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Frequency-selective measurement of heteronuclear scalar couplings in solid-state NMR
Solid State Sciences 6 (2004) 1089–1095 www.elsevier.com/locate/ssscie
Frequency-selective measurement of heteronuclear scalar couplings in solid-state NMR J. Trébosc a , J.P. Amoureux a,∗ , L. Delevoye a , J.W. Wiench b , M. Pruski b a LCPS, universite de Lille-1, Villeneuve d’Ascq, 59652, France b Ames Laboratory, Iowa State University, Ames, IA 50011, USA
Received 30 March 2004; accepted 4 April 2004 Available online 25 September 2004
Abstract A new technique is proposed for selective measurement of heteronuclear scalar J couplings between spins in solids. The method, referred to as FS-J -RES (Frequency-Selective-J -RESolved) NMR, uses frequency-selective irradiation at the I (nonobserved) spin frequency to target a specific pair of spins in a multispin system. In addition, the technique provides direct information about the number of identical I spins chemically bonded to the observed S nucleus. A reference spectrum, recorded without irradiating the I spins, accounts for transverse relaxation, pulse imperfections and dephasing due to homonuclear J couplings between S nuclei, which can be simultaneously measured with this method. 2004 Elsevier SAS. All rights reserved.
1. Introduction Scalar (J ) couplings, which reflect the characteristics of chemical bonds, are commonly used in liquid state NMR for spectral assignment and for establishing through bond correlations between atoms. In solids, J couplings are more difficult to measure and utilize because of the dominant size of other interactions involved. In relatively mobile solid materials, such as adamantane, 13 C–1 H J couplings were directly observed by combining magic-angle spinning (MAS) with homonuclear 1 H–1 H decoupling via Lee–Goldburg [1] or multipulse techniques [2]. Subsequent studies used the J couplings for editing of solid state 13 C NMR spectra based on multiplicities without inspecting the specific multiplet structures [3–6]. Lack of orientational dependence and insensitivity to molecular motion provided strong incentives for the development of homo- or heteronuclear J spectroscopy, based on the mixing techniques known for solutions and new schemes invented for solids [7–15]. These * Corresponding author.
E-mail address: [email protected] (J.P. Amoureux). 1293-2558/$ – see front matter 2004 Elsevier SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2004.04.019
techniques represent an attractive supplement to the group of methods based on cross polarization via dipolar (through space) couplings. Again, no spectrally resolved J couplings are required to perform such experiments, as long as the inhomogeneous broadenings can be refocused and the intrinsic (homogeneous) line width allows for the desired transfer of coherences to take place. The J spectroscopy proved useful in uncovering the geometries of multispin systems and for accurate determination of chemical shifts in solids. Examples of homonuclear studies include INADEQUATE [7,8], COSY [8] and TOBSY [9] experiments. The through bond polarization transfer between heteronuclei was mostly carried out by using the INEPT schemes, both in one-dimensional [10,11] and two-dimensional (HETCOR) [12,13] experiments. The heteronuclear scalar couplings were also utilized in 2D J -resolved NMR [14], the HMQC experiment [15]. Recently, accurate measurements of 15 N–15 N J coupling have also been introduced to solid state NMR, which use rotor-synchronized spin echo experiments to separate the scalar couplings, typically on the order of 1–102 Hz, from the chemical shift anisotropy (CSA, 102 –105 Hz) and/or dipolar (102–104 Hz) interactions [16]. The transverse re-
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laxation times, which are typically short in solids compared to 1/J , are introduced as fitted parameters. In the present work, we describe a rotor synchronized REDOR-like [17] approach to measure heteronuclear J couplings in solid samples. This J -resolved (J -RES) experiment offers several additional advantages: (i) removes the effects of transverse relaxation, pulse imperfections and homonuclear J couplings between the observed nuclei, (ii) provides direct information about the number of identical I spins chemically bonded to the S nucleus, and (iii) can be combined with frequency selective (FS) RF irradiation of I or S spins in order to target a specific coupling in a multi-spin system [18]. We will first describe the FS-J -RES method within the framework of ideal RF pulses. The effect of pulse imperfections will be analyzed numerically and analytically, especially with regard to selectivity. The FS-J -RES method has been tested by measuring the JSI values between 13 C and 15 N in histidine and glycine.
2. Theoretical The basic MAS pulse echo sequence for this experiment, shown in Fig. 1, uses two rotor synchronized pulses at the frequency of the observed S spins and a single π pulse at the I spin frequency, which can be nonselective (Fig. 1a and 1b) or selective (Fig. 1c). We first analyze the echo signal corresponding to the specific resonance Sp under ideal (infinitely short) RF pulses applied to I and S spins. We further assume that all homonuclear dipolar interactions are negligible under MAS. This assumption may not hold in strongly coupled systems involving 1 H or 19 F nuclei, but proved to be valid for 15 N and 13 C, as will be shown in Section 3. The dephasings related to shielding and heteronuclear dipolar interactions are refocused at the end of the sequence, leaving only the S–S and I–S J couplings. Since the homo- and het-
Fig. 1. Pulse sequence (a,b) and echo coherence pathway for S spins (d) used in the J -RES experiment. The echo is measured using (a) and (b), while the reference experiment uses only (a). The frequency selective version (c) uses a long π pulse at the frequency of Ik and/or Sp spin(s) to selectively invert the targeted magnetizations.
