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Garg R, Pandey MK, Ramachandran R. Bimodal Floquet theory of phase-modulated heteronuclear decoupling experiments in solid-state NMR spectroscopy. J Chem Phys 2021; 155:104102. [PMID: 34525823 DOI: 10.1063/5.0061883] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A prescription based on bimodal Floquet theory is proposed to describe the nuances of phase-modulated supercycled decoupling experiments in solids. The frequency dependent interaction frames relevant to a particular supercycle are identified to facilitate faster convergence of perturbation corrections to the derived effective Hamiltonians. In contrast to silico-based methods, the proposed analytic method offers an attractive platform for faster optimization of experiments in solids. Additionally, the relevance of supercycling at ultrafast spinning conditions is also discussed.
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Affiliation(s)
- Rajat Garg
- Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, Manauli P.O. Box-140306, Mohali, Punjab, India
| | - Manoj Kumar Pandey
- Department of Chemistry, Indian Institute of Technology (IIT) Ropar, P.O. Box-140001, Rupnagar, Punjab, India
| | - Ramesh Ramachandran
- Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, Manauli P.O. Box-140306, Mohali, Punjab, India
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2
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Garg R, Ramachandran R. A theoretical perspective on the suitability of bimodal Floquet theory in the description of heteronuclear decoupling in solids. J Chem Phys 2020; 153:034105. [DOI: 10.1063/5.0012894] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Rajat Garg
- Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, Manauli P.O. Box-140306, Mohali, Punjab, India
| | - Ramesh Ramachandran
- Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, Manauli P.O. Box-140306, Mohali, Punjab, India
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3
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Theoretical approaches to control spin dynamics in solid-state nuclear magnetic resonance. J CHEM SCI 2015. [DOI: 10.1007/s12039-015-0977-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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4
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Pandey MK, Qadri Z, Ramachandran R. Understanding cross-polarization (CP) NMR experiments through dipolar truncation. J Chem Phys 2013; 138:114108. [PMID: 23534628 DOI: 10.1063/1.4794856] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A theoretical model based on the phenomenon of dipolar truncation is proposed to explain the nuances of polarization transfer from abundant to less-abundant nuclei in cross-polarization (CP) NMR experiments. Specifically, the transfer of polarization from protons to carbons (in solids) in strongly coupled systems is described in terms of effective Hamiltonians based on dipolar truncation. Through suitable model spin systems, the important role of dipolar truncation in the propagation of spin polarization in CP experiments is outlined. We believe that the analytic theory presented herein provides a convenient framework for modeling polarization transfer in strongly coupled systems.
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Affiliation(s)
- Manoj Kumar Pandey
- Department of Chemical Sciences, Indian Institute of Science Education and Research Mohali, Sector 81, Manauli P.O. Box-140306, Mohali, Punjab, India
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Tatton AS, Frantsuzov I, Brown SP, Hodgkinson P. Unexpected effects of third-order cross-terms in heteronuclear spin systems under simultaneous radio-frequency irradiation and magic-angle spinning NMR. J Chem Phys 2012; 136:084503. [DOI: 10.1063/1.3684879] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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6
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Mananga ES, Charpentier T. Introduction of the Floquet-Magnus expansion in solid-state nuclear magnetic resonance spectroscopy. J Chem Phys 2011; 135:044109. [DOI: 10.1063/1.3610943] [Citation(s) in RCA: 61] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Pandey MK, Krishnan MS. Effective Floquet Hamiltonians for dipolar and quadrupolar coupled N-spin systems in solid state nuclear magnetic resonance under magic angle spinning. J Chem Phys 2010; 133:174121. [DOI: 10.1063/1.3496407] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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8
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Leskes M, Madhu PK, Vega S. Floquet theory in solid-state nuclear magnetic resonance. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2010; 57:345-380. [PMID: 20920756 DOI: 10.1016/j.pnmrs.2010.06.002] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2010] [Accepted: 06/11/2010] [Indexed: 05/29/2023]
Affiliation(s)
- Michal Leskes
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
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Scholz I, van Beek JD, Ernst M. Operator-based Floquet theory in solid-state NMR. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2010; 37:39-59. [PMID: 20573488 DOI: 10.1016/j.ssnmr.2010.04.003] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2010] [Accepted: 04/30/2010] [Indexed: 05/14/2023]
Abstract
This article reviews the application of operator-based Floquet theory in solid-state NMR. Basic expressions for calculating effective Hamiltonians based on van Vleck perturbation theory are reviewed for problems with a single frequency or multiple incommensurate frequencies. Such a treatment allows calculation of effective Hamiltonians for resonant and non-resonant problems. Examples from literature are given for single-mode to triple-mode Floquet problems, covering a wide range of applications in solid-state NMR under magic-angle spinning and radio-frequency irradiation of a single nucleus or multiple nuclei.
