Journal of Magnetic Resonance 246 (2014) 104–109
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Efficient heteronuclear decoupling in MAS solid-state NMR using non-rotor-synchronized rCW irradiation Asif Equbal a, Subhradip Paul b, Venus Singh Mithu c, P.K. Madhu d,e,⇑, Niels Chr. Nielsen a,⇑ a Center for Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, Gustav Wieds Vej 14, DK-8000 Aarhus C, Denmark b Department of Chemistry, Center for Excellence in Basic Sciences, University of Mumbai and Department of Atomic Energy, Health Centre, University of Mumbai, Vidhyanagari Campus, Mumbai 400098, India c Department of Chemistry, Guru Nanak Dev University, Amritsar 143005, India d Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India e TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500 075, India
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Article history: Received 21 April 2014 Revised 30 June 2014 Available online 19 July 2014
We present new non-rotor-synchronized variants of the recently introduced refocused continuous wave (rCW) heteronuclear decoupling method significantly improving the performance relative to the original rotor-synchronized variants. Under non-rotor-synchronized conditions the rCW decoupling sequences provide more efficient decoupling, are easier to setup, and prove more robust towards experimental parameters such as radio frequency (rf) field amplitude and spinning frequency. This is demonstrated through numerical simulations substantiated with experimental results under different sample spinning and rf field amplitude conditions for powder samples of U-13C-glycine and U-13C-L-histidineHClH2O. Ó 2014 Elsevier Inc. All rights reserved.
Keywords: Solid-state NMR Magic-angle spinning Heteronuclear dipolar decoupling rCW decoupling Non-rotor-synchronization
1. Introduction Heteronuclear decoupling is vital in solid-state magic-anglespinning (MAS) NMR experiments involving abundant 1H spins coupled to low-gyromagnetic-ratio nuclear spin species such as 13 C and 15N [1,2]. Continuous wave (CW), although the simplest decoupling sequence, is typically not sufficiently efficient for high-resolution applications. Two-pulse phase-modulation (TPPM) decoupling introduced in 1995 by Bennett et al. [3] improved the decoupling performance considerably relative to CW decoupling through phase alternation of the decoupling rf irradiation. One of the basic problems of TPPM, however, is its lack of robustness towards experimental parameters like rf field offset, phase, and amplitude in turn also rendering it difficult to setup for optimal performance. This has inspired the development of a large variety of phase or amplitude-modulated pulse sequences for heteronuclear decoupling [4–20]. Recently, Vinther et al. [21,22] introduced an alternative concept to heteronuclear decoupling by interleaving CW irradiation with p refocusing pulses. This scheme was denoted rCW. Five ⇑ Corresponding authors. E-mail addresses: (N.C. Nielsen).
[email protected]
(P.K.
http://dx.doi.org/10.1016/j.jmr.2014.07.006 1090-7807/Ó 2014 Elsevier Inc. All rights reserved.
Madhu),
[email protected]
different rCW variants, namely, rCWA, rCWB, rCWC, rCWD, and rCWE, were introduced as schematically illustrated in Fig. 1. The variants are presented in their original form with the interleaving rf pulses incorporated under rotor-synchronized conditions. Scheme A is the simplest approach having a y-phase p pulse inserted between two blocks of x-phase CW irradiation. Scheme B involves two rCWA sequences concatenated by an x-phase p pulse. Schemes C and D are super-cycled versions of rCWA and rCWB, respectively. Scheme E has p/2 purging pulses inserted into scheme D. Ideally, in the rCW sequences, the p pulses are infinitesimally short in length (corresponding to infinite rf field amplitude). In experimental realizations this is not possible to accomplish and the p pulses will have finite amplitude and length. To ensure rotor synchronization, it was suggested that the p pulses were incorporated into the timings of the CW blocks. This implies that the length of each CW block in rotor-synchronized rCWA and rCWC sequences will be sr —0:5sp with sr representing a rotor period and sp the duration of a p pulse. In the rotor-synchronized rCWB and rCWD decoupling sequences, the length of each CW block will be sr —0:75sp , whereas for the rCWE scheme, it will be sr —0:875sp . Finite p pulse rCW sequences are shown in Fig. 1. The p pulses in rCW serve to eliminate the residual nonresonant high-order terms in the effective Hamiltonian originating from interactions between heteronuclear dipolar coupling and the
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Fig. 1. Schematic representation of CW and rotor-synchronized rCWX ðX ¼ A; B; C; D, and E) decoupling sequences as proposed by Vinther et al. [21,22]. The schematic shows that for finite p pulse the length of the CW blocks are adjusted to ensure rotor-synchronization. In this case length sCW becomes sr —0:5sp ; sr —0:75sp ; sr —0:5sp ; sr —0:75sp , and sr —0:875sp for rCWA, rCWB, rCWC, rCWD, and rCWE, respectively. 1
H-spin chemical shift anisotropy. Fig. 2 shows the resonant freeinduction decay (FID) of 13C belonging to a 13CH2 spin system as a function of time during a period of acquisition with rCWA used for 1H decoupling. From the figure, it is clear that the decay in the 13C signal during the first CW block in rCWA sequence is refocused by the p pulse during the second CW block. This provides a nice justification of the notation of refocused continuous-wave (rCW) decoupling. Two important conditions were set in order to achieve efficient decoupling using rCW irradiation. The first condition required the duration of each CW block interleaved with p pulses to be an integer multiple of the rotor period. The second condition implied a large rf field amplitude of p pulse as a prerequisite for efficient refocusing. With these two conditions fulfilled, the decoupling performance of rCW schemes was shown to be much better than standard CW irradiation and better than or comparable to state-of-the-art decoupling sequences such as TPPM and refined variants under typical experimental conditions. It seems relevant here to mention that the rCW sequences were developed using effective (average) Hamiltonian theory [23–25]