eronuclear scalar couplings commute, the in-phase part of the echo signal can be written n 2mTR e Shomo cos(2πmTR JSp −Ik ), Sp (2mTR ) = exp − T2e k=1 (1) where m is an integer number, TR is the rotor period and n is the number of I spins coupled to Sp . The echo intensity , due to nonrefocusable loss decays with relaxation time T2e of transverse magnetization under the applied experimental conditions. The effect of homonuclear isotropic scalar coupling between S spins is given by cos(2πmTR JSp −Sq ). Shomo (2mTR ) = (2) q
A reference signal Spr (2mTR ) is also acquired without sending the dephasing π pulse to the I channel. This echo signal 2mTR Shomo (2mTR ), Spr (2mTR ) = exp − (3) T2r is also governed by the S–S scalar interactions and has been recently used to measure homonuclear J couplings in solids by Brown et al. [16]. In analogy to REDOR [17], we define the normalized difference between the two signals, referred to as the J -RES fraction, Rp (2mTR ) = 1 −
Spe (2mTR ) Spr (2mTR )
n T −T = 1 − exp 2mTR 2e 2r cos(2πmTR JSp −Ik ), (4) T2e T2r k=1
which is modulated by JSp −Ik . Since the nonsecular terms associated with JSp −Ik should have negligible effect on re ∼ T . Additional changes in laxation, we expect that T2r = 2e the transverse relaxation rates may occur in the presence of 1 H decoupling, whose efficiency may be affected by the π pulse at the I spin frequency. Clearly, the range of J couplings accessible to this method is controlled by transverse relaxation effects, which reduce the sensitivity at longer dephasing times. We note that J couplings are usually measured in liquids using the pulse sequence of Fig. 1 without using the reference spectrum [19]. The resulting 2D data set can be Fourier transformed versus the dephasing time to yield information about the homo- and heteronuclear scalar couplings. This method is difficult to apply in solids where homo- and heteronuclear effects are difficult to separate and T2 relaxation times are short compared to 1/J . However, our approach is similar to the spin echo difference experiment used in liquids for the measurement of small heteronuclear J coupling constants that cannot be directly resolved [20–22]. In case of n = 1, the coupling constant can be easily determined by fitting the J -RES curve with a single parameter JSp −I . However, the deconvolution of individual JSp −Ik components must be carried out for n > 1. Although for isotropic J couplings such a deconvolution may not be as complex as in case of dipolar couplings (which are a vector
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Fig. 2. J -RES fraction for Ij S spin system (j = 1, 2, 3), simulated assum = T . Dephasing time is given in the reduced ing ideal excitation and T2e 2r units of 1/JSI .
Fig. 3. J -RES fractions calculated for JSI = 100 Hz, CSAI = 15 kHz, νR = 10 kHz, νSrf = 62.5 kHz (hard pulses), and the I spin π pulse being rectangular with a duration of 1 µs (circles) and 4 ms (squares). Continuous curves were fitted using Eq. (6) with A = 1, t = 0 ms (a) and A = 0.90, t = 1.5 ms (b).
sum of the relevant anisotropic dipolar interactions), a direct measurement of JSp −Ik couplings for the selected Ik spin would constitute a preferable approach. An elegant solution to a similar problem has recently been presented in the form of the frequency-selective (FS) REDOR experiment [18], which generates a REDOR curve dependent solely on the dipolar dephasing between two isolated spins I and S. The same scheme can be used for J -experiments (FS-J -RES), simply by applying a soft, on-resonance π pulse to the selected Ik spin, as shown in Fig. 1c. This pulse reverses the Ik magnetization, without ‘touching’ the Ir=k components, which implies the existence of sufficient resolution. As demonstrated in Fig. 2, the analysis of FS-J -RES curve can provide the number j of I spins that resonate in the selected frequency range and are bonded to Sp with the same scalar couplings. Indeed, for j = 1 the curve reaches its first maximum of 2 at time 2mTR = 1/JS−I , for j = 2 a maximum value of 1 is observed at 2mTR = 1/2JS−I , whereas for j = 3 the curve exhibits a null derivative with an inflection point at 2mTR = 1/2JS−I and maximum of 2 at 2mTR = 1/JS−I . When the transverse relaxation times T2r and T2e are not equal, the maxima of the FS-J -RES curves are observed at approximately the same dephasing times. However, the corresponding maximum values of Rp can be lowered for j = 1 or 3. Assuming JSp −Ik = JSp −I (k = 1, 2, 3), we obtain T2e − T2r . Rpmax = 1 + exp (5) T J T2e 2r Sp −I
experiments performed under fast MAS, the RF irradiation is applied during a substantial fraction of the rotor period. Thus, we have performed a series of numerical simulations of the J -RES curves under realistic experimental conditions. The simulations were performed using SIMPSON [23], for an isolated pair of spin-½ nuclei I and S in the presence of chemical shift anisotropy CSAI = (σzz − σiso )ν0I (with ηI = 0) and scalar coupling JSI . We found that the heteronuclear dipolar and CSAS interactions had a negligible effect on S magnetization under rotor synchronization. The nonselective π/2 and π pulses at the S spin frequency used an RF magnetic field νSrf = 62.5 kHz and the sample rotation rate νR was 10 kHz. For frequency selective pulses, we used a Gaussian pulse truncated at 10% of its maximum amplitude. The transverse relaxation was not included in the simulations. In Fig. 3 we demonstrate the effect of selective and nonselective pulses on the J -RES curves in the presence of large CSAI for JS−I = 100 Hz. Curve (a), which follows Eq. (4) , reaches a maximum value of 2 at for n = 1 and T2r = T2e 2mTR = 10 ms, as discussed earlier. The results of numerical simulations, which are also shown in the figure (circles), agree exactly with Eq. (4). When the selective pulse is used (squares), the J -RES curve exhibits a lower maximum, which is also delayed. This curve can be well described by the modified equation Rp (2mTR ) = A 1 − cos π(2mTR − t)JS−I , (6)