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Affiliation(s)
- Ingo Scholz
- Physical Chemistry, ETH Zürich, Wolfgang-Pauli-Strasse 10, 8093 Zürich, Switzerland
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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] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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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. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2009; 196:133-41. [PMID: 19028122 DOI: 10.1016/j.jmr.2008.10.019] [Citation(s) in RCA: 84] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2008] [Revised: 10/29/2008] [Accepted: 10/29/2008] [Indexed: 05/10/2023]
Abstract
The advantages offered by ultra-fast (>60 kHz) magic angle spinning (MAS) rotation for the study of biological samples, notably containing paramagnetic centers are explored. It is shown that optimal conditions for performing solid-state (13)C NMR under 60 kHz MAS are obtained with low-power CW (1)H decoupling, as well as after a low-power (1)H,(13)C cross-polarization step at a double-quantum matching condition. Acquisition with low-power decoupling highlights the existence of rotational decoupling sidebands. The sideband intensities and the existence of first and second rotary conditions are explained in the framework of the Floquet-van Vleck theory. As a result, optimal (13)C spectra of the oxidized, paramagnetic form of human copper zinc superoxide dismutase (SOD) can be obtained employing rf-fields which do not exceed 40 kHz during the whole experiment. This enables the removal of unwanted heating which can lead to deterioration of the sample. Furthermore, combined with the short (1)H T(1)s, this allows the repetition rate of the experiments to be shortened from 3 s to 500 ms, thus compensating for the sensitivity loss due to the smaller sample volume in a 1.3 mm rotor. The result is that 2D (13)C-(13)C correlation could be acquired in about 24 h on less than 1 mg of SOD sample.
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Affiliation(s)
- Ségolène Laage
- Université de Lyon, CNRS/ENS Lyon/UCB-Lyon 1, Centre RMN à Très Hauts Champs, 5 rue de la Doua, 69100 Villeurbanne, France
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Bayro MJ, Ramachandran R, Caporini MA, Eddy MT, Griffin RG. Radio frequency-driven recoupling at high magic-angle spinning frequencies: homonuclear recoupling sans heteronuclear decoupling. J Chem Phys 2008; 128:052321. [PMID: 18266438 DOI: 10.1063/1.2834736] [Citation(s) in RCA: 70] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We describe solid-state NMR homonuclear recoupling experiments at high magic-angle spinning (MAS) frequencies using the radio frequency-driven recoupling (RFDR) scheme. The effect of heteronuclear decoupling interference during RFDR recoupling at high spinning frequencies is investigated experimentally and via numerical simulations, resulting in the identification of optimal decoupling conditions. The effects of MAS frequency, RF field amplitude, bandwidth, and chemical shift offsets are examined. Most significantly, it is shown that broadband homonuclear correlation spectra can be efficiently obtained using RFDR without decoupling during the mixing period in fully protonated samples, thus considerably reducing the rf power requirements for acquisition of (13)C-(13)C correlation spectra. The utility of RFDR sans decoupling is demonstrated with broadband correlation spectra of a peptide and a model protein at high MAS frequencies and high magnetic field.
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Affiliation(s)
- Marvin J Bayro
- Francis Bitter Magnet Laboratory and Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Willans MJ, Sears DN, Wasylishen RE. The effectiveness of 1H decoupling in the 13C MAS NMR of paramagnetic solids: an experimental case study incorporating copper(II) amino acid complexes. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2008; 191:31-46. [PMID: 18086543 DOI: 10.1016/j.jmr.2007.11.012] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2007] [Revised: 11/17/2007] [Accepted: 11/21/2007] [Indexed: 05/25/2023]
Abstract
The use of continuous-wave (CW) 1H decoupling has generally provided little improvement in the 13C MAS NMR spectroscopy of paramagnetic organic solids. Recent solid-state 13C NMR studies have demonstrated that at rapid magic-angle spinning rates CW decoupling can result in reductions in signal-to-noise and that 1H decoupling should be omitted when acquiring 13C MAS NMR spectra of paramagnetic solids. However, studies of the effectiveness of modern 1H decoupling sequences are lacking, and the performance of such sequences over a variety of experimental conditions must be investigated before 1H decoupling is discounted altogether. We have studied the performance of several commonly used advanced decoupling pulse sequences, namely the TPPM, SPINAL-64, XiX, and eDROOPY sequences, in 13C MAS NMR experiments performed under four combinations of the magnetic field strength (7.05 or 11.75T), rotor frequency (15 or 30kHz), and 1H rf-field strength (71, 100, or 140kHz). The effectiveness of these sequences has been evaluated by comparing the 13C signal intensity, linewidth at half-height, LWHH, and coherence lifetimes, T2('), of the methine carbon of copper(II) bis(dl-alanine) monohydrate, Cu(ala)(2).H2O, and methylene carbon of copper(II) bis(dl-2-aminobutyrate), Cu(ambut)(2), obtained with the advanced sequences to those obtained without 1H decoupling, with CW decoupling, and for fully deuterium labelled samples. The latter have been used as model compounds with perfect 1H decoupling and provide a measure of the efficiency of the 1H decoupling sequence. Overall, the effectiveness of 1H decoupling depends strongly on the decoupling sequence utilized, the experimental conditions and the sample studied. Of the decoupling sequences studied, the XiX sequence consistently yielded the best results, although any of the advanced decoupling sequences strongly outperformed the CW sequence and provided improvements over no 1H decoupling. Experiments performed at 7.05T demonstrate that the XiX decoupling sequence is the least sensitive to changes in the 1H transmitter frequency and may explain the superior performance of this decoupling sequence. Overall, the most important factor in the effectiveness of 1H decoupling was the carbon type studied, with the methylene carbon of Cu(ambut)(2) being substantially more sensitive to 1H decoupling than the methine carbon of Cu(ala)(2).H2O. An analysis of the various broadening mechanisms contributing to 13C linewidths has been performed in order to rationalize the different sensitivities of the two carbon sites under the four experimental conditions.
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Affiliation(s)
- Mathew J Willans
- Department of Chemistry, University of Alberta, Edmonton, Alta., Canada T6G 2G2
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14
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Effective Floquet Hamiltonian for spin I = 1 in magic angle spinning NMR using contact transformation. J CHEM SCI 2008. [DOI: 10.1007/s12039-007-0054-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Scholz I, Meier BH, Ernst M. Operator-based triple-mode Floquet theory in solid-state NMR. J Chem Phys 2007; 127:204504. [DOI: 10.1063/1.2800319] [Citation(s) in RCA: 61] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ramachandran R, Griffin RG. Description of depolarization effects in double-quantum solid state nuclear magnetic resonance experiments using multipole-multimode Floquet theory. J Chem Phys 2007; 125:44510. [PMID: 16942159 DOI: 10.1063/1.2216711] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using an analytical model based on multipole-multimode Floquet theory (MMFT), we describe the polarization loss (or depolarization) observed in double-quantum (DQ) dipolar recoupling magic angle spinning (MAS) experiments. Specifically, the factors responsible for depolarization are analyzed in terms of higher order corrections to the spin Hamiltonian in addition to the usual phenomenological decay rate constant. From the MMFT model and the effective Hamiltonians, we elucidate the rationale behind the inclusion of a phenomenological damping term in DQ recoupling experiments. As a test of this theoretical approach, the recoupling efficiency of one class of (13)C-(13)C and (13)C-(15)N resonance width dipolar recoupling experiments are investigated at different magnetic field strengths and compared with the more exact numerical simulations. In contrast to existing analytical treatments, the role of higher order corrections is clearly explained in the context of the MMFT approach leading to a better understanding of the underlying spin physics. Furthermore, the analytical model presented herein provides a general framework for describing coherent and incoherent effects in homonuclear and heteronuclear DQ MAS recoupling experiments.
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Affiliation(s)
- Ramesh Ramachandran
- Francis Bitter Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Leskes M, Thakur RS, Madhu PK, Kurur ND, Vega S. Bimodal Floquet description of heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance. J Chem Phys 2007; 127:024501. [PMID: 17640131 DOI: 10.1063/1.2746039] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A theoretical treatment of heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance is presented here based on bimodal Floquet theory. The conditions necessary for good heteronuclear decoupling are derived. An analysis of a few of the decoupling schemes implemented until date is presented with regard to satisfying such decoupling conditions and efficiency of decoupling. Resonance conditions for efficient heteronuclear dipolar decoupling are derived with and without the homonuclear (1)H-(1)H dipolar couplings and their influence on heteronuclear dipolar decoupling is pointed out. The analysis points to the superior efficiency of the newly introduced swept two-pulse phase-modulation (SW(f)-TPPM) sequence. It is shown that the experimental robustness of SW(f)-TPPM as compared to the original TPPM sequence results from an adiabatic sweeping of the modulation frequencies. Based on this finding alternative strategies are compared here. The theoretical findings are corroborated by both numerical simulations and representative experiments.
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Affiliation(s)
- Michal Leskes
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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Sachleben JR, Gaba J, Emsley L. Floquet-van Vleck analysis of heteronuclear spin decoupling in solids: the effect of spinning and decoupling sidebands on the spectrum. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2006; 29:30-51. [PMID: 16289719 DOI: 10.1016/j.ssnmr.2005.09.009] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2005] [Revised: 09/23/2005] [Indexed: 05/05/2023]
Abstract
We investigate the effect of magic angle spinning on heteronuclear spin decoupling in solids. We use an analytical Floquet-van Vleck formalism to derive expressions for the powder-averaged signal as a function of time. These expressions show that the spectrum consists of a centerband at the isotropic frequency of the observed spin, omega(0), and rotational decoupling sidebands at omega(0)+/-omega(1)+/-momega(r), where omega(1) is the decoupling field strength and omega(r) is the rotation frequency. Rotary resonance occurs when the rotational decoupling sidebands overlap with the centerband. Away from the rotary resonance conditions, the intensity of the centerband as a function of omega(r)/omega(1) is simply related to the total intensity of the rotational decoupling sidebands. Notably, in the absence of offset terms it is shown that as omega(1) decreases, the centerband intensity can decrease without any associated broadening. Furthermore, the centerband width is shown to be independent of spinning speed, to second order for the effects we consider. The effects of I spin chemical shift anisotropy and homonuclear dipolar couplings are also investigated. The analytical results are compared to simulations and experiments.
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