which can describe the evolution of the density operator stroboscopically during MAS experiments, only at fixed time intervals, corresponding to an overall periodicity of the Hamiltonian. In the more general case with less restrictive timing constraints, methods such as Floquet theory [26–32] will be of better use. In this paper, we take a simpler approach and resort to numerical and experimental investigations to describe the efficiency of rCW decoupling sequences under rotor as well as non-rotor-synchronized conditions. We demonstrate that better decoupling can be obtained at non-rotor-synchronized conditions. 2. Experimental and numerical All experiments were carried out on a Bruker Avance III 700 MHz NMR spectrometer (Bruker Biospin, Rheinstetten) using a standard 2.5 mm triple-resonance probe on commercially available U-13C-L-histidineHClH2O and U-13C-glycine (Sigma–Aldrich) powder samples. Nutation experiments were performed on a sample of adamantane (Sigma–Aldrich) to calibrate the 1H and 13C rf field amplitudes. All simulations were performed using the SIMPSON [33,34] open-source simulation package for typical parameters of a CH2 spin system (assuming conditions of a 700 MHz NMR spectrometer): iso dCSA ¼ 2450 Hz, dCSA ¼ 0 Hz, gCSA ¼ 0 kHz, diso H C H1 ¼ 0 Hz, dH2 ¼200Hz, J iso D D dC ¼0Hz, xHC =2p ¼23:3kHz, xHH =2p ¼21:3kHz, xHC =2p ¼0Hz, and xJHH =2p ¼0Hz using the notation in Ref. [33]. Powder averaging was mimicked with the REPULSION scheme [35] employing 144 aCR ; bCR crystallite orientations and 12 cCR angles. Simulations were performed as a function of spinning frequency, rf field amplitude, and duration of the CW blocks in the rCW sequences. To ensure easier implementation of the rCW experiments, the refocusing p pulse was assumed to have the same rf field amplitude as used for the CW irradiation. For all experiments, the initial polarization to 13C was transferred from protons using rampedamplitude cross polarization (CP) [36]. 3. Results and discussion
Fig. 2. The overlaid FID profiles for 13C resonance of a 13CH2 spin system acquired during rCWA (black) and CW (red) decoupling under the conditions of m1 ¼ 125 kHz, mr ¼ 10 kHz, and sA ¼ 500 ls (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).
To explore the performance of rCW decoupling under nonrotorsynchronized conditions, simulations and experiments were undertaken using the CH2 group in glycine as the model system
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upon varying the length of the CW irradiation blocks at different MAS frequencies. For simplicity, we define timing parameters sA ; sB ; sC ; sD , and sE as sums of sCW and incorporated sp durations of each CW block for the rCWA, rCWB, rCWC, rCWD, and rCWE decoupling schemes, respectively. With reference to the pulse sequence schematics in Fig. 1, we define sA ¼ sC ¼ sCW þ0:5sp ; sB ¼ sD ¼ sCW þ 0:75sp , and sE ¼ sCW þ 0:875sp . Fig. 3 shows the experimental peak height observed for the 13C resonance of U-13C-glycine as a function of sA and sB , varied from 0.9sr to 1.1sr for the rCWA and rCWB decoupling schemes, respectively. The rf field amplitude, m1 , for the CW blocks and the p pulses was fixed at 104.5 kHz and the spinning frequency, mr , was fixed at 30 kHz (Fig. 3a and b) and 20 kHz (Fig. 3c and d). The rf field phases for the CW blocks and p pulses were the same as proposed by Vinther et al. (cf. Fig. 1). The plots clearly reveal a dip in the 13C signal peak height at the rotor-synchronized conditions. The corresponding dips suggest that recoupling of some anisotropic nuclear spin interactions may be taking place under these circumstances (vide infra). It is also seen that the dip in the peak height at 30 kHz spinning frequency is more pronounced than the one obversed for the lower spinning frequency of 20 kHz. At 30 kHz sample spinning, the signal height at the dips were 61.8% and 36.9% for rCWA and rCWB sequences, respectively, with respect to the maximum peak height observed when varying sA and sB from 0.9sr to 1.1sr in the two cases. The marked decrease in decoupling performance upon rotor synchronization was also observed in numerical simulations. Fig. 4 shows the numerically simulated FID intensity obtained after 10 ms of acquisition for the 13C resonance in a 13CH2 spin system as function of sA =sr and sB =sr for rCWA and rCWB decoupling, respectively. The rf field amplitude was set to 104.5 kHz for the CW blocks as in the experiments. It is evident that improved decoupling may be obtained under non-rotor-synchronized conditions. The dips in 13C signal appear more prominent for rCWA as compared to rCWB. It is relevant to mention that for rCWE decoupling (not shown), the dips in signal at rotor-synchronized conditions were visible only at very high spinning frequencies (i.e., mr > 30 kHz). Detailed experimental and numerical analysis of rCW decoupling suggests that there are strong recoupling/residual dipolar coupling effects at conditions where sX ðX ¼ A; B; C; D, and E) matches positive integral multiples of 0.125sr . In a numerical sim-
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Fig. 4. Numerically simulated FID intensity for a typical 13C resonance of a 13CH2 spin system obtained after 10 ms of acquisition for the (a) rCWA and (b) rCWB decoupling sequences. sA and sB are varied from 0.9sr to 1.1sr in steps of 0.00625sr while the spinning frequency is varied from 5 to 30 kHz in steps of 1 kHz. m1 is fixed at 104.5 kHz.