For given relaxation times, the difference with respect to the theoretical value of 2 increases with decreasing JS−I scalar couplings. For j = 2 or 4, the amplitude of the first maximum remains close to 1 because the exponential term vanishes. In practice, the pulses used in frequency-selective experiments can last tens of rotor periods. Even in the nonselective
where A denotes the scaling factor and t is the delay. The signal attenuation, which has been earlier observed in similar experiments [18,24], is due to incomplete reversal of I spin magnetization in the presence of offsets due to CSAI , whereas the delay results from slower nutation of I spins during the selective pulse. The scaling factor reaches a minimum when the selective pulse length Tsel approaches TR ,
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before leveling off at a value that depends on the CSAI /νR ratio (see Fig. 4a). For long selective pulses, the effect of CSAI on A can be considerable, as demonstrated in Fig. 4b. Our simulations also showed that the delay t is proportional to Tsel , is somewhat dependent of the pulse shape and the CSAI /νR ratio, and is nearly independent on the magnitude of the JS−I coupling constant. The details of these calculations are not shown here, because the exact origin of A and t is of limited practical significance. The most important results of the simulations can be summarized as follows:
3. Experimental The experiments were performed at 9.4 T on a BrukerAvance spectrometer equipped with a triple resonance 4 mm MAS probe. To test the FS-J -RES method we examined histidine and glycine, fully enriched in 13 C and 15 N, whose structures and well-known MAS spectra are shown in Figs. 5 and 6. A glycine sample labeled at C-1 and N sites was also studied. In all experiments reported here we have used 1 H TPPM decoupling at 50 kHz during evolution and observation periods in order to minimize the transverse re-
(i) the FS-J -RES curves should be measured under fast MAS to minimize the CSAI /νR ratio (see Fig. 4b) and (ii) the JSI couplings can be obtained from Eq. (6) using A and t as fitted parameters (even if simple rectangular pulses are used for selective irradiation).
Fig. 5. 13 C (a) and 15 N (b) MAS spectra of fully enriched histidine under 1 H TPPM decoupling at 50 kHz and MAS at 13 kHz.
Fig. 4. (a) Scaling factor A corresponding to the CSAI values of 5, 10, 20 and 40 kHz as a function of the selective pulse length Tsel . (b) Scaling factor A versus CSAI /νR ratio at Tsel 2TR . All calculations used νR = 10 kHz and νSrf = 62.5 kHz.
Fig. 6. 13 C (a) and 15 N (b) MAS spectra of fully enriched glycine under 1 H TPPM decoupling at 50 kHz and MAS at 10 kHz. Two conformations are present [31], which yield two resonances for C-2 and an extra shoulder for C-1. A doublet due to J C1–C2 can be clearly observed.
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Fig. 7. J -RES fractions for C-6 carbon in histidine: (N,C-6)—triangles, (N-1,C-6)—diamonds, (N-2,C-6)—circles and (N-3,C-6)—squares. The parameters of the selective pulse were described in the text. Other experimental conditions were as follows: νR = 13 kHz, νCrf = 40 kHz and νNrf = 2 kHz for nonselective pulses.
laxation effects on the observed nucleus. As predicted earlier, efficient 1 H decoupling proved essential in these experiments. For example, the standard continuous wave decoupling yielded much shorter T2 values, by a factor of at least two at comparable RF fields, which made the FS-J RES measurements impractical in these samples. The decoupling efficiency was particularly important in measurements of small J coupling values, where the RF power was applied for several hundreds of ms. The selective excitation in the I channel was accomplished by using an on-resonance Gaussian π pulse of 5 ms duration, truncated at 10% of its maximum intensity. We have verified that the resulting selectivity sufficed to excite individually the targeted carbon or nitrogen resonances in both samples. To simplify the discussion, we denote the J -RES and FSJ -RES curves as (I, Sp ) and (Ik , Sp ), respectively, where Sp represents the observed spin. The results of (N-1,C-6), (N-2,C-6), (N-3,C-6), and (N,C-6) experiments on histidine are shown in Fig. 7. The (N-1,C-6), (N-2,C-6) curves have a similar maximum value of approximately 1.9, as is expected and for isolated spin pairs with similar relaxation times T2e T2r . The curves were fitted using Eq. (4), which yielded the J coupling constants JC6–N1 = 13.5 ± 0.5 Hz and JC6–N2 = 14.8 ± 0.5 Hz. The similarity between J C6–N1 and J C6–N2 is consistent with both double bonds being delocalized in the imidazolium ring. As expected, the (N,C-6) curve in Fig. 7 has a maximum of 1.0, as C-6 interacts with both N-1 and N-2 in the nonselective case. By using the nonselective experiment, we obtained J C6–N values of 14.5 ± 1 and 15.5 ± 1 Hz, which agree within the experimental error with the results of FS-J -RES measurements. The (N-3,C-6) curve demonstrates that J C-6,N-3 coupling is negligible (< 0.1 Hz), as expected. It also shows that Spe (2mTR ) and Spr (2mTR ) experience the same transverse relaxation processes. In particular, the dephasing due to dipolar coupling, which in this
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Fig. 8. FS-J -RES fractions for C-6 carbon in histidine measured by observing 13 C and 15 N nuclei: (N-2,C-6)—circles, (C-6,N-1)—squares and (C-6,N-2)—triangles.
