → I x cos

90 y

t 2

( ) + I sin ( ) →−I cos ( ) + I sin ( ) → δI t1

°

δI t1

2

δI t1

90 y

2

y

δI t1

2

z

Gz

2

y

( ) →−C I cos ( ) − C S cos ( ) →−C I cos ( ) − C S cos ( ) ( )  →−C cos ( ) I cos ( ) + I sin ( )  − C cos ( ) S cos ( ) + S sin ( ) 

−I z cos

δ I t1

δ I t1

τ m mixing

1 z

2

δI t1

t1 2

1

2

δ I t1

2

2

δI t1

x

2

z

Echo pathway  → 12 −C1I x − C2 Sx cos selection  

((

2

) − S sin ( ( y

2

δI −δS )t1 2

δ I t1

2

2

δS t1

δ I t1

2

2

δI −δS )t1

δ I t1

1 x

2

δ I t1

y

°

90 y

x

)

2

x

2

δS t1

y

2

[1]

Here, δI and δS are the chemical shifts of spin I and spin S respectively; the exchange process is characterized by:


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Iz→C1Iz + C2Sz

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[2]

C1 and C2 are mixing time dependent coefficients. It is clear from the above that there is a crucial difference between a diagonal peak and a cross peak. The former arises from magnetization that has the opposite frequencies during the two halves of the evolution time, and thus ends up aligned along its original x direction in the rotating frame, not bearing the imprint of any oscillation during evolution. The latter, on the other hand, arises from magnetization that rotates with different frequencies of unequal magnitude during the two halves of the evolution period and thus has both an x, as well as a y component9, and is thus modulated during the evolution time. This difference at once offers opportunities to suppress the former (albeit along with some components of the latter). In the specific case in question, one approach would be to issue a final 90° pulse along the y direction of the rotating frame just before the start of acquisition. The result would be a signal exclusively

 (δ − δ S )  from the term − 12 C2 sin  I t1  S y , leading to a cross peak. Alternatively, a final 180° 2   pulse may be issued in alternate scans along the y direction of the rotating frame just before the start of signal acquisition. In this case, co-addition of two scans, one with and the other without the final 180° pulse results again in a signal that arises exclusively from the term

 (δ − δ S )  −C2 sin  I t1  S y . 2   While the situation is a little more complex in a correlation spectroscopy experiment where scalar couplings are involved, it may be readily seen that essentially similar strategies for diagonal suppression would prevail. In a SECSY experiment, a non-selective refocusing pulse of


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90° flip angle is employed, as in the original Hahn echo. When applied to a system of coupled spins, however, this serves the dual purposes of leading to echo formation, as well as magnetization transfer (or, in a generalized sense, coherence transfer). It may be recalled that while the echo generated by a non-selective refocusing pulse rephases shifts, it does not rephase evolution of magnetization under homonuclear scalar couplings7. At the fixed point of time corresponding to the echo top, therefore, part of the magnetization that has not undergone transfer returns in-phase to its original ‘reference’ direction in the rotating frame since its frequency merely changes sign during the two halves of the evolution/echo time; while another part is oriented precisely in the orthogonal direction, but as a pair of anti-phase vectors. Magnetization that has been transferred on the other hand has different chemical shift frequencies in the two halves of the evolution period (or echo time) before and after the refocusing 90° pulse. At the end of the evolution time, it is therefore oriented somewhere in the transverse plane in accordance with the relevant parameters: viz., the evolution time, the chemical shift difference, and the coupling constant. In addition to two components as for untransferred magnetization, it thus has a transverse in-phase component orthogonal to the reference direction, besides an anti-phase component in phase quadrature. This distinguishes diagonal peaks from cross peaks in the 2D experiment, which may be performed either by varying the echo time in the standard 2D manner, or by operating in the ‘constant time’ mode. The transformation of the state of the spin system from equilibrium (longitudinal magnetization) to the echo maximum may be summarized as follows for a two-spin-1/2 system, taking both spin couplings and chemical shifts into account (the detailed calculation is given in Supporting Information):


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1 I z →  −ca2 I x − sb I y S z − cδ sa2 S x + cδ sb I z S y + sδ sa2 S y + sδ sb I z S x  2

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[3]