ulation for a 13CH2 spin system, sA and the spinning frequency were varied while keeping the rf field amplitude of the CW block fixed at 104.5 kHz. Fig. 5 maps the 13C FID intensity at 10 ms upon rCWA decoupling. It is evident that when sA matches a positive integral multiple of sr =8, one observes a marked decrease in the decoupling performance. These resonance conditions appear more pronounced for higher spinning frequencies and shorter rCW cycle times. The simulations were performed under assumption of ideal refocusing p pulses. We did simulations assuming finite p pulses of amplitude 104.5 kHz, revealing similar resonance conditions for rCW decoupling. These resonance conditions were also observed experimentally. Fig. 6 illustrates the results of an experimental optimization of the sA duration for rCWA decoupling for U-13C-L-histidineHClH2O at 20 kHz (Fig. 6a) and 10 kHz (Fig. 6b) spinning frequencies and 104.5 kHz rf field amplitude for both CW blocks and p pulses. The dips in peak height at the resonance conditions as predicted by simulations are clearly evident. Preliminary Floquet theory investigations indicate that these resonances originate from firstorder heteronuclear recoupling and second-order resonant cross terms between 1H chemical shift anisotropy and heteronuclear dipolar coupling as well as cross terms between homonuclear and heteronuclear couplings. Overall, our numerical and experimental analysis reveal that rCW sequences display more efficient decoupling performance
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0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 0.9
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Fig. 3. Experimental optimization of (a, c) rCWA and (b, d) rCWB decoupling upon variation of the durations of sA and sB from 0.9sr to 1.1sr for rCWA and rCWB, respectively, under conditions of (a, b) mr ¼ 30 kHz and m1 ¼ 104:5 kHz and (c, d) mr ¼ 20 kHz and m1 ¼ 104:5 kHz.
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The decoupling efficiency of the non-rotor-synchronized rCW sequences was compared with CW, TPPM, and SWf-TPPM decoupling for U-13C-L-histidineHClH2O characterized by six 13C resonances. Fig. 7 illustrates the peak height of all the carbon atoms of histidine for different decoupling sequences and different experimental conditions. The comparisons were done under conditions of (a) mr ¼ 10 kHz and m1 ¼ 75 kHz, (b) mr ¼ 10 kHz and m1 ¼ 104:5 kHz, and (c) mr ¼ 20 kHz and m1 ¼ 104:5 kHz. The length of the refocusing pulse was 4.8 ls and 6.66 ls for m1 ¼ 104:5 and 75 kHz, respectively. These lengths correspond to a p pulse in each case. All decoupling sequences (rCWA, rCWB, rCWC, CW, TPPM, and SWf-TPPM) were optimized for the best decoupling at the given rf field amplitude and spinning frequency. For the sake of simplicity, rCWD and rCWE sequences were not considered for this comparison, their performance are virtually identical to the simpler rCW sequences upon optimization. The intensity for each peak was normalized with respect to the TPPM value.
Fig. 5. Numerical analysis of decoupling performance of rCWA for a 13CH2 spin system assuming a 700 MHz 1H Larmor frequency and m1 ¼ 104:5 kHz. mr is varied from 5 to 30 kHz in steps of 1 kHz. sA is varied between 0.00625sr to 2.125sr in steps of 0.00625sr . The contours shows the FID intensity for a 13C resonance of 13 CH2 spin system at 10 ms of acquisition.
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Fig. 6. Experimental analysis of decoupling performance of rCWA based on 13C MAS spectra for U-13C-glycine recorded using (a) mr ¼ 20 kHz and m1 ¼ 104:5 kHz and (b) mr ¼ 10 kHz and m1 ¼ 104:5 kHz. The peak height for carbon resonance is normalized with respect to its best peak height value obtained. sA is varied in steps of 1 ls.
when implemented under non-rotor-synchronized conditions. It is evident that a wealth of good decoupling conditions can be found for the investigated range of spinning frequencies between 5 and 30 kHz. To provide simple guidelines, good decoupling was achieved for rCWA when sA lies in the range 50 0:125sr ls (see dashed boxes in Fig. 6), for rCWB when sB is in the range 0:5sr 0:125sr ls, sr 0:125sr ls, or 1:5sr 0:125sr ls, and for rCWC when sC is in the range sr 0:125sr ls.
Fig. 7. Experimental mapping of the efficiency of rCWA, rCWB, rCWC, CW, TPPM, and SWf-TPPM decoupling as observed for a sample of U-13C-L-histidineHClH2O. The experiments were performed at (a) mr ¼ 10 kHz and m1 ¼ 75 kHz, (b) mr ¼ 10 kHz and m1 ¼ 105 kHz, and (c) mr ¼ 20 kHz and m1 ¼ 105 kHz. For TPPM and SWf-TPPM decoupling the optimized pulse flip angles and phases were (a) 172°, / ¼ 15 (TPPM) and 178°, / = 12°(SWf-TPPM), (b) 175°, / = 11°(TPPM) and 191°, / = 15°(SWf-TPPM), and (c) 186°, / = 19°(TPPM) and 185°, / = 15°(SWf-TPPM).
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(a)
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Fig. 8. (a) Experimental analysis of TPPM, rCWA, rCWB, rCWC, and SWf-TPPM decoupling as function of the rf field offset dependence for C a resonance of U-13C-glycine under conditions of mr ¼ 10 kHz and m1 ¼ 104:5 kHz. (b) Normalized peak height of C a resonance of U-13C-glycine as a function of flip angle of refocusing pulse under experimental conditions with mr ¼ 10 kHz and m1 ¼ 104:5 kHz. The pulse sequence parameters were (a) rCWA: sA ¼ 53:4 ls, rCWB: sB ¼ 51:1 ls, rCWC: sC ¼ 100:4 ls, TPPM: pulse flip angle 185°, / = 11°, SWf-TPPM: pulse flip angle 193°, / = 15°and (b) rCWA: sA ¼ 53:4 ls.