case is approximately 50 Hz, has no effect on the FS-J -RES fraction. The following values were obtained for other single bond couplings in this sample: JC2–N3 = 5.5 ± 1 Hz, JC4–N1 = 10.0 ± 0.5 Hz and JC5–N2 = 11.5 ± 0.5 Hz. Furthermore, we used the inverted experiment, in which the 15 N nuclei were detected, to measure the FS-J -RES curves (C,N). In Fig. 8 we show that the results of (C-6,N-1) and (C-6,N-2) experiments are indeed consistent with the previously shown (N-2,C-6) curve. This result also shows that the dephasing due to homonuclear scalar coupling is negated by using the reference spectrum. The above JCN values are in good agreement with the solution NMR data [25,26]. Although the J -RES fraction cancels the effect of homonuclear scalar coupling, this interaction can affect the observed spectra. First, it generates an antiphase signal with null integrated intensity, which can distort the spectral lines, as shown in Fig. 9. This antiphase signal can be eliminated by using a z-filter, as demonstrated by Griffin et al. [27]. Second, it modulates both Spe and Spr , see Eqs. (1)–(4), causing zero crossings in their evolution time [27]. In case of Jhomo JS−I , this strongly reduces the S/N ratio in the spectra and may produce diverging points in the J -RES curves, which have to be removed before fitting. Even in such case, however, it has been our experience that fitting the J -RES curve yields more accurate data than extracting from Eq. (3) and using them as fitting parameShomo and T2r ters in Eq. (1). All these nuisances can be evaded, however, by using a selective pulse on the observed channel. We also note that the heteronuclear JSI couplings can create spectral distortions and S/N losses due to antiphase signal, as well. This can be seen in the Spe spectra of carbon C-6 in histidine (Fig. 10), which improved dramatically under 15 N decoupling. In order to obtain homonuclear carbon–carbon scalar couplings, we fitted the evolution of the reference signal using Eq. (3). The results, which are shown in Table 1, agree
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ponding FS-J -RES fractions (N,C-1) and (C-1,N) in fully and selectively enriched samples using dephasing times of up to 200 ms. All four experiments yielded the same value of JC1–N = 5.5 ± 1 Hz, which further indicated that the FS-J -RES method eliminated the effect of much stronger homonuclear scalar couplings. In addition, a J C1–C2 value of 51 ± 2 Hz was measured in the fully enriched sample. Again, these results are in agreement with the existing literature data [29,30].
4. Conclusion
Fig. 9. 13 C spectra of fully enriched histidine: (a) aromatic region of the MAS spectrum of Fig. 5a, (b) the corresponding FS-J -RES spectrum observed for 2mTR = 6 ms.
In summary, we have demonstrated that heteronuclear scalar couplings in solids can be accurately measured under MAS using a simple rotor-synchronized experiment. The method uses a REDOR-like approach, which effectively eliminates the dephasing due to transverse relaxation and homonuclear J coupling between the observed nuclei. The experiment is sensitive to multiplicity in Ij S spin systems, which can be easily determined. It can also be used in a frequency selective manner, both at I and S spin frequencies. Although the range of J coupling constants that can be accurately measured with this method is restricted by the transverse relaxation processes, couplings as small as 5.5 Hz were measured in model compounds of histidine and glycine. More efficient heteronuclear decoupling schemes may offer further improvement in sensitivity for such measurements. Efforts are currently under way to demonstrate that a similar approach can be applied to the quadrupolar nuclei.
Acknowledgements Fig. 10. 13 C spectra of C-6 carbon in histidine recorded using the sequence of Fig. 1a and 1c, under 13 kHz MAS, for Tsel = 250 µs and 2mTR = 25 ms without (a) and with (b) continuous wave 15 N decoupling at 2 kHz. The spectral distortions disappeared in spectrum (b). Table 1 Homonuclear JCC scalar couplings in histidine. For carbon C6 the values were too small to be accurately measured C C1 C2 C3 C4 C5 C6
JCC (Hz) 56 (C2) 34 (C3), 57 (C1) 34 (C2), 51 (C4) 73 (C5) 50 (C3) 73 (C4) –
(ms) T2r
35 19 11 17 17 23
well with the J couplings reported in Ref. [28]. Note that the homonuclear scalar couplings J C5–C4, J C4–C3 and J C4–C5 can be measured directly in the MAS spectra of Figs. 5 and 9. In case of glycine, only carbon C-1 has a nonnegligible scalar coupling with nitrogen. We have recorded the corres-
This research was supported at Ames Laboratory by the U.S. DOE, Office of Basic Energy Sciences, Division of Chemical Sciences, under Contract W-7405-Eng-82, JT, JPA and LD thank the Region Nord/Pas de Calais and FEDER for their financial support.
