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Camenisch GM, Wili N, Jeschke G, Ernst M. Pulsed dynamic nuclear polarization: a comprehensive Floquet description. Phys Chem Chem Phys 2024; 26:17666-17683. [PMID: 38868989 PMCID: PMC11202326 DOI: 10.1039/d4cp01788a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2024] [Accepted: 06/05/2024] [Indexed: 06/14/2024]
Abstract
Dynamic nuclear polarization (DNP) experiments using microwave (mw) pulse sequences are one approach to transfer the larger polarization on the electron spin to nuclear spins of interest. How the result of such experiments depends on the external magnetic field and the excitation power is part of an ongoing debate and of paramount importance for applications that require high chemical-shift resolution. To date numerical simulations using operator-based Floquet theory have been used to predict and explain experimental data. However, such numerical simulations provide only limited insight into parameters relevant for efficient polarization transfer, such as transition amplitudes or resonance offsets. Here we present an alternative method to describe pulsed DNP experiments by using matrix-based Floquet theory. This approach leads to analytical expressions for the transition amplitudes and resonance offsets. We validate the method by comparing computations by these analytical expressions to their numerical counterparts and to experimental results for the XiX, TOP and TPPM DNP sequences. Our results explain the experimental data and are in very good agreement with the numerical simulations. The analytical expressions allow for the discussion of the scaling behaviour of pulsed DNP experiments with respect to the external magnetic field. We find that the transition amplitudes scale inversely with the external magnetic field.
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Affiliation(s)
- Gian-Marco Camenisch
- Department of Chemistry and Applied Biosciences, ETH Zürich, Zürich, Switzerland.
| | - Nino Wili
- Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, Aarhus, Denmark
| | - Gunnar Jeschke
- Department of Chemistry and Applied Biosciences, ETH Zürich, Zürich, Switzerland.
| | - Matthias Ernst
- Department of Chemistry and Applied Biosciences, ETH Zürich, Zürich, Switzerland.
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Nishiyama Y, Hou G, Agarwal V, Su Y, Ramamoorthy A. Ultrafast Magic Angle Spinning Solid-State NMR Spectroscopy: Advances in Methodology and Applications. Chem Rev 2023; 123:918-988. [PMID: 36542732 PMCID: PMC10319395 DOI: 10.1021/acs.chemrev.2c00197] [Citation(s) in RCA: 39] [Impact Index Per Article: 39.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Solid-state NMR spectroscopy is one of the most commonly used techniques to study the atomic-resolution structure and dynamics of various chemical, biological, material, and pharmaceutical systems spanning multiple forms, including crystalline, liquid crystalline, fibrous, and amorphous states. Despite the unique advantages of solid-state NMR spectroscopy, its poor spectral resolution and sensitivity have severely limited the scope of this technique. Fortunately, the recent developments in probe technology that mechanically rotate the sample fast (100 kHz and above) to obtain "solution-like" NMR spectra of solids with higher resolution and sensitivity have opened numerous avenues for the development of novel NMR techniques and their applications to study a plethora of solids including globular and membrane-associated proteins, self-assembled protein aggregates such as amyloid fibers, RNA, viral assemblies, polymorphic pharmaceuticals, metal-organic framework, bone materials, and inorganic materials. While the ultrafast-MAS continues to be developed, the minute sample quantity and radio frequency requirements, shorter recycle delays enabling fast data acquisition, the feasibility of employing proton detection, enhancement in proton spectral resolution and polarization transfer efficiency, and high sensitivity per unit sample are some of the remarkable benefits of the ultrafast-MAS technology as demonstrated by the reported studies in the literature. Although the very low sample volume and very high RF power could be limitations for some of the systems, the advantages have spurred solid-state NMR investigation into increasingly complex biological and material systems. As ultrafast-MAS NMR techniques are increasingly used in multidisciplinary research areas, further development of instrumentation, probes, and advanced methods are pursued in parallel to overcome the limitations and challenges for widespread applications. This review article is focused on providing timely comprehensive coverage of the major developments on instrumentation, theory, techniques, applications, limitations, and future scope of ultrafast-MAS technology.