For mr ¼ 10 kHz and m1 ¼ 75 kHz, rCWA displayed optimal performance when sA was 53.8 ls. The most efficient decoupling performance for rCWB and rCWC was obtained when sB and sC attained values of 51.9 and 102.8 ls, respectively. Under this particular experimental condition, all the three rCW sequences were up to 10–25% more efficient than TPPM. For mr ¼ 10 kHz and m1 ¼ 104:5 kHz, rCWA, rCWB, and rCWC were optimal when the durations sA ; sB , and sC were 54.4, 51.6, and 99.4 ls, respectively. For mr ¼ 20 kHz and m1 ¼ 104:5 kHz, the most efficient rCWA, rCWB, and rCWC decoupling was obtained upon setting sA ; sB , and sC to 52.6, 51.0, and 49.2 ls, respectively. Under these conditions, all rCW schemes showed similar decoupling capability in all cases better than CW, TPPM, and SWf-TPPM. It is generally observed that
maximum improvement relative to TPPM is seen at lower spinning frequency and higher rf field amplitudes. The experimental robustness of the above-mentioned decoupling sequences is explored in Fig. 8. To map the tolerance towards the position of the rf carrier frequency, the rf offset was varied and the efficiency of decoupling for the 13Ca resonance of U-13C-glycine was observed at a spinning frequency of 10 kHz and an rf field amplitude of 104.5 kHz. The peak height observed upon varying the offset from 10 to 10 kHz for each sequence was normalized to 1 for the on-resonance condition. We found that all rCW sequences display equally good performance and display increased robustness towards rf offset variation relative to TPPM and SWfTPPM (see Fig. 8a). Accordingly, non-rotor-synchronized rCW
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Fig. 9. Numerically calculated 13C FID intensities for a CH2 spin system at 10 ms of acquisition under the influence of (a, b) rCWA and (c, d) rCWB decoupling as a function of the rf field amplitude and spinning frequency under (a, c) rotor-synchronized and (b, d) non-rotor-synchronized conditions. In case of rotor-synchronization, the lengths sA and sB are set to sr , while in the non-rotor synchronized case, sA and sB are adjusted to 0.97sr .
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decoupling should be the method of choice for samples like polypeptides having a large number of different spin systems. Experimental analysis was also accomplished to explore the robustness of non-rotor-synchronized rCW decoupling towards deviation of the refocusing p pulse from the 180° flip angle. The analysis was conducted for glycine at 10 kHz spinning and 104.5 kHz rf amplitude conditions. The flip angle of the refocusing pulse in an optimized rCWA sequence was varied from 140° to 220 degrees keeping sA to the optimized value for this spinning frequency and rf field amplitude. It appears clearly that the rCW sequence is very robust towards deviation in the refocusing p pulse flip angle. Deviation of 40 on either side of a refocusing pulse of 180 leads to an attenuation of less than 10% in peak height as evident from Fig. 8b. Finally, to demonstrate the ease of setup for rCW decoupling under non-rotor-synchronized conditions relative to the corresponding rotor-synchronized situation, we have numerically optimized the rCWA and rCWB sequences for a 13CH2 spin system while varying the spinning frequency and the rf field amplitude. The results are illustrated in Fig. 9. Under rotor-synchronized conditions, sA and sB were fixed to sr while for the non-rotor-synchronization condition they were 0.96sr . This analysis reveals clearly that non-rotor-synchronized conditions simplify optimization and improve experimental robustness significantly. The intensity maps suggest that the residual/recoupled dipolar coupling in the rotor-synchronized case is larger than for the corresponding non-rotor-synchronized case. A theoretical investigation aimed at understanding the observed resonances is in progress using Floquet theory.
4. Conclusions We conclude here that rCW decoupling may readily be improved by adjusting the timings to slight non-rotor-synchronized conditions. Good decoupling performance can be easily optimized using these sequences as there is only one parameter,sX , which needs to be optimized. Not just in terms of efficiency but also in terms of robustness towards experimental parameters, non-rotor-synchronized rCW sequences perform equally or better than current heteronuclear decoupling sequences. All variants of rCW decoupling are equally good when optimized to its best. But for the sake of simplicity the rCWA and rCWB decoupling schemes may be considered the methods of choice, overall leading to a generally recommended decoupling strategy for a wide range of solidstate NMR applications. Acknowledgments The project was supported by grants from the Danish National Research Foundation (DNRF59) and the European Commission under the Seventh Framework Programme (FP7), contract BioNMR 261863. We acknowledge the National Facility for High Field NMR, TIFR, Mumbai, and technical assistance of M.V. Naik. References [1] M. Ernst, Heteronuclear spin decoupling in solid-state NMR under magic-angle sample spinning, J. Magn. Reson. 162 (2003) 1. [2] P. Hodgkinson, Heteronuclear decoupling in the NMR of solids, Progr. Nucl. Magn. Reson. Spectrosc. 46 (2005) 159. [3] A.E. Bennett, C.M. Rienstra, M. Auger, K.V. Lakshmi, R.G. Griffin, Heteronuclear decoupling in rotating solids, J. Chem. Phys. 103 (1995) 6951. [4] A.L. Bloom, J.N. Shoolery, Effects of perturbing radiofrequency fields on nuclear spin coupling, Phys. Rev. 97 (1955) 1261. [5] P. Tekely, P. Palmas, D. Canet, Effect of proton spin exchange on the residual 13C MAS NMR linewidths. Phase-modulated irradiation for efficient heteronuclear decoupling in rapidly rotating solids, J. Magn. Reson. A107 (1994) 129.