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Frequency-selective measurement of heteronuclear scalar couplings in solid-state NMR J. Trébosc a , J.P. Amoureux a,∗ , L. Delevoye a , J.W. Wiench b , M. Pruski b a LCPS, universite de Lille-1, Villeneuve d’Ascq, 59652, France b Ames Laboratory, Iowa State University, Ames, IA 50011, USA
Received 30 March 2004; accepted 4 April 2004 Available online 25 September 2004
Abstract A new technique is proposed for selective measurement of heteronuclear scalar J couplings between spins in solids. The method, referred to as FS-J -RES (Frequency-Selective-J -RESolved) NMR, uses frequency-selective irradiation at the I (nonobserved) spin frequency to target a specific pair of spins in a multispin system. In addition, the technique provides direct information about the number of identical I spins chemically bonded to the observed S nucleus. A reference spectrum, recorded without irradiating the I spins, accounts for transverse relaxation, pulse imperfections and dephasing due to homonuclear J couplings between S nuclei, which can be simultaneously measured with this method. 2004 Elsevier SAS. All rights reserved.
1. Introduction Scalar (J ) couplings, which reflect the characteristics of chemical bonds, are commonly used in liquid state NMR for spectral assignment and for establishing through bond correlations between atoms. In solids, J couplings are more difficult to measure and utilize because of the dominant size of other interactions involved. In relatively mobile solid materials, such as adamantane, 13 C–1 H J couplings were directly observed by combining magic-angle spinning (MAS) with homonuclear 1 H–1 H decoupling via Lee–Goldburg [1] or multipulse techniques [2]. Subsequent studies used the J couplings for editing of solid state 13 C NMR spectra based on multiplicities without inspecting the specific multiplet structures [3–6]. Lack of orientational dependence and insensitivity to molecular motion provided strong incentives for the development of homo- or heteronuclear J spectroscopy, based on the mixing techniques known for solutions and new schemes invented for solids [7–15]. These * Corresponding author.
E-mail address: [email protected] (J.P. Amoureux). 1293-2558/$ – see front matter 2004 Elsevier SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2004.04.019
techniques represent an attractive supplement to the group of methods based on cross polarization via dipolar (through space) couplings. Again, no spectrally resolved J couplings are required to perform such experiments, as long as the inhomogeneous broadenings can be refocused and the intrinsic (homogeneous) line width allows for the desired transfer of coherences to take place. The J spectroscopy proved useful in uncovering the geometries of multispin systems and for accurate determination of chemical shifts in solids. Examples of homonuclear studies include INADEQUATE [7,8], COSY [8] and TOBSY [9] experiments. The through bond polarization transfer between heteronuclei was mostly carried out by using the INEPT schemes, both in one-dimensional [10,11] and two-dimensional (HETCOR) [12,13] experiments. The heteronuclear scalar couplings were also utilized in 2D J -resolved NMR [14], the HMQC experiment [15]. Recently, accurate measurements of 15 N–15 N J coupling have also been introduced to solid state NMR, which use rotor-synchronized spin echo experiments to separate the scalar couplings, typically on the order of 1–102 Hz, from the chemical shift anisotropy (CSA, 102 –105 Hz) and/or dipolar (102–104 Hz) interactions [16]. The transverse re-
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laxation times, which are typically short in solids compared to 1/J , are introduced as fitted parameters. In the present work, we describe a rotor synchronized REDOR-like [17] approach to measure heteronuclear J couplings in solid samples. This J -resolved (J -RES) experiment offers several additional advantages: (i) removes the effects of transverse relaxation, pulse imperfections and homonuclear J couplings between the observed nuclei, (ii) provides direct information about the number of identical I spins chemically bonded to the S nucleus, and (iii) can be combined with frequency selective (FS) RF irradiation of I or S spins in order to target a specific coupling in a multi-spin system [18]. We will first describe the FS-J -RES method within the framework of ideal RF pulses. The effect of pulse imperfections will be analyzed numerically and analytically, especially with regard to selectivity. The FS-J -RES method has been tested by measuring the JSI values between 13 C and 15 N in histidine and glycine.
2. Theoretical The basic MAS pulse echo sequence for this experiment, shown in Fig. 1, uses two rotor synchronized pulses at the frequency of the observed S spins and a single π pulse at the I spin frequency, which can be nonselective (Fig. 1a and 1b) or selective (Fig. 1c). We first analyze the echo signal corresponding to the specific resonance Sp under ideal (infinitely short) RF pulses applied to I and S spins. We further assume that all homonuclear dipolar interactions are negligible under MAS. This assumption may not hold in strongly coupled systems involving 1 H or 19 F nuclei, but proved to be valid for 15 N and 13 C, as will be shown in Section 3. The dephasings related to shielding and heteronuclear dipolar interactions are refocused at the end of the sequence, leaving only the S–S and I–S J couplings. Since the homo- and het-
Fig. 1. Pulse sequence (a,b) and echo coherence pathway for S spins (d) used in the J -RES experiment. The echo is measured using (a) and (b), while the reference experiment uses only (a). The frequency selective version (c) uses a long π pulse at the frequency of Ik and/or Sp spin(s) to selectively invert the targeted magnetizations.