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Affiliation(s)
- Yusuke Nishiyama
- JEOL Ltd., Akishima, Tokyo196-8558, Japan
- RIKEN-JEOL Collaboration Center, Yokohama, Kanagawa230-0045, Japan
| | - Guangjin Hou
- State Key Laboratory of Catalysis, Dalian National Laboratory for Clean Energy, 2011-Collaborative Innovation Center of Chemistry for Energy Materials, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Zhongshan Road 457, Dalian116023, China
| | - Vipin Agarwal
- Tata Institute of Fundamental Research, Sy. No. 36/P, Gopanpally, Hyderabad500 046, India
| | - Yongchao Su
- Analytical Research and Development, Merck & Co., Inc., Rahway, New Jersey07065, United States
| | - Ayyalusamy Ramamoorthy
- Biophysics, Department of Chemistry, Biomedical Engineering, Macromolecular Science and Engineering, Michigan Neuroscience Institute, University of Michigan, Ann Arbor, Michigan41809-1055, United States
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3
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Abstract
In the last two decades, solid-state nuclear magnetic resonance (ssNMR) spectroscopy has transformed from a spectroscopic technique investigating small molecules and industrial polymers to a potent tool decrypting structure and underlying dynamics of complex biological systems, such as membrane proteins, fibrils, and assemblies, in near-physiological environments and temperatures. This transformation can be ascribed to improvements in hardware design, sample preparation, pulsed methods, isotope labeling strategies, resolution, and sensitivity. The fundamental engagement between nuclear spins and radio-frequency pulses in the presence of a strong static magnetic field is identical between solution and ssNMR, but the experimental procedures vastly differ because of the absence of molecular tumbling in solids. This review discusses routinely employed state-of-the-art static and MAS pulsed NMR methods relevant for biological samples with rotational correlation times exceeding 100's of nanoseconds. Recent developments in signal filtering approaches, proton methodologies, and multiple acquisition techniques to boost sensitivity and speed up data acquisition at fast MAS are also discussed. Several examples of protein structures (globular, membrane, fibrils, and assemblies) solved with ssNMR spectroscopy have been considered. We also discuss integrated approaches to structurally characterize challenging biological systems and some newly emanating subdisciplines in ssNMR spectroscopy.
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Affiliation(s)
- Sahil Ahlawat
- Tata Institute of Fundamental Research Hyderabad, Survey No. 36/P Gopanpally, Serilingampally, Ranga Reddy District, Hyderabad 500046, Telangana, India
| | - Kaustubh R Mote
- Tata Institute of Fundamental Research Hyderabad, Survey No. 36/P Gopanpally, Serilingampally, Ranga Reddy District, Hyderabad 500046, Telangana, India
| | - Nils-Alexander Lakomek
- University of Düsseldorf, Institute for Physical Biology, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Vipin Agarwal
- Tata Institute of Fundamental Research Hyderabad, Survey No. 36/P Gopanpally, Serilingampally, Ranga Reddy District, Hyderabad 500046, Telangana, India
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4
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Ivanov KL, Mote KR, Ernst M, Equbal A, Madhu PK. Floquet theory in magnetic resonance: Formalism and applications. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2021; 126-127:17-58. [PMID: 34852924 DOI: 10.1016/j.pnmrs.2021.05.002] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2020] [Revised: 04/30/2021] [Accepted: 05/19/2021] [Indexed: 06/13/2023]
Abstract
Floquet theory is an elegant mathematical formalism originally developed to solve time-dependent differential equations. Besides other fields, it has found applications in optical spectroscopy and nuclear magnetic resonance (NMR). This review attempts to give a perspective of the Floquet formalism as applied in NMR and shows how it allows one to solve various problems with a focus on solid-state NMR. We include both matrix- and operator-based approaches. We discuss different problems where the Hamiltonian changes with time in a periodic way. Such situations occur, for example, in solid-state NMR experiments where the time dependence of the Hamiltonian originates either from magic-angle spinning or from the application of amplitude- or phase-modulated radiofrequency fields, or from both. Specific cases include multiple-quantum and multiple-frequency excitation schemes. In all these cases, Floquet analysis allows one to define an effective Hamiltonian and, moreover, to treat cases that cannot be described by the more popularly used and simpler-looking average Hamiltonian theory based on the Magnus expansion. An important example is given by spin dynamics originating from multiple-quantum phenomena (level crossings). We show that the Floquet formalism is a very general approach for solving diverse problems in spectroscopy.
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Affiliation(s)
- Konstantin L Ivanov
- International Tomographic Center, Institutskaya 3A, Novosibirsk 630090, Russia; Novosibirsk State University, Pirogova 1, Novosibirsk 630090, Russia
| | - Kaustubh R Mote
- Tata Institute of Fundamental Research Hyderabad, 36/P Gopanpally Village, Ranga Reddy District, Hyderabad 500046, India
| | - Matthias Ernst
- ETH Zurich, Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Asif Equbal
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, CA 93106, United States
| | - Perunthiruthy K Madhu
- Tata Institute of Fundamental Research Hyderabad, 36/P Gopanpally Village, Ranga Reddy District, Hyderabad 500046, India.