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Journal of Magnetic Resonance journal homepage: www.elsevier.com/locate/jmr
Efficient heteronuclear decoupling in MAS solid-state NMR using non-rotor-synchronized rCW irradiation Asif Equbal a, Subhradip Paul b, Venus Singh Mithu c, P.K. Madhu d,e,⇑, Niels Chr. Nielsen a,⇑ a Center for Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, Gustav Wieds Vej 14, DK-8000 Aarhus C, Denmark b Department of Chemistry, Center for Excellence in Basic Sciences, University of Mumbai and Department of Atomic Energy, Health Centre, University of Mumbai, Vidhyanagari Campus, Mumbai 400098, India c Department of Chemistry, Guru Nanak Dev University, Amritsar 143005, India d Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India e TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500 075, India
a r t i c l e
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a b s t r a c t
Article history: Received 21 April 2014 Revised 30 June 2014 Available online 19 July 2014
We present new non-rotor-synchronized variants of the recently introduced refocused continuous wave (rCW) heteronuclear decoupling method significantly improving the performance relative to the original rotor-synchronized variants. Under non-rotor-synchronized conditions the rCW decoupling sequences provide more efficient decoupling, are easier to setup, and prove more robust towards experimental parameters such as radio frequency (rf) field amplitude and spinning frequency. This is demonstrated through numerical simulations substantiated with experimental results under different sample spinning and rf field amplitude conditions for powder samples of U-13C-glycine and U-13C-L-histidineHClH2O. Ó 2014 Elsevier Inc. All rights reserved.
Keywords: Solid-state NMR Magic-angle spinning Heteronuclear dipolar decoupling rCW decoupling Non-rotor-synchronization
1. Introduction Heteronuclear decoupling is vital in solid-state magic-anglespinning (MAS) NMR experiments involving abundant 1H spins coupled to low-gyromagnetic-ratio nuclear spin species such as 13 C and 15N [1,2]. Continuous wave (CW), although the simplest decoupling sequence, is typically not sufficiently efficient for high-resolution applications. Two-pulse phase-modulation (TPPM) decoupling introduced in 1995 by Bennett et al. [3] improved the decoupling performance considerably relative to CW decoupling through phase alternation of the decoupling rf irradiation. One of the basic problems of TPPM, however, is its lack of robustness towards experimental parameters like rf field offset, phase, and amplitude in turn also rendering it difficult to setup for optimal performance. This has inspired the development of a large variety of phase or amplitude-modulated pulse sequences for heteronuclear decoupling [4–20]. Recently, Vinther et al. [21,22] introduced an alternative concept to heteronuclear decoupling by interleaving CW irradiation with p refocusing pulses. This scheme was denoted rCW. Five ⇑ Corresponding authors. E-mail addresses: (N.C. Nielsen).
[email protected]
(P.K.
http://dx.doi.org/10.1016/j.jmr.2014.07.006 1090-7807/Ó 2014 Elsevier Inc. All rights reserved.
Madhu),
[email protected]
different rCW variants, namely, rCWA, rCWB, rCWC, rCWD, and rCWE, were introduced as schematically illustrated in Fig. 1. The variants are presented in their original form with the interleaving rf pulses incorporated under rotor-synchronized conditions. Scheme A is the simplest approach having a y-phase p pulse inserted between two blocks of x-phase CW irradiation. Scheme B involves two rCWA sequences concatenated by an x-phase p pulse. Schemes C and D are super-cycled versions of rCWA and rCWB, respectively. Scheme E has p/2 purging pulses inserted into scheme D. Ideally, in the rCW sequences, the p pulses are infinitesimally short in length (corresponding to infinite rf field amplitude). In experimental realizations this is not possible to accomplish and the p pulses will have finite amplitude and length. To ensure rotor synchronization, it was suggested that the p pulses were incorporated into the timings of the CW blocks. This implies that the length of each CW block in rotor-synchronized rCWA and rCWC sequences will be sr —0:5sp with sr representing a rotor period and sp the duration of a p pulse. In the rotor-synchronized rCWB and rCWD decoupling sequences, the length of each CW block will be sr —0:75sp , whereas for the rCWE scheme, it will be sr —0:875sp . Finite p pulse rCW sequences are shown in Fig. 1. The p pulses in rCW serve to eliminate the residual nonresonant high-order terms in the effective Hamiltonian originating from interactions between heteronuclear dipolar coupling and the
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Fig. 1. Schematic representation of CW and rotor-synchronized rCWX ðX ¼ A; B; C; D, and E) decoupling sequences as proposed by Vinther et al. [21,22]. The schematic shows that for finite p pulse the length of the CW blocks are adjusted to ensure rotor-synchronization. In this case length sCW becomes sr —0:5sp ; sr —0:75sp ; sr —0:5sp ; sr —0:75sp , and sr —0:875sp for rCWA, rCWB, rCWC, rCWD, and rCWE, respectively. 1
H-spin chemical shift anisotropy. Fig. 2 shows the resonant freeinduction decay (FID) of 13C belonging to a 13CH2 spin system as a function of time during a period of acquisition with rCWA used for 1H decoupling. From the figure, it is clear that the decay in the 13C signal during the first CW block in rCWA sequence is refocused by the p pulse during the second CW block. This provides a nice justification of the notation of refocused continuous-wave (rCW) decoupling. Two important conditions were set in order to achieve efficient decoupling using rCW irradiation. The first condition required the duration of each CW block interleaved with p pulses to be an integer multiple of the rotor period. The second condition implied a large rf field amplitude of p pulse as a prerequisite for efficient refocusing. With these two conditions fulfilled, the decoupling performance of rCW schemes was shown to be much better than standard CW irradiation and better than or comparable to state-of-the-art decoupling sequences such as TPPM and refined variants under typical experimental conditions. It seems relevant here to mention that the rCW sequences were developed using effective (average) Hamiltonian theory [23–25]