eronuclear scalar couplings commute, the in-phase part of the echo signal can be written n 2mTR e Shomo cos(2πmTR JSp −Ik ), Sp (2mTR ) = exp − T2e k=1 (1) where m is an integer number, TR is the rotor period and n is the number of I spins coupled to Sp . The echo intensity , due to nonrefocusable loss decays with relaxation time T2e of transverse magnetization under the applied experimental conditions. The effect of homonuclear isotropic scalar coupling between S spins is given by cos(2πmTR JSp −Sq ). Shomo (2mTR ) = (2) q
A reference signal Spr (2mTR ) is also acquired without sending the dephasing π pulse to the I channel. This echo signal 2mTR Shomo (2mTR ), Spr (2mTR ) = exp − (3) T2r is also governed by the S–S scalar interactions and has been recently used to measure homonuclear J couplings in solids by Brown et al. [16]. In analogy to REDOR [17], we define the normalized difference between the two signals, referred to as the J -RES fraction, Rp (2mTR ) = 1 −
Spe (2mTR ) Spr (2mTR )
n T −T = 1 − exp 2mTR 2e 2r cos(2πmTR JSp −Ik ), (4) T2e T2r k=1
which is modulated by JSp −Ik . Since the nonsecular terms associated with JSp −Ik should have negligible effect on re ∼ T . Additional changes in laxation, we expect that T2r = 2e the transverse relaxation rates may occur in the presence of 1 H decoupling, whose efficiency may be affected by the π pulse at the I spin frequency. Clearly, the range of J couplings accessible to this method is controlled by transverse relaxation effects, which reduce the sensitivity at longer dephasing times. We note that J couplings are usually measured in liquids using the pulse sequence of Fig. 1 without using the reference spectrum [19]. The resulting 2D data set can be Fourier transformed versus the dephasing time to yield information about the homo- and heteronuclear scalar couplings. This method is difficult to apply in solids where homo- and heteronuclear effects are difficult to separate and T2 relaxation times are short compared to 1/J . However, our approach is similar to the spin echo difference experiment used in liquids for the measurement of small heteronuclear J coupling constants that cannot be directly resolved [20–22]. In case of n = 1, the coupling constant can be easily determined by fitting the J -RES curve with a single parameter JSp −I . However, the deconvolution of individual JSp −Ik components must be carried out for n > 1. Although for isotropic J couplings such a deconvolution may not be as complex as in case of dipolar couplings (which are a vector
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Fig. 2. J -RES fraction for Ij S spin system (j = 1, 2, 3), simulated assum = T . Dephasing time is given in the reduced ing ideal excitation and T2e 2r units of 1/JSI .
Fig. 3. J -RES fractions calculated for JSI = 100 Hz, CSAI = 15 kHz, νR = 10 kHz, νSrf = 62.5 kHz (hard pulses), and the I spin π pulse being rectangular with a duration of 1 µs (circles) and 4 ms (squares). Continuous curves were fitted using Eq. (6) with A = 1, t = 0 ms (a) and A = 0.90, t = 1.5 ms (b).
sum of the relevant anisotropic dipolar interactions), a direct measurement of JSp −Ik couplings for the selected Ik spin would constitute a preferable approach. An elegant solution to a similar problem has recently been presented in the form of the frequency-selective (FS) REDOR experiment [18], which generates a REDOR curve dependent solely on the dipolar dephasing between two isolated spins I and S. The same scheme can be used for J -experiments (FS-J -RES), simply by applying a soft, on-resonance π pulse to the selected Ik spin, as shown in Fig. 1c. This pulse reverses the Ik magnetization, without ‘touching’ the Ir=k components, which implies the existence of sufficient resolution. As demonstrated in Fig. 2, the analysis of FS-J -RES curve can provide the number j of I spins that resonate in the selected frequency range and are bonded to Sp with the same scalar couplings. Indeed, for j = 1 the curve reaches its first maximum of 2 at time 2mTR = 1/JS−I , for j = 2 a maximum value of 1 is observed at 2mTR = 1/2JS−I , whereas for j = 3 the curve exhibits a null derivative with an inflection point at 2mTR = 1/2JS−I and maximum of 2 at 2mTR = 1/JS−I . When the transverse relaxation times T2r and T2e are not equal, the maxima of the FS-J -RES curves are observed at approximately the same dephasing times. However, the corresponding maximum values of Rp can be lowered for j = 1 or 3. Assuming JSp −Ik = JSp −I (k = 1, 2, 3), we obtain T2e − T2r . Rpmax = 1 + exp (5) T J T2e 2r Sp −I
experiments performed under fast MAS, the RF irradiation is applied during a substantial fraction of the rotor period. Thus, we have performed a series of numerical simulations of the J -RES curves under realistic experimental conditions. The simulations were performed using SIMPSON [23], for an isolated pair of spin-½ nuclei I and S in the presence of chemical shift anisotropy CSAI = (σzz − σiso )ν0I (with ηI = 0) and scalar coupling JSI . We found that the heteronuclear dipolar and CSAS interactions had a negligible effect on S magnetization under rotor synchronization. The nonselective π/2 and π pulses at the S spin frequency used an RF magnetic field νSrf = 62.5 kHz and the sample rotation rate νR was 10 kHz. For frequency selective pulses, we used a Gaussian pulse truncated at 10% of its maximum amplitude. The transverse relaxation was not included in the simulations. In Fig. 3 we demonstrate the effect of selective and nonselective pulses on the J -RES curves in the presence of large CSAI for JS−I = 100 Hz. Curve (a), which follows Eq. (4) , reaches a maximum value of 2 at for n = 1 and T2r = T2e 2mTR = 10 ms, as discussed earlier. The results of numerical simulations, which are also shown in the figure (circles), agree exactly with Eq. (4). When the selective pulse is used (squares), the J -RES curve exhibits a lower maximum, which is also delayed. This curve can be well described by the modified equation Rp (2mTR ) = A 1 − cos π(2mTR − t)JS−I , (6)