Here, the coefficients ca, sa, sb, cδ and sδ oscillate in time t1 as a function of couplings and chemical shift differences: ca = cos πJt1/2, sa = sin πJt1/2, sb = sin πJt1, cδ = cos(δI − δS)t1/2, and sδ = sin(δI − δS)t1/2. From Eq. [3], it is evident that the diagonal peak, which arises from transverse magnetization that has not undergone any transfer, now has two components owing to coupling as described in the foregoing (cf. the first two terms of Eq. [3]). On the other hand, magnetization that has been transferred from spin I to spin S has four components as described earlier (cf. the last four terms of Eq. [3]). A 90° pulse of phase y issued just before the start of acquisition eliminates the first four terms by converting them into unobservable longitudinal magnetization components (the first and third terms of Eq. [3]) or multiple quantum coherences (the second and fourth terms of Eq. [3]), leaving the last two terms observable. However, it must be noted that this final 90° pulse effects additional coherence transfer, as exemplified by its effect on the last term, which it converts to −sbsδSzIx. Besides, it also converts longitudinal magnetization or multiple quantum coherence present during the second half of the evolution time into observable signal. This necessitates a second scan with phase alternation of the final 90° pulse and co-addition of the signal, although diagonal peaks themselves are suppressed in every single scan. Because this final pulse effects additional coherence transfer, however, additional ‘artifact’ peaks could also result in high resolution conditions in larger spin systems (the behavior of the AX2 system, for example, is described in Supporting Information), when anti-phase magnetization is readily observable. Hence this strategy would not work in high resolution conditions in general. However, under conditions where the signal acquisition time is short and the resolution in the direct dimension is limited, such ‘artifact’ peaks are normally not


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observed, since in-phase magnetization terms contribute predominantly to the observed signal. This simple strategy has proved successful under conditions of volume localized MRS, ultrafast NMR, and Overhauser DNP enhanced NMR, and has been termed DISSECT (DIagonal Suppressed Spin Echo Correlation specTroscopy)10-12. On the other hand, the alternative strategy of using a 180° pulse of phase y on alternate scans with co-addition of signals works perfectly under high resolution conditions, although it does require two scans to suppress the diagonal peaks. The sequence is shown in Figure 2. From Eq. [3], the signal observed after issuing a final 180° pulse in alternate scans and co-addition in the receiver is given below: I z →  sa2 sδ S y + sb sδ I z S x 

[4]

with the symbols defined as before. This experiment may therefore be termed HR-DISSECT.

Figure 2. Pulse sequence for 2D homonuclear diagonal suppressed correlation spectroscopy in high resolution mode (HR-DISSECT). The 180° (y, −y)/0° pulse [which could be replaced respectively with two 90° pulses, each with phase ±y and ±y, or ±y and my respectively] is issued in alternate scans and signals are added in the receiver. Echo pathway selection is accomplished by using gradient pulses, Gz.


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EXPERIMENTAL DETAILS A. DISSEXSY Exchange experiments were performed on a Bruker GmbH AVANCETM III 400 MHz spectrometer equipped with broadband observe (BBO) probe on a sample of 10% N, N−dimethylacetamide (v/v) in C6D6. The experimental parameters used for 2D DISSEXSY were: pre-relaxation delay: 40 s; number of scans: 4; number of complex points in F1: 44 and in F2: 2048; spectral width in F1: 1.5 kHz and in F2: 5 kHz. Measurement time for each mixing time: ca. 2 hr 20 min. As 2D EXSY8 experiments are time consuming, we acquired all our data in ultrafast (UF) acquisition mode13,14 for the determination of activation energy. The ultrafast version of DISSEXSY is shown in the Figure 3.

Figure 3. Pulse sequence diagram for the acquisition of diagonal suppressed 2D exchange in ultrafast mode13. τm is the mixing time (100 ms to 4 s). For ultrafast acquisition of the DISSEXSY spectrum, incremented evolution periods are replaced with two pairs of frequency swept CHIRP pulses (constant time mode), while the acquisition is of EPI15 type.

The experimental parameters for UF-DISSEXSY were: pre-relaxation delay: 40 s; number of scans: 16; number of read gradient pairs N: 128; two pairs of CHIRP pulses, each 7.5 ms long, with bandwidth of 30 kHz; Ge: 3.5 G/cm; Ga: 11.83 G/cm; Gd: −4.5 G/cm; ∆t2/2: 446 µs.


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Measurement time for each mixing time: ca. 12 min. For the calculation of activation energy, experiments were performed at four different temperatures (35° C to 50° C) with different mixing times (100 ms to 4 s). B. HR-DISSECT All experiments were performed on a Bruker GmbH AVANCETM II 500 MHz equipped with a triple axis gradient inverse probe with: (i) 50 mM 2,3-dibromopropionic acid (DBPA); (ii) 0.45 M strychnine in CDCl3; and (iii) 50 mM vinyl acetate in D2O. The experiment parameters for SECSY and HR-DISSECT were: pre-relaxation delay: 1 s; number of scans: 4 (8 for vinyl acetate); spectral width in indirect dimension (F1): 800 Hz, and in direct dimension (F2): 1500 Hz for DBPA, 2500 Hz (F1) and 5500 Hz (F2) for strychnine, 3000 Hz (F1) and 4000 Hz (F2) for vinyl acetate; number of complex points in F2: 2048; number of complex points in F1: 128 for DBPA and vinyl acetate, and 256 for Strychnine. RESULTS AND DISCUSSION We have tested DISSEXSY sequences (termination with 90° DISSECT pulse) on N, N−dimethylacetamide (DMA, 10% v/v) in C6D6. The exchange kinetics of DMA is well established. The two methyl groups bonded to nitrogen are involved in the exchange process, arising from restricted (or slow) rotation around the C−N bond. Figure 4a shows the 2D UFDISSEXSY spectrum of DMA at 40° C with a mixing time 700 ms. A series of spectra (both in normal and ultrafast mode) with different mixing times are given in Supplementary Information (S1, S2). In both cases (normal and ultrafast mode of acquisition) diagonal suppression was excellent. Suppression of the chemical site that is not involved in exchange was also good.


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a

b

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c

Figure 4. (a) 2D UF-DISSEXSY spectrum of DMA at 40° C with mixing time 700 ms and relaxation delay 40 s; (b) variation of intensity of one of the cross peaks with mixing time at 40° C, the equation used for fitting and for the determination of rate contastant, k being: y = a exp(x/T1)(1−exp(2kx); (c) Arrhenius plot for the calculation of activation energy of

exchange: k = A exp(−Ea/RT).

Figure 4b shows the variation of intensity of one of the cross peaks with mixing time (100 ms to 4 s) at 40° C and fitted with y = a exp(x/T1)(1−exp(2kx)) [8], where T1 is the spin-lattice relaxation time and k is the first order rate constant. Figure 4c shows the Arrhenius plot; the activation energy for the amide bond rotation was found to be 21.4 kcal/mol (cf. 22 kcal/mol, 10% DMA in DMSO)16. We have evaluated the performance of our HR-DISSECT sequence on three samples: 50 mM DBPA, 0.5 M strychnine in CDCl3 and 50 mM vinyl acetate in D2O. Figure 5a and figure 5b show the 2D SECSY and HR-DISSECT spectra of DBPA respectively. Figure 5c is acquired with the difference method proposed earlier by Nagayama et al3. In HR-DISSECT the suppression of the diagonal peak is clearly superior compared to the earlier method.


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a

b

c

Figure 5. 2D NMR spectra of DBPA acquired with pulse sequence (a) SECSY; (b) HRDISSECT and (c) difference SECSY in magnitude mode. Cross peaks are shown connected with tie lines.

The cross peak intensities (volume integrals) in HR-DISSECT were 2 times lower than the cross peak intensities in SECSY due to amplitude modulation, but about 15% higher than the cross peak intensities in difference SECSY. Our original DISSECT sequence10 which was employed with great success for single scan diagonal suppression in low resolution / short acquisition time mode (vide supra) is also seen to suppress diagonal peaks efficiently. But as discussed above, the last 90° DISSECT pulse effects additional coherence transfer and hence additional cross peaks are seen in the spectrum in high resolution mode (cf. Supplementary Information, S3). Figure 6a and Figure 6b show SECSY and HR-DISSECT spectra of strychnine, together with a few F1 traces respectively. The F1 traces show excellent diagonal suppression. In most cases the efficiency of diagonal suppression is more than 90% except at (F1, F2) = (0, 1.18 ppm). Cross peaks in the regions (F1, F2 = 0, 3.9 - 4.2 ppm) and (F1, F2 = 0, 6.9 - 7.3 ppm) appear as though they were ‘diagonal peaks’ because of insufficient F1 resolution. Figure 7a and 7b show the


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a

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b

Figure 6. 2D (a) SECSY and (b) HR-DISSECT spectra (in magnitude mode) of strychnine in CDCl3 together with F1 traces of a few cross-peaks indicated with arrows.

Figure 7 exhibits SECSY and HR-DISSECT spectra of 50 mM vinyl acetate in D2O. In particular, from Figure 7a it is evident that strong diagonal peaks mask the cross peaks of the geminal protons of vinyl acetate (which resonate at 4.57 ppm and 4.89 ppm). On the contrary, in the HR-DISSECT spectrum (Figure 7b) the cross peaks are well resolved due to excellent quality of diagonal suppression.

a

b

Figure 7. 2D SECSY(a) and HR-DISSECT(b) spectra of 50 mM vinyl acetate in D2O in magnitude mode.