which can describe the evolution of the density operator stroboscopically during MAS experiments, only at fixed time intervals, corresponding to an overall periodicity of the Hamiltonian. In the more general case with less restrictive timing constraints, methods such as Floquet theory [26–32] will be of better use. In this paper, we take a simpler approach and resort to numerical and experimental investigations to describe the efficiency of rCW decoupling sequences under rotor as well as non-rotor-synchronized conditions. We demonstrate that better decoupling can be obtained at non-rotor-synchronized conditions. 2. Experimental and numerical All experiments were carried out on a Bruker Avance III 700 MHz NMR spectrometer (Bruker Biospin, Rheinstetten) using a standard 2.5 mm triple-resonance probe on commercially available U-13C-L-histidineHClH2O and U-13C-glycine (Sigma–Aldrich) powder samples. Nutation experiments were performed on a sample of adamantane (Sigma–Aldrich) to calibrate the 1H and 13C rf field amplitudes. All simulations were performed using the SIMPSON [33,34] open-source simulation package for typical parameters of a CH2 spin system (assuming conditions of a 700 MHz NMR spectrometer): iso dCSA ¼ 2450 Hz, dCSA ¼ 0 Hz, gCSA ¼ 0 kHz, diso H C H1 ¼ 0 Hz, dH2 ¼200Hz, J iso D D dC ¼0Hz, xHC =2p ¼23:3kHz, xHH =2p ¼21:3kHz, xHC =2p ¼0Hz, and xJHH =2p ¼0Hz using the notation in Ref. [33]. Powder averaging was mimicked with the REPULSION scheme [35] employing 144 aCR ; bCR crystallite orientations and 12 cCR angles. Simulations were performed as a function of spinning frequency, rf field amplitude, and duration of the CW blocks in the rCW sequences. To ensure easier implementation of the rCW experiments, the refocusing p pulse was assumed to have the same rf field amplitude as used for the CW irradiation. For all experiments, the initial polarization to 13C was transferred from protons using rampedamplitude cross polarization (CP) [36]. 3. Results and discussion
Fig. 2. The overlaid FID profiles for 13C resonance of a 13CH2 spin system acquired during rCWA (black) and CW (red) decoupling under the conditions of m1 ¼ 125 kHz, mr ¼ 10 kHz, and sA ¼ 500 ls (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).
To explore the performance of rCW decoupling under nonrotorsynchronized conditions, simulations and experiments were undertaken using the CH2 group in glycine as the model system
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upon varying the length of the CW irradiation blocks at different MAS frequencies. For simplicity, we define timing parameters sA ; sB ; sC ; sD , and sE as sums of sCW and incorporated sp durations of each CW block for the rCWA, rCWB, rCWC, rCWD, and rCWE decoupling schemes, respectively. With reference to the pulse sequence schematics in Fig. 1, we define sA ¼ sC ¼ sCW þ0:5sp ; sB ¼ sD ¼ sCW þ 0:75sp , and sE ¼ sCW þ 0:875sp . Fig. 3 shows the experimental peak height observed for the 13C resonance of U-13C-glycine as a function of sA and sB , varied from 0.9sr to 1.1sr for the rCWA and rCWB decoupling schemes, respectively. The rf field amplitude, m1 , for the CW blocks and the p pulses was fixed at 104.5 kHz and the spinning frequency, mr , was fixed at 30 kHz (Fig. 3a and b) and 20 kHz (Fig. 3c and d). The rf field phases for the CW blocks and p pulses were the same as proposed by Vinther et al. (cf. Fig. 1). The plots clearly reveal a dip in the 13C signal peak height at the rotor-synchronized conditions. The corresponding dips suggest that recoupling of some anisotropic nuclear spin interactions may be taking place under these circumstances (vide infra). It is also seen that the dip in the peak height at 30 kHz spinning frequency is more pronounced than the one obversed for the lower spinning frequency of 20 kHz. At 30 kHz sample spinning, the signal height at the dips were 61.8% and 36.9% for rCWA and rCWB sequences, respectively, with respect to the maximum peak height observed when varying sA and sB from 0.9sr to 1.1sr in the two cases. The marked decrease in decoupling performance upon rotor synchronization was also observed in numerical simulations. Fig. 4 shows the numerically simulated FID intensity obtained after 10 ms of acquisition for the 13C resonance in a 13CH2 spin system as function of sA =sr and sB =sr for rCWA and rCWB decoupling, respectively. The rf field amplitude was set to 104.5 kHz for the CW blocks as in the experiments. It is evident that improved decoupling may be obtained under non-rotor-synchronized conditions. The dips in 13C signal appear more prominent for rCWA as compared to rCWB. It is relevant to mention that for rCWE decoupling (not shown), the dips in signal at rotor-synchronized conditions were visible only at very high spinning frequencies (i.e., mr > 30 kHz). Detailed experimental and numerical analysis of rCW decoupling suggests that there are strong recoupling/residual dipolar coupling effects at conditions where sX ðX ¼ A; B; C; D, and E) matches positive integral multiples of 0.125sr . In a numerical sim-
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Fig. 4. Numerically simulated FID intensity for a typical 13C resonance of a 13CH2 spin system obtained after 10 ms of acquisition for the (a) rCWA and (b) rCWB decoupling sequences. sA and sB are varied from 0.9sr to 1.1sr in steps of 0.00625sr while the spinning frequency is varied from 5 to 30 kHz in steps of 1 kHz. m1 is fixed at 104.5 kHz.