For given relaxation times, the difference with respect to the theoretical value of 2 increases with decreasing JS−I scalar couplings. For j = 2 or 4, the amplitude of the first maximum remains close to 1 because the exponential term vanishes. In practice, the pulses used in frequency-selective experiments can last tens of rotor periods. Even in the nonselective
where A denotes the scaling factor and t is the delay. The signal attenuation, which has been earlier observed in similar experiments [18,24], is due to incomplete reversal of I spin magnetization in the presence of offsets due to CSAI , whereas the delay results from slower nutation of I spins during the selective pulse. The scaling factor reaches a minimum when the selective pulse length Tsel approaches TR ,
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before leveling off at a value that depends on the CSAI /νR ratio (see Fig. 4a). For long selective pulses, the effect of CSAI on A can be considerable, as demonstrated in Fig. 4b. Our simulations also showed that the delay t is proportional to Tsel , is somewhat dependent of the pulse shape and the CSAI /νR ratio, and is nearly independent on the magnitude of the JS−I coupling constant. The details of these calculations are not shown here, because the exact origin of A and t is of limited practical significance. The most important results of the simulations can be summarized as follows:
3. Experimental The experiments were performed at 9.4 T on a BrukerAvance spectrometer equipped with a triple resonance 4 mm MAS probe. To test the FS-J -RES method we examined histidine and glycine, fully enriched in 13 C and 15 N, whose structures and well-known MAS spectra are shown in Figs. 5 and 6. A glycine sample labeled at C-1 and N sites was also studied. In all experiments reported here we have used 1 H TPPM decoupling at 50 kHz during evolution and observation periods in order to minimize the transverse re-
(i) the FS-J -RES curves should be measured under fast MAS to minimize the CSAI /νR ratio (see Fig. 4b) and (ii) the JSI couplings can be obtained from Eq. (6) using A and t as fitted parameters (even if simple rectangular pulses are used for selective irradiation).
Fig. 5. 13 C (a) and 15 N (b) MAS spectra of fully enriched histidine under 1 H TPPM decoupling at 50 kHz and MAS at 13 kHz.
Fig. 4. (a) Scaling factor A corresponding to the CSAI values of 5, 10, 20 and 40 kHz as a function of the selective pulse length Tsel . (b) Scaling factor A versus CSAI /νR ratio at Tsel 2TR . All calculations used νR = 10 kHz and νSrf = 62.5 kHz.
Fig. 6. 13 C (a) and 15 N (b) MAS spectra of fully enriched glycine under 1 H TPPM decoupling at 50 kHz and MAS at 10 kHz. Two conformations are present [31], which yield two resonances for C-2 and an extra shoulder for C-1. A doublet due to J C1–C2 can be clearly observed.
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Fig. 7. J -RES fractions for C-6 carbon in histidine: (N,C-6)—triangles, (N-1,C-6)—diamonds, (N-2,C-6)—circles and (N-3,C-6)—squares. The parameters of the selective pulse were described in the text. Other experimental conditions were as follows: νR = 13 kHz, νCrf = 40 kHz and νNrf = 2 kHz for nonselective pulses.
laxation effects on the observed nucleus. As predicted earlier, efficient 1 H decoupling proved essential in these experiments. For example, the standard continuous wave decoupling yielded much shorter T2 values, by a factor of at least two at comparable RF fields, which made the FS-J RES measurements impractical in these samples. The decoupling efficiency was particularly important in measurements of small J coupling values, where the RF power was applied for several hundreds of ms. The selective excitation in the I channel was accomplished by using an on-resonance Gaussian π pulse of 5 ms duration, truncated at 10% of its maximum intensity. We have verified that the resulting selectivity sufficed to excite individually the targeted carbon or nitrogen resonances in both samples. To simplify the discussion, we denote the J -RES and FSJ -RES curves as (I, Sp ) and (Ik , Sp ), respectively, where Sp represents the observed spin. The results of (N-1,C-6), (N-2,C-6), (N-3,C-6), and (N,C-6) experiments on histidine are shown in Fig. 7. The (N-1,C-6), (N-2,C-6) curves have a similar maximum value of approximately 1.9, as is expected and for isolated spin pairs with similar relaxation times T2e T2r . The curves were fitted using Eq. (4), which yielded the J coupling constants JC6–N1 = 13.5 ± 0.5 Hz and JC6–N2 = 14.8 ± 0.5 Hz. The similarity between J C6–N1 and J C6–N2 is consistent with both double bonds being delocalized in the imidazolium ring. As expected, the (N,C-6) curve in Fig. 7 has a maximum of 1.0, as C-6 interacts with both N-1 and N-2 in the nonselective case. By using the nonselective experiment, we obtained J C6–N values of 14.5 ± 1 and 15.5 ± 1 Hz, which agree within the experimental error with the results of FS-J -RES measurements. The (N-3,C-6) curve demonstrates that J C-6,N-3 coupling is negligible (< 0.1 Hz), as expected. It also shows that Spe (2mTR ) and Spr (2mTR ) experience the same transverse relaxation processes. In particular, the dephasing due to dipolar coupling, which in this
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Fig. 8. FS-J -RES fractions for C-6 carbon in histidine measured by observing 13 C and 15 N nuclei: (N-2,C-6)—circles, (C-6,N-1)—squares and (C-6,N-2)—triangles.
