Radio-frequency field inhomogeneity is one of the most common imperfections in NMR experiments. They can lead to imperfect flip angles of applied radio-frequency (rf) pulses or to a mismatch of resonance conditions, resulting in artefacts or degraded performance of experiments. In solid-state NMR under magic angle spinning (MAS), the radial component becomes time-dependent because the rf irradiation amplitude and phase is modulated with integer multiples of the spinning frequency. We analyse the influence of such time-dependent MAS-modulated rf fields on the performance of some commonly used building blocks of solid-state NMR experiments. This analysis is based on analytical Floquet calculations and numerical simulations, taking into account the time dependence of the rf field. We find that, compared to the static part of the rf field inhomogeneity, such time-dependent modulations play a very minor role in the performance degradation of the investigated typical solid-state NMR experiments.

Department of Chemistry Faculty of Science Charles University Hlavova 8 12842 Prague 2 Czech Republic

Physical Chemistry ETH Zürich Vladimir Prelog Weg 2 8093 Zurich Switzerland

Zobrazit více v PubMed

Aebischer K, Wili N, Tošner Z, Ernst M. Using nutation-frequency-selective pulses to reduce radio-frequency field inhomogeneity in solid-state NMR. Magn Reson. 2020;1:187–195. doi: 10.5194/mr-1-187-2020. PubMed DOI PMC

Aebischer K, Tošner Z, Ernst M. 2021. Effects of radial radio-frequency field inhomogeneity on MAS solid-state NMR experiments. ETH Zurich [data set] PubMed DOI PMC

Barnaal D, Lowe IJ. Effects of Rotating Magnetic Fields on Free-Induction Decay Shapes. Phys Rev Lett. 1963;11:258–260. doi: 10.1103/PhysRevLett.11.258. DOI

Bielecki A, Kolbert AC, Levitt MH. Frequency-switched pulse sequences: homonuclear decoupling and dilute spin NMR in solids. Chem Phys Lett. 1989;155:341–346.

Bielecki A, Kolbert AC, De Groot HJM, Griffin RG, Levitt MH. Frequency-switched Lee–Goldburg sequences in solids. Advances in Magnetic and Optical Resonance. 1990;14:111–124.

Charmont P, Lesage A, Steuernagel S, Engelke F, Emsley L. Sample Restriction Using Magnetic Field Gradients in High-Resolution Solid-State NMR. J Magn Reson. 2000;145:334–339. doi: 10.1006/jmre.2000.2117. PubMed DOI

Charmont P, Sakellariou D, Emsley L. Sample Restriction Using Radiofrequency Field Selective Pulses in High-Resolution Solid-State NMR. J Magn Reson. 2002;154:136–141. doi: 10.1006/jmre.2001.2467. PubMed DOI

Cheng V, Suzukawa H, Wolfsberg M. Investigations of a nonrandom numerical method for multidimensional integration. J Chem Phys. 1973;59:3992–3999.

Dyson FJ. The Radiation Theories of Tomonaga, Schwinger, and Feynman. Phys Rev. 1949;75:486–502. doi: 10.1103/PhysRev.75.486. DOI

Elbayed K, Dillmann B, Raya J, Piotto M, Engelke F. Field modulation effects induced by sample spinning: application to high-resolution magic angle spinning NMR. J Magn Reson. 2005;174:2–26. doi: 10.1016/j.jmr.2004.11.017. PubMed DOI

Engelke F. Electromagnetic wave compression and radio frequency homogeneity in NMR solenoidal coils: computational approach. Concept Magnetic Res. 2002;15:129–155.

Frantsuzov I, Vasa SK, Ernst M, Brown SP, Zorin V, Kentgens APM, Hodgkinson P. Rationalising Heteronuclear Decoupling in Refocussing Applications of Solid-State NMR Spectroscopy. ChemPhysChem. 2017;18:394–405. doi: 10.1002/cphc.201601003. PubMed DOI PMC

Geen H, Freeman R. Band-selective radiofrequency pulses. J Magn Reson. 1991;93:93–141.

Goldburg WI, Lee M. Nuclear Magnetic Resonance Line Narrowing by a Rotating rf Field. Phys Rev Lett. 1963;11:255–258. doi: 10.1103/PhysRevLett.11.255. DOI

Goldman M, Tekely P. Effect of radial RF field on MAS spectra. CR Acad Sci II C. 2001;4:795–800.

Guenneugues M, Berthault P, Desvaux H. A Method for Determining PubMed DOI

Gullion T, Schaefer J. Rotational-echo double-resonance NMR. J Magn Reson. 1989;81:196–200. doi: 10.1016/0022-2364(89)90280-1. a. PubMed DOI

Gullion T, Schaefer J. Detection of Weak Heteronuclear Dipolar Coupling by Rotational-Echo Double-Resonance Nuclear Magnetic Resonance. Advances in Magnetic and Optical Resonance. 1989;13:57–83. doi: 10.1016/B978-0-12-025513-9.50009-4. b. DOI

Gullion T, Baker DB, Conradi MS. New, compensated Carr-Purcell sequences. J Magn Reson. 1990;89:479–484. doi: 10.1016/0022-2364(90)90331-3. DOI

Hartmann SR, Hahn EL. Nuclear double resonance in the rotating frame. Phys Rev. 1962;128:2042. doi: 10.1103/PhysRev.128.2042. DOI

Hediger S, Meier BH, Ernst RR. Adiabatic passage Hartmann–Hahn cross polarization in NMR under magic angle sample spinning. Chem Phys Lett. 1995;240:449–456.

Hellwagner J, Sharma K, Tan KO, Wittmann JJ, Meier BH, Madhu PK, Ernst M. Optimizing symmetry-based recoupling sequences in solid-state NMR by pulse-transient compensation and asynchronous implementation. J Chem Phys. 2017;146:244202. doi: 10.1063/1.4989542. PubMed DOI

Hellwagner J, Grunwald L, Ochsner M, Zindel D, Meier BH, Ernst M. Origin of the residual line width under frequency-switched Lee–Goldburg decoupling in MAS solid-state NMR. Magn Reson. 2020;1:13–25. doi: 10.5194/mr-1-13-2020. PubMed DOI PMC

Hohwy M, Jakobsen HJ, Eden M, Levitt MH, Nielsen NC. Broadband dipolar recoupling in the nuclear magnetic resonance of rotating solids: A compensated C7 pulse sequence. J Chem Phys. 1998;108:2686–2694.

Hong M. Oligomeric Structure, Dynamics, and Orientation of Membrane Proteins from Solid-State NMR. Structure. 2006;14:1731–1740. doi: 10.1016/j.str.2006.10.002. PubMed DOI

Hoult DI, Richards RE. The signal-to-noise ratio of the nuclear magnetic resonance experiment. J Magn Reson. 1976;24:71–85. doi: 10.1016/0022-2364(76)90233-X. PubMed DOI

Idziak S, Haeberlen U. Design and construction of a high homogeneity rf coil for solid-state multiple-pulse NMR. J Magn Reson. 1982;50:281–288. doi: 10.1016/0022-2364(82)90058-0. DOI

Jain MG, Mote KR, Hellwagner J, Rajalakshmi G, Ernst M, Madhu PK, Agarwal V. Measuring strong one-bond dipolar couplings using REDOR in magic-angle spinning solid-state NMR. J Chem Phys. 2019;150:134201. doi: 10.1063/1.5088100. PubMed DOI

Jaroniec CP, Tounge BA, Rienstra CM, Herzfeld J, Griffin RG. Recoupling of heteronuclear dipolar interactions with rotational-echo double-resonance at high magic-angle spinning frequencies. J Magn Reson. 2000;146:132–139. PubMed

Jia L, Liang S, Sackett K, Xie L, Ghosh U, Weliky DP. REDOR solid-state NMR as a probe of the membrane locations of membrane-associated peptides and proteins. J Magn Reson. 2015;253:154–165. doi: 10.1016/j.jmr.2014.12.020. PubMed DOI PMC

Lee M, Goldburg WI. Nuclear–Magnetic–Resonance Line Narrowing by a Rotating rf Field. Phys Rev. 1965;140:A1261–A1271. doi: 10.1103/PhysRev.140.A1261. DOI

Lee YK, Kurur ND, Helmle M, Johannessen OG, Nielsen NC, Levitt MH. Efficient dipolar recoupling in the NMR of rotating solids. A sevenfold symmetric radiofrequency pulse sequence. Chem Phys Lett. 1995;242:304–309.

Leskes M, Madhu P, Vega S. Floquet theory in solid-state nuclear magnetic resonance. Prog Nucl Mag Res Sp. 2010;57:345–380. doi: 10.1016/j.pnmrs.2010.06.002. PubMed DOI

Levitt MH. In: eMagRes. Harris RK, Wasylishen RL, editors. John Wiley; Chichester: 2007. Symmetry-Based Pulse Sequences in Magic-Angle Spinning Solid-State NMR. DOI

Levitt MH, Oas TG, Griffin RG. Rotary Resonance Recoupling in Heteronuclear Spin Pair Systems. Israel J Chem. 1988;28:271–282.

Li C, Mo Y, Hu J, Chekmenev E, Tian C, Gao FP, Fu R, Gor'kov P, Brey W, Cross TA. Analysis of RF heating and sample stability in aligned static solid-state NMR spectroscopy. J Magn Reson. 2006;180:51–57. doi: 10.1016/j.jmr.2006.01.013. PubMed DOI

Lindon JC, Beckonert OP, Holmes E, Nicholson JK. High-resolution magic angle spinning NMR spectroscopy: Application to biomedical studies. Prog Nucl Mag Res Sp. 2009;2:79–100.

Maier LC, Slater JC. Field Strength Measurements in Resonant Cavities. J Appl Phys. 1952;23:68–77. doi: 10.1063/1.1701980. DOI

Metz G, Wu X, Smith S. Ramped-Amplitude Cross Polarization in Magic-Angle-Spinning NMR. J Magn Reson Ser A. 1994;110:219–227. doi: 10.1006/jmra.1994.1208. DOI

Michal CA, Jelinski LW. REDOR 3D: Heteronuclear Distance Measurements in Uniformly Labeled and Natural Abundance Solids. J Am Chem Soc. 1997;119:9059–9060. doi: 10.1021/ja9711730. DOI

Mithu VS, Tan KO, Madhu PK. Selective inversion of 1H resonances in solid-state nuclear magnetic resonance: Use of double-DANTE pulse sequence. J Magn Reson. 2013;237:11–16. PubMed

Mote KR, Agarwal V, Madhu PK. Five decades of homonuclear dipolar decoupling in solid-state NMR: Status and outlook. Prog Nucl Mag Res Sp. 2016;97:1–39. PubMed

Nielsen NC, Strassø LA, Nielsen AB. Dipolar Recoupling. Springer Berlin Heidelberg; Berlin, Heidelberg: 2012. pp. 1–45. DOI

Nishimura K, Fu R, Cross TA. The Effect of RF Inhomogeneity on Heteronuclear Dipolar Recoupling in Solid State NMR: Practical Performance of SFAM and REDOR. J Magn Reson. 2001;152:227–233. doi: 10.1006/jmre.2001.2410. DOI

Odedra S, Wimperis S. Imaging of the PubMed DOI

Paulson EK, Martin RW, Zilm KW. Cross polarization, radio frequency field homogeneity, and circuit balancing in high field solid state NMR probes. J Magn Reson. 2004;171:314–323. doi: 10.1016/j.jmr.2004.09.009. PubMed DOI

Piotto M, Bourdonneau M, Furrer J, Bianco A, Raya J, Elbayed K. Destruction of magnetization during TOCSY experiments performed under magic angle spinning: effect of radial B1 inhomogeneities. J Magn Reson. 2001;149:114–118. doi: 10.1006/jmre.2001.2287. DOI

Privalov AF, Dvinskikh SV, Vieth H-M. Coil Design for Large-Volume High- DOI

Purusottam RN, Bodenhausen G, Tekely P. Effects of inherent rf field inhomogeneity on heteronuclear decoupling in solid-state NMR. Chem Phys Lett. 2015;635:157–162. doi: 10.1016/j.cplett.2015.06.051. DOI

Rienstra CM, Tucker-Kellogg L, Jaroniec CP, Hohwy M, Reif B, McMahon MT, Tidor B, Lozano-Pérez T, Griffin RG. De novo determination of peptide structure with solid-state magic-angle spinning NMR spectroscopy. P Natl Acad Sci USA. 2002;99:10260–10265. doi: 10.1073/pnas.152346599. PubMed DOI PMC

Schanda P, Meier BH, Ernst M. Quantitative analysis of protein backbone dynamics in microcrystalline ubiquitin by solid-state NMR spectroscopy. J Am Chem Soc. 2010;132:15957–15967. PubMed

Schanda P, Meier BH, Ernst M. Accurate measurement of one-bond H–X heteronuclear dipolar couplings in MAS solid-state NMR. J Magn Reson. 2011;210:246–259. PubMed

Scholz I, Hodgkinson P, Meier BH, Ernst M. Understanding two-pulse phase-modulated decoupling in solid-state NMR. J Chem Phys. 2009;130:114510. doi: 10.1063/1.3086936. PubMed DOI

Scholz I, van Beek JD, Ernst M. Operator-based Floquet theory in solid-state NMR. Solid State Nucl Mag. 2010;37:39–59. doi: 10.1016/j.ssnmr.2010.04.003. PubMed DOI

Smith S, Levante T, Meier B, Ernst R. Computer simulations in magnetic resonance. An object-oriented programming approach. J Magn Reson. 1994;106:75–105.

States DJ, Haberkorn RA, Ruben DJ. A two-dimensional nuclear Overhauser experiment with pure absorption phase in four quadrants. J Magn Reson. 1982;48:286–292.

Stejskal E, Schaefer J, Waugh J. Magic-angle spinning and polarization transfer in proton-enhanced NMR. J Magn Reson. 1977;28:105–112.

Tan KO, Rajeswari M, Madhu PK, Ernst M. Asynchronous symmetry-based sequences for homonuclear dipolar recoupling in solid-state nuclear magnetic resonance. J Chem Phys. 2015;142:065101. doi: 10.1063/1.4907275. PubMed DOI

Tan KO, Agarwal V, Meier BH, Ernst M. A generalized theoretical framework for the description of spin decoupling in solid-state MAS NMR: Offset effect on decoupling performance. J Chem Phys. 2016;145:094201. doi: 10.1063/1.4961909. PubMed DOI

Tekely P, Goldman M. Radial-field sidebands in MAS. J Magn Reson. 2001;148:135–141. PubMed

Torrey HC. Transient Nutations in Nuclear Magnetic Resonance. Phys Rev. 1949;76:1059–1068. doi: 10.1103/PhysRev.76.1059. DOI

Tošner Z, Purea A, Struppe JO, Wegner W, Engelke F, Glaser SJ, Reif B. Radiofrequency fields in MAS solid state NMR probes. J Magn Reson. 2017;284:20–32. doi: 10.1016/j.jmr.2017.09.002. PubMed DOI

Tošner Z, Sarkar R, Becker-Baldus J, Glaubitz C, Wegner S, Engelke F, Glaser SJ, Reif B. Overcoming Volume Selectivity of Dipolar Recoupling in Biological Solid-State NMR Spectroscopy. Angew Chem Int Edit. 2018;57:14514–14518. doi: 10.1002/anie.201805002. PubMed DOI

Performance of the cross-polarization experiment in conditions of radiofrequency field inhomogeneity and slow to ultrafast magic angle spinning (MAS)

Maximizing efficiency of dipolar recoupling in solid-state NMR using optimal control sequences

Effects of radial radio-frequency field inhomogeneity on MAS solid-state NMR experiments