ulation for a 13CH2 spin system, sA and the spinning frequency were varied while keeping the rf field amplitude of the CW block fixed at 104.5 kHz. Fig. 5 maps the 13C FID intensity at 10 ms upon rCWA decoupling. It is evident that when sA matches a positive integral multiple of sr =8, one observes a marked decrease in the decoupling performance. These resonance conditions appear more pronounced for higher spinning frequencies and shorter rCW cycle times. The simulations were performed under assumption of ideal refocusing p pulses. We did simulations assuming finite p pulses of amplitude 104.5 kHz, revealing similar resonance conditions for rCW decoupling. These resonance conditions were also observed experimentally. Fig. 6 illustrates the results of an experimental optimization of the sA duration for rCWA decoupling for U-13C-L-histidineHClH2O at 20 kHz (Fig. 6a) and 10 kHz (Fig. 6b) spinning frequencies and 104.5 kHz rf field amplitude for both CW blocks and p pulses. The dips in peak height at the resonance conditions as predicted by simulations are clearly evident. Preliminary Floquet theory investigations indicate that these resonances originate from firstorder heteronuclear recoupling and second-order resonant cross terms between 1H chemical shift anisotropy and heteronuclear dipolar coupling as well as cross terms between homonuclear and heteronuclear couplings. Overall, our numerical and experimental analysis reveal that rCW sequences display more efficient decoupling performance
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Fig. 3. Experimental optimization of (a, c) rCWA and (b, d) rCWB decoupling upon variation of the durations of sA and sB from 0.9sr to 1.1sr for rCWA and rCWB, respectively, under conditions of (a, b) mr ¼ 30 kHz and m1 ¼ 104:5 kHz and (c, d) mr ¼ 20 kHz and m1 ¼ 104:5 kHz.
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The decoupling efficiency of the non-rotor-synchronized rCW sequences was compared with CW, TPPM, and SWf-TPPM decoupling for U-13C-L-histidineHClH2O characterized by six 13C resonances. Fig. 7 illustrates the peak height of all the carbon atoms of histidine for different decoupling sequences and different experimental conditions. The comparisons were done under conditions of (a) mr ¼ 10 kHz and m1 ¼ 75 kHz, (b) mr ¼ 10 kHz and m1 ¼ 104:5 kHz, and (c) mr ¼ 20 kHz and m1 ¼ 104:5 kHz. The length of the refocusing pulse was 4.8 ls and 6.66 ls for m1 ¼ 104:5 and 75 kHz, respectively. These lengths correspond to a p pulse in each case. All decoupling sequences (rCWA, rCWB, rCWC, CW, TPPM, and SWf-TPPM) were optimized for the best decoupling at the given rf field amplitude and spinning frequency. For the sake of simplicity, rCWD and rCWE sequences were not considered for this comparison, their performance are virtually identical to the simpler rCW sequences upon optimization. The intensity for each peak was normalized with respect to the TPPM value.
Fig. 5. Numerical analysis of decoupling performance of rCWA for a 13CH2 spin system assuming a 700 MHz 1H Larmor frequency and m1 ¼ 104:5 kHz. mr is varied from 5 to 30 kHz in steps of 1 kHz. sA is varied between 0.00625sr to 2.125sr in steps of 0.00625sr . The contours shows the FID intensity for a 13C resonance of 13 CH2 spin system at 10 ms of acquisition.
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Fig. 6. Experimental analysis of decoupling performance of rCWA based on 13C MAS spectra for U-13C-glycine recorded using (a) mr ¼ 20 kHz and m1 ¼ 104:5 kHz and (b) mr ¼ 10 kHz and m1 ¼ 104:5 kHz. The peak height for carbon resonance is normalized with respect to its best peak height value obtained. sA is varied in steps of 1 ls.
when implemented under non-rotor-synchronized conditions. It is evident that a wealth of good decoupling conditions can be found for the investigated range of spinning frequencies between 5 and 30 kHz. To provide simple guidelines, good decoupling was achieved for rCWA when sA lies in the range 50 0:125sr ls (see dashed boxes in Fig. 6), for rCWB when sB is in the range 0:5sr 0:125sr ls, sr 0:125sr ls, or 1:5sr 0:125sr ls, and for rCWC when sC is in the range sr 0:125sr ls.
Fig. 7. Experimental mapping of the efficiency of rCWA, rCWB, rCWC, CW, TPPM, and SWf-TPPM decoupling as observed for a sample of U-13C-L-histidineHClH2O. The experiments were performed at (a) mr ¼ 10 kHz and m1 ¼ 75 kHz, (b) mr ¼ 10 kHz and m1 ¼ 105 kHz, and (c) mr ¼ 20 kHz and m1 ¼ 105 kHz. For TPPM and SWf-TPPM decoupling the optimized pulse flip angles and phases were (a) 172°, / ¼ 15 (TPPM) and 178°, / = 12°(SWf-TPPM), (b) 175°, / = 11°(TPPM) and 191°, / = 15°(SWf-TPPM), and (c) 186°, / = 19°(TPPM) and 185°, / = 15°(SWf-TPPM).
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Fig. 8. (a) Experimental analysis of TPPM, rCWA, rCWB, rCWC, and SWf-TPPM decoupling as function of the rf field offset dependence for C a resonance of U-13C-glycine under conditions of mr ¼ 10 kHz and m1 ¼ 104:5 kHz. (b) Normalized peak height of C a resonance of U-13C-glycine as a function of flip angle of refocusing pulse under experimental conditions with mr ¼ 10 kHz and m1 ¼ 104:5 kHz. The pulse sequence parameters were (a) rCWA: sA ¼ 53:4 ls, rCWB: sB ¼ 51:1 ls, rCWC: sC ¼ 100:4 ls, TPPM: pulse flip angle 185°, / = 11°, SWf-TPPM: pulse flip angle 193°, / = 15°and (b) rCWA: sA ¼ 53:4 ls.