case is approximately 50 Hz, has no effect on the FS-J -RES fraction. The following values were obtained for other single bond couplings in this sample: JC2–N3 = 5.5 ± 1 Hz, JC4–N1 = 10.0 ± 0.5 Hz and JC5–N2 = 11.5 ± 0.5 Hz. Furthermore, we used the inverted experiment, in which the 15 N nuclei were detected, to measure the FS-J -RES curves (C,N). In Fig. 8 we show that the results of (C-6,N-1) and (C-6,N-2) experiments are indeed consistent with the previously shown (N-2,C-6) curve. This result also shows that the dephasing due to homonuclear scalar coupling is negated by using the reference spectrum. The above JCN values are in good agreement with the solution NMR data [25,26]. Although the J -RES fraction cancels the effect of homonuclear scalar coupling, this interaction can affect the observed spectra. First, it generates an antiphase signal with null integrated intensity, which can distort the spectral lines, as shown in Fig. 9. This antiphase signal can be eliminated by using a z-filter, as demonstrated by Griffin et al. [27]. Second, it modulates both Spe and Spr , see Eqs. (1)–(4), causing zero crossings in their evolution time [27]. In case of Jhomo JS−I , this strongly reduces the S/N ratio in the spectra and may produce diverging points in the J -RES curves, which have to be removed before fitting. Even in such case, however, it has been our experience that fitting the J -RES curve yields more accurate data than extracting from Eq. (3) and using them as fitting parameShomo and T2r ters in Eq. (1). All these nuisances can be evaded, however, by using a selective pulse on the observed channel. We also note that the heteronuclear JSI couplings can create spectral distortions and S/N losses due to antiphase signal, as well. This can be seen in the Spe spectra of carbon C-6 in histidine (Fig. 10), which improved dramatically under 15 N decoupling. In order to obtain homonuclear carbon–carbon scalar couplings, we fitted the evolution of the reference signal using Eq. (3). The results, which are shown in Table 1, agree
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ponding FS-J -RES fractions (N,C-1) and (C-1,N) in fully and selectively enriched samples using dephasing times of up to 200 ms. All four experiments yielded the same value of JC1–N = 5.5 ± 1 Hz, which further indicated that the FS-J -RES method eliminated the effect of much stronger homonuclear scalar couplings. In addition, a J C1–C2 value of 51 ± 2 Hz was measured in the fully enriched sample. Again, these results are in agreement with the existing literature data [29,30].
4. Conclusion
Fig. 9. 13 C spectra of fully enriched histidine: (a) aromatic region of the MAS spectrum of Fig. 5a, (b) the corresponding FS-J -RES spectrum observed for 2mTR = 6 ms.
In summary, we have demonstrated that heteronuclear scalar couplings in solids can be accurately measured under MAS using a simple rotor-synchronized experiment. The method uses a REDOR-like approach, which effectively eliminates the dephasing due to transverse relaxation and homonuclear J coupling between the observed nuclei. The experiment is sensitive to multiplicity in Ij S spin systems, which can be easily determined. It can also be used in a frequency selective manner, both at I and S spin frequencies. Although the range of J coupling constants that can be accurately measured with this method is restricted by the transverse relaxation processes, couplings as small as 5.5 Hz were measured in model compounds of histidine and glycine. More efficient heteronuclear decoupling schemes may offer further improvement in sensitivity for such measurements. Efforts are currently under way to demonstrate that a similar approach can be applied to the quadrupolar nuclei.
Acknowledgements Fig. 10. 13 C spectra of C-6 carbon in histidine recorded using the sequence of Fig. 1a and 1c, under 13 kHz MAS, for Tsel = 250 µs and 2mTR = 25 ms without (a) and with (b) continuous wave 15 N decoupling at 2 kHz. The spectral distortions disappeared in spectrum (b). Table 1 Homonuclear JCC scalar couplings in histidine. For carbon C6 the values were too small to be accurately measured C C1 C2 C3 C4 C5 C6
JCC (Hz) 56 (C2) 34 (C3), 57 (C1) 34 (C2), 51 (C4) 73 (C5) 50 (C3) 73 (C4) –
(ms) T2r
35 19 11 17 17 23
well with the J couplings reported in Ref. [28]. Note that the homonuclear scalar couplings J C5–C4, J C4–C3 and J C4–C5 can be measured directly in the MAS spectra of Figs. 5 and 9. In case of glycine, only carbon C-1 has a nonnegligible scalar coupling with nitrogen. We have recorded the corres-
This research was supported at Ames Laboratory by the U.S. DOE, Office of Basic Energy Sciences, Division of Chemical Sciences, under Contract W-7405-Eng-82, JT, JPA and LD thank the Region Nord/Pas de Calais and FEDER for their financial support.
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