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It may be noted further that the ability to generate pure phase 2D spectra is limited by the admixture of in-phase as well as quadrature anti-phase terms that contribute to the signal when applying either the DISSECT or the HR-DISSECT approach. On the other hand, it is easily seen that for a two-spin system, co-addition of two scans of DISSECT, and two scans of HRDISSECT (one each with and without the final 180° pulse) cancels the quadrature anti-phase contribution, thus leading to pure phase 2D spectra. This is possible because either with or without a 180° pulse, the last term of Eq. 3 remains unchanged in phase, whereas it changes sign with a 90° pulse. This basic four step cycle may be further elaborated into an eight step cycle by including phase alternation of the 180° pulse (four DISSECT scans, plus two HR-DISSECT scans each with and without the 180° pulse, in the former case with phase alternation).

CONCLUSIONS We have demonstrated in the foregoing that one may take advantage of the difference between diagonal and cross peaks that originates in echo characteristics, to design a pair of diagonal suppression experiments that appear to have general validity in a number of homonuclear 2D protocols:

in

particular,

correlation

spectroscopy

and

exchange

spectroscopy.

The

modification(s) to the standard echo experiment are straightforward and comprise the addition of a single pulse of suitable flip angle. While one of these experiments (DISSECT) efficiently suppresses diagonal peaks in each scan of a two scan procedure under conditions of chemical exchange or of limited spectral resolution in the direct dimension, the other experiment (HRDISSECT) is a two-scan procedure that is valid under high resolution 2D conditions. Diagonal suppression in the TOCSY17 environment are currently being explored in our Laboratory.


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Acknowledgments: The authors acknowledge with pleasure a spectrometer grant by the Department of Science and Technology, India (DST). NC gratefully acknowledges the award of a J.C. Bose National Fellowship by DST.

Supporting Information Available: Exchange data with different mixing times; product operator calculation of DISSECT for 3-spin system. This material is available free of charge via the Internet at http://pubs.acs.org.


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(5) Nagayama, K.; Wüthrich, K.; Ernst, R. R. Two-Dimensional Spin Echo Correlated Spectroscopy (SECSY) for 1H NMR Studies of Biological Macromolecules. Biochem. Biophys. Res. Comm. 1979, 90, 305–311.

(6) Glanzer, S.; Schrank, E.; Zangger, K. A General Method for Diagonal Peak Suppression in Homonuclear Correlated NMR Spectra by Spatially and Frequency Selective Pulses. J. Magn. Reson. 2013, 232, 1–6.

(7) Hahn, E. L. Spin Echoes. Phys. Rev. 1950, 80, 580-594. (8) Jeener, J.; Meier, B.H.; Bachmann, P.; Ernst, R.R. Investigation of Exchange Processes by Two-Dimensional NMR Spectroscopy. J. Chem. Phys.1979, 71, 4546-4553. (9) Harbison, G. S.; Feigon, J.; Ruben, D. J.; Herzfeld, J and Griffin, R. G. Diagonal Peak Suppression in 2D-NOE Spectra, J. Am. Chem. Soc. 1985, 107, 5567–5569. (10) Banerjee, A.; Chandrakumar, N. Volume Localized Spin Echo Correlation Spectroscopy with Suppression of 'Diagonal' Peaks. J. Magn. Reson. 2014, 239, 69-74. (11) Banerjee, A.; Chandrakumar, N. Communication: Ultrafast Homonuclear Correlation Spectroscopy with Diagonal Suppression. J. Chem. Phys. 2014, 140, 231103-4.


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(12) George, C.; Chandrakumar, N. Chemical Shift Resolved 19F NMR between 13.5-135 MHz: ODNP Enhanced Diagonal Suppressed Correlation Spectroscopy. Angew. Chem. Intl. Edn. 2014, 53, 8441-8444.

(13) Frydman, L.; Scherf, T.; Lupulescu, A. The Acquisition of Multidimensional NMR Spectra within a Single Scan. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 15858-15862. (14) Shapira, B.; Frydman, L. Arrayed Acquisition of 2D Exchange NMR Spectra within a Single Scan Experiment. J. Magn. Reson. 2003, 165, 320-324. (15) Mansfield, P. Multi-Planar Image Formation using NMR Spin Echoes. J. Phys. C: Solid State Phys. 1977, 10, L55-L58.

(16) Ramey, K. C.; Louick, D. J.; Whitehurst, P. W.; Wise, W. B.; Mukherjee, R.; Moriarty, R. M. A Line Width Method for Determining Chemical Exchange Rates from NMR Spectra. Org. Magn. Reson. 1971, 3, 201-216. (17) Braunschweiler, L.; Ernst, R. R. Coherence Transfer by Isotropic Mixing: Application to Protein Correlation Spectroscopy. J. Magn. Reson. 1983, 53, 521-528.


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Two-Dimensional Nuclear Magnetic Resonance: Exploiting Spin

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