For mr ¼ 10 kHz and m1 ¼ 75 kHz, rCWA displayed optimal performance when sA was 53.8 ls. The most efficient decoupling performance for rCWB and rCWC was obtained when sB and sC attained values of 51.9 and 102.8 ls, respectively. Under this particular experimental condition, all the three rCW sequences were up to 10–25% more efficient than TPPM. For mr ¼ 10 kHz and m1 ¼ 104:5 kHz, rCWA, rCWB, and rCWC were optimal when the durations sA ; sB , and sC were 54.4, 51.6, and 99.4 ls, respectively. For mr ¼ 20 kHz and m1 ¼ 104:5 kHz, the most efficient rCWA, rCWB, and rCWC decoupling was obtained upon setting sA ; sB , and sC to 52.6, 51.0, and 49.2 ls, respectively. Under these conditions, all rCW schemes showed similar decoupling capability in all cases better than CW, TPPM, and SWf-TPPM. It is generally observed that
maximum improvement relative to TPPM is seen at lower spinning frequency and higher rf field amplitudes. The experimental robustness of the above-mentioned decoupling sequences is explored in Fig. 8. To map the tolerance towards the position of the rf carrier frequency, the rf offset was varied and the efficiency of decoupling for the 13Ca resonance of U-13C-glycine was observed at a spinning frequency of 10 kHz and an rf field amplitude of 104.5 kHz. The peak height observed upon varying the offset from 10 to 10 kHz for each sequence was normalized to 1 for the on-resonance condition. We found that all rCW sequences display equally good performance and display increased robustness towards rf offset variation relative to TPPM and SWfTPPM (see Fig. 8a). Accordingly, non-rotor-synchronized rCW
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Fig. 9. Numerically calculated 13C FID intensities for a CH2 spin system at 10 ms of acquisition under the influence of (a, b) rCWA and (c, d) rCWB decoupling as a function of the rf field amplitude and spinning frequency under (a, c) rotor-synchronized and (b, d) non-rotor-synchronized conditions. In case of rotor-synchronization, the lengths sA and sB are set to sr , while in the non-rotor synchronized case, sA and sB are adjusted to 0.97sr .
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decoupling should be the method of choice for samples like polypeptides having a large number of different spin systems. Experimental analysis was also accomplished to explore the robustness of non-rotor-synchronized rCW decoupling towards deviation of the refocusing p pulse from the 180° flip angle. The analysis was conducted for glycine at 10 kHz spinning and 104.5 kHz rf amplitude conditions. The flip angle of the refocusing pulse in an optimized rCWA sequence was varied from 140° to 220 degrees keeping sA to the optimized value for this spinning frequency and rf field amplitude. It appears clearly that the rCW sequence is very robust towards deviation in the refocusing p pulse flip angle. Deviation of 40 on either side of a refocusing pulse of 180 leads to an attenuation of less than 10% in peak height as evident from Fig. 8b. Finally, to demonstrate the ease of setup for rCW decoupling under non-rotor-synchronized conditions relative to the corresponding rotor-synchronized situation, we have numerically optimized the rCWA and rCWB sequences for a 13CH2 spin system while varying the spinning frequency and the rf field amplitude. The results are illustrated in Fig. 9. Under rotor-synchronized conditions, sA and sB were fixed to sr while for the non-rotor-synchronization condition they were 0.96sr . This analysis reveals clearly that non-rotor-synchronized conditions simplify optimization and improve experimental robustness significantly. The intensity maps suggest that the residual/recoupled dipolar coupling in the rotor-synchronized case is larger than for the corresponding non-rotor-synchronized case. A theoretical investigation aimed at understanding the observed resonances is in progress using Floquet theory.
4. Conclusions We conclude here that rCW decoupling may readily be improved by adjusting the timings to slight non-rotor-synchronized conditions. Good decoupling performance can be easily optimized using these sequences as there is only one parameter,sX , which needs to be optimized. Not just in terms of efficiency but also in terms of robustness towards experimental parameters, non-rotor-synchronized rCW sequences perform equally or better than current heteronuclear decoupling sequences. All variants of rCW decoupling are equally good when optimized to its best. But for the sake of simplicity the rCWA and rCWB decoupling schemes may be considered the methods of choice, overall leading to a generally recommended decoupling strategy for a wide range of solidstate NMR applications. Acknowledgments The project was supported by grants from the Danish National Research Foundation (DNRF59) and the European Commission under the Seventh Framework Programme (FP7), contract BioNMR 261863. We acknowledge the National Facility for High Field NMR, TIFR, Mumbai, and technical assistance of M.V. Naik. References [1] M. Ernst, Heteronuclear spin decoupling in solid-state NMR under magic-angle sample spinning, J. Magn. Reson. 162 (2003) 1. [2] P. Hodgkinson, Heteronuclear decoupling in the NMR of solids, Progr. Nucl. Magn. Reson. Spectrosc. 46 (2005) 159. [3] A.E. Bennett, C.M. Rienstra, M. Auger, K.V. Lakshmi, R.G. Griffin, Heteronuclear decoupling in rotating solids, J. Chem. Phys. 103 (1995) 6951. [4] A.L. Bloom, J.N. Shoolery, Effects of perturbing radiofrequency fields on nuclear spin coupling, Phys. Rev. 97 (1955) 1261. [5] P. Tekely, P. Palmas, D. Canet, Effect of proton spin exchange on the residual 13C MAS NMR linewidths. Phase-modulated irradiation for efficient heteronuclear decoupling in rapidly rotating solids, J. Magn. Reson. A107 (1994) 129.
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