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Nakai T. Perturbation Approach for NMR Signals with Infinite-Order Corrections and Its Application to Solid-State MAS INADEQUATE Spectra Exhibiting Auto-Correlation Peaks due to Chemically-Equivalent Spin Pairs: Analogy to Renormalization Theory. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2021. [DOI: 10.1246/bcsj.20200360] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Toshihito Nakai
- JEOL RESONANCE Inc., 3-1-2 Musashino, Akishima, Tokyo 196-8558, Japan
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6
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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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7
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Garg R, Ramachandran R. Theory of coherent averaging in magnetic resonance using effective Hamiltonians. J Chem Phys 2020; 153:034106. [DOI: 10.1063/5.0012892] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [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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8
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Mananga ES. Application of Floquet-Magnus and Fer expansion approaches during spin-locking radiation in solid-state NMR. Chem Phys Lett 2019. [DOI: 10.1016/j.cplett.2019.05.054] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Sharma K, Equbal A, Nielsen NC, Madhu PK. A unified heteronuclear decoupling picture in solid-state NMR under low radio-frequency amplitude and fast magic-angle-spinning frequency regime. J Chem Phys 2019; 150:144201. [PMID: 30981235 DOI: 10.1063/1.5082352] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Heteronuclear spin decoupling is a highly important component of solid-state NMR experiments to remove undesired coupling interactions between unlike spins for spectral resolution. Recently, experiments using a unification strategy of standard decoupling schemes were presented for high radio-frequency (RF) amplitudes and slow-intermediate magic-angle-spinning (MAS) frequencies, in the pursuit of deeper understanding of spin decoupling under phase-modulated RF irradiation [A. Equbal et al., J. Chem. Phys. 142, 184201 (2015)]. The approach, unified two-pulse heteronuclear decoupling (UTPD), incorporates the simultaneous time- and phase-modulation strategies, commonly used in solid-state NMR. Here, the UTPD based decoupling scheme is extended to the experimentally increasingly important regime of low RF amplitudes and fast MAS frequencies. The unified decoupling approach becomes increasingly effective in identifying the deleterious dipole-dipole and, in particular, J recoupling conditions which become critical for the low-amplitude RF regime. This is because J coupling is isotropic and therefore not averaged out by sample spinning unlike the anisotropic dipole-dipole coupling. Numerical simulations and analytic theory are used to understand the effects of various nuclear spin interactions on the decoupling performance of UTPD, in particular, the crucial difference between the low-phase and high-phase UTPD conditions with respect to J coupling. In the UTPD scheme, when the cycle-frequency of the pulse-sequence is comparable to the RF nutation frequency, the existence of a non-zero effective rotation in the basic two-pulse scheme becomes an essential feature for the efficient and robust averaging out of the scalar J coupling. This broad viewpoint is expected to bring different optimum low-power decoupling pulse schemes under a common footing.
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Affiliation(s)
- Kshama Sharma
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Gopanpally, Hyderabad 500 107, India
| | - Asif Equbal
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Gopanpally, Hyderabad 500 107, India
| | - Niels Chr Nielsen
- 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
| | - P K Madhu
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Gopanpally, Hyderabad 500 107, India
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10
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Jain MG, Sreedevi KN, Equbal A, Madhu PK, Agarwal V. Refocusing pulses: A strategy to improve efficiency of phase-modulated heteronuclear decoupling schemes in MAS solid-state NMR. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2017; 284:59-65. [PMID: 28961478 DOI: 10.1016/j.jmr.2017.09.010] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2017] [Revised: 09/04/2017] [Accepted: 09/16/2017] [Indexed: 06/07/2023]
Abstract
The strategy of using π pulses in conjunction with continuous-wave radio-frequency fields to refocus spin interactions has lead to robust and efficient family of heteronuclear decoupling schemes in magic-angle spinning solid-state NMR, denoted as, rCW schemes. Here, we investigate the generality of the application of such refocussing pulses in other phase-modulated decoupling schemes, notably the super-cycled XiX decoupling. XiX is a commonly used heteronuclear decoupling scheme under conditions of fast MAS and low-amplitude radio-frequency irradiation. The refocussing of interactions is achieved by inserting π pulses with a phase of 135° in the supercycled XiX scheme. The refocussed XiX, rXiX, scheme has improved decoupling efficiency, better offset tolerance, and easier experimental setup compared to the XiX scheme.
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Affiliation(s)
- Mukul G Jain
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research Hyderabad, Sy. No. 36/P, Gopanpally, Ranga Reddy District, Hyderabad 500 017, India
| | - K N Sreedevi
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research Hyderabad, Sy. No. 36/P, Gopanpally, Ranga Reddy District, Hyderabad 500 017, India
| | - Asif Equbal
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research Hyderabad, Sy. No. 36/P, Gopanpally, Ranga Reddy District, Hyderabad 500 017, India
| | - P K Madhu
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research Hyderabad, Sy. No. 36/P, Gopanpally, Ranga Reddy District, Hyderabad 500 017, India; Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Vipin Agarwal
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research Hyderabad, Sy. No. 36/P, Gopanpally, Ranga Reddy District, Hyderabad 500 017, India.
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11
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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 2017; 145:094201. [PMID: 27608994 DOI: 10.1063/1.4961909] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a generalized theoretical framework that allows the approximate but rapid analysis of residual couplings of arbitrary decoupling sequences in solid-state NMR under magic-angle spinning conditions. It is a generalization of the tri-modal Floquet analysis of TPPM decoupling [Scholz et al., J. Chem. Phys. 130, 114510 (2009)] where three characteristic frequencies are used to describe the pulse sequence. Such an approach can be used to describe arbitrary periodic decoupling sequences that differ only in the magnitude of the Fourier coefficients of the interaction-frame transformation. It allows a ∼100 times faster calculation of second-order residual couplings as a function of pulse sequence parameters than full spin-dynamics simulations. By comparing the theoretical calculations with full numerical simulations, we show the potential of the new approach to examine the performance of decoupling sequences. We exemplify the usefulness of this framework by analyzing the performance of commonly used high-power decoupling sequences and low-power decoupling sequences such as amplitude-modulated XiX (AM-XiX) and its super-cycled variant SC-AM-XiX. In addition, the effect of chemical-shift offset is examined for both high- and low-power decoupling sequences. The results show that the cross-terms between the dipolar couplings are the main contributions to the line broadening when offset is present. We also show that the SC-AM-XIX shows a better offset compensation.
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Affiliation(s)
- Kong Ooi Tan
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Vipin Agarwal
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Beat H Meier
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Matthias Ernst
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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12
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Equbal A, Shankar R, Leskes M, Vega S, Nielsen NC, Madhu PK. Significance of symmetry in the nuclear spin Hamiltonian for efficient heteronuclear dipolar decoupling in solid-state NMR: A Floquet description of supercycled rCW schemes. J Chem Phys 2017; 146:104202. [PMID: 28298092 DOI: 10.1063/1.4977738] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Symmetry plays an important role in the retention or annihilation of a desired interaction Hamiltonian in NMR experiments. Here, we explore the role of symmetry in the radio-frequency interaction frame Hamiltonian of the refocused-continuous-wave (rCW) pulse scheme that leads to efficient 1H heteronuclear decoupling in solid-state NMR. It is demonstrated that anti-periodic symmetry of single-spin operators (Ix, Iy, Iz) in the interaction frame can lead to complete annihilation of the 1H-1H homonuclear dipolar coupling effects that induce line broadening in solid-state NMR experiments. This symmetry also plays a critical role in cancelling or minimizing the effect of 1H chemical-shift anisotropy in the effective Hamiltonian. An analytical description based on Floquet theory is presented here along with experimental evidences to understand the decoupling efficiency of supercycled (concatenated) rCW scheme.
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Affiliation(s)
- Asif Equbal
- 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
| | - Ravi Shankar
- 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
| | - Michal Leskes
- Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Shimon Vega
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Niels Chr Nielsen
- 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
| | - P K Madhu
- TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500 075, India
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13
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Equbal A, Madhu PK, Meier BH, Nielsen NC, Ernst M, Agarwal V. Parameter independent low-power heteronuclear decoupling for fast magic-angle spinning solid-state NMR. J Chem Phys 2017; 146:084202. [DOI: 10.1063/1.4976997] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Asif Equbal
- TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500 075, India
- Center for Insoluble Protein Structures (inSpin) and Center for Ultrahigh-Field NMR Spectroscopy, Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, Gustav Wieds Vej 14, DK-8000 Aarhus C, Denmark
| | - P. K. Madhu
- TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500 075, India
- Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Beat H. Meier
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Niels Chr. Nielsen
- