In this paper, we provide an analytical description of the performance of the cross-polarization (CP) experiment, including linear ramps and adiabatic tangential sweeps, using effective Hamiltonians and simple rotations in 3D space. It is shown that radiofrequency field inhomogeneity induces a reduction in the transfer efficiency at increasing magic angle spinning (MAS) frequencies for both the ramp and the adiabatic CP experiments. The effect depends on the ratio of the dipolar coupling constant and the sample rotation frequency. In particular, our simulations show that for small dipolar couplings (1 kHz) and ultrafast MAS (above 100 kHz) the transfer efficiency is below 40 % when extended contact times up to 20 ms are used and relaxation losses are ignored. New recoupling and magnetization transfer techniques that are designed explicitly to account for inhomogeneous radiofrequency fields are needed.

Bayerisches NMR Zentrum Lichtenbergstr 4 85747 Garching Germany

Department of Chemistry Faculty of Science Charles University Albertov 6 12842 Prague Czech Republic

Helmholtz Zentrum München Deutsches Forschungszentrum für Gesundheit und Umwelt 85764 Neuherberg Germany

Institute of Organic Chemistry and Biochemistry of the CAS Flemingovo náměstí 2 16610 Prague Czech Republic

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Aebischer K, Tošner Z, Ernst M. Effects of radial radio-frequency field inhomogeneity on MAS solid-state NMR experiments. Magn Reson. 2021;2:523–543. doi: 10.5194/mr-2-523-2021. PubMed DOI PMC

Andrew ER, Bradbury A, Eades RG. Nuclear Magnetic Resonance Spectra from a Crystal rotated at High Speed. Nature. 1958;182:1659–1659. doi: 10.1038/1821659a0. DOI

Bak M, Rasmussen JT, Nielsen NC. SIMPSON: A general simulation program for solid-state NMR spectroscopy. J Magn Reson. 2000;147:296–330. doi: 10.1006/jmre.2000.2179. PubMed DOI

Baum J, Tycko R, Pines A. Broadband and adiabatic inversion of a two-level system by phase-modulated pulses. Phys Rev A (Coll Park) 1985;32:3435–3447. doi: 10.1103/PhysRevA.32.3435. PubMed DOI

Brinkmann A. Introduction to average Hamiltonian theory. I. Basics. Concep Magn Reson A. 2016;45A:e21414. doi: 10.1002/cmr.a.21414. DOI

Engelke F. Electromagnetic wave compression and radio frequency homogeneity in NMR solenoidal coils: Computational approach. Concept Magnetic Res. 2002;15:129–155. doi: 10.1002/cmr.10029. DOI

Gupta R, Hou G, Polenova T, Vega AJ. RF inhomogeneity and how it controls CPMAS. Solid State Nucl Mag. 2015;72:17–26. doi: 10.1016/j.ssnmr.2015.09.005. PubMed DOI PMC

Hartmann SR, Hahn EL. Nuclear Double Resonance in the Rotating Frame. Phys Rev. 1962;128:2042–2053.

Hassan A, Quinn CM, Struppe J, Sergeyev IV, Zhang C, Guo C, Runge B, Theint T, Dao HH, Jaroniec CP, Berbon M, Lends A, Habenstein B, Loquet A, Kuemmerle R, Perrone B, Gronenborn AM, Polenova T. Sensitivity boosts by the CPMAS CryoProbe for challenging biological assemblies. J Magn Reson. 2020;311:106680. doi: 10.1016/j.jmr.2019.106680. PubMed DOI PMC

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. doi: 10.1016/0009-2614(95)00505-x. DOI

Hoult DI. The principle of reciprocity in signal strength calculations – A mathematical guide. Concept Magnetic Res. 2000;12:173–187. doi: 10.1002/1099-0534(2000)12:4<173::aid-cmr1>3.0.co;2-q. 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

Kelz JI, Kelly JE, Martin RW. 3D-printed dissolvable inserts for efficient and customizable fabrication of NMR transceiver coils. J Magn Reson. 2019;305:89–92. doi: 10.1016/j.jmr.2019.06.008. PubMed DOI PMC

Krahn A, Priller U, Emsley L, Engelke F. Resonator with reduced sample heating and increased homogeneity for solid-state NMR. J Magn Reson. 2008;191:78–92. doi: 10.1016/j.jmr.2007.12.004. PubMed DOI

Laage S, Sachleben JR, Steuernagel S, Pierattelli R, Pintacuda G, Emsley L. Fast acquisition of multi-dimensional spectra in solid-state NMR enabled by ultra-fast MAS. J Magn Reson. 2009;196:133–141. doi: 10.1016/j.jmr.2008.10.019. PubMed DOI

Levitt MH. Heteronuclear cross polarization in liquid-state nuclear magnetic resonance: Mismatch compensation and relaxation behavior. J Chem Phys. 1991;94:30–38. doi: 10.1063/1.460398. DOI

Lowe IJ. Free Induction Decays of Rotating Solids. Phys Rev Lett. 1959;2:285–287. doi: 10.1103/PhysRevLett.2.285. DOI

Marica F, Snider RF. An analytical formulation of CPMAS. Solid State Nucl Mag. 2003;23:28–49. doi: 10.1016/S0926-2040(02)00013-9. PubMed DOI

Marks D, Vega S. A Theory for Cross-Polarization NMR of Nonspinning and Spinning Samples. J Magn Reson Ser A. 1996;118:157–172. doi: 10.1006/jmra.1996.0024. DOI

Meier BH. Cross polarization under fast magic angle spinning: thermodynamical considerations. Chem Phys Lett. 1992;188:201–207. doi: 10.1016/0009-2614(92)90009-C. DOI

Metz G, Wu XL, Smith SO. 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

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

Peersen OB, Wu XL, Smith SO. Enhancement of CP-MAS Signals by Variable-Amplitude Cross Polarization. Compensation for Inhomogeneous B1 Fields. J Magn Reson Ser A. 1994;106:127–131. doi: 10.1006/jmra.1994.1014. DOI

Pines A, Gibby MG, Waugh JS. Proton-enhanced NMR of dilute spins in solids. J Chem Phys. 1973;59:569–590. doi: 10.1063/1.1680061. DOI

Privalov AF, Dvinskikh SV, Vieth HM. Coil design for large-volume high-B-1 homogeneity for solid-state NMR applications. J Magn Reson Ser A. 1996;123:157–160. doi: 10.1006/jmra.1996.0229. DOI

Ray S, Ladizhansky V, Vega S. Simulation of CPMAS signals at high spinning speeds. J Magn Reson. 1998;135:427–434. doi: 10.1006/jmre.1998.1562. PubMed DOI

Rovnyak D. Tutorial on analytic theory for cross-polarization in solid state NMR. Concep Magn Reson A. 2008;32A:254–276. doi: 10.1002/cmr.a.20115. DOI

Schaefer J. Encyclopedia of Magnetic Resonance. John Wiley & Sons, Ltd; Chichester, UK: 2007. A Brief History of the Combination of Cross Polarization and Magic Angle Spinning. DOI

Stejskal EO, Schaefer J, Waugh JS. Magic-angle spinning and polarization transfer in proton-enhanced NMR. J Magn Reson (1969) 1977;28:105–112. doi: 10.1016/0022-2364(77)90260-8. DOI

Tošner Z, Andersen R, Stevenss B, Eden M, Nielsen NC, Vosegaard T, Stevensson B, Eden M, Nielsen NC, Vosegaard T. Computer-intensive simulation of solid-state NMR experiments using SIMPSON. J Magn Reson. 2014;246:79–93. doi: 10.1016/j.jmr.2014.07.002. PubMed DOI

Tošner Z, Purea A, Struppe JO, Wegner S, 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

Wu XL, Zilm KW. Cross Polarization with High-Speed Magic-Angle Spinning. J Magn Reson Ser A. 1993;104:154–165. doi: 10.1006/jmra.1993.1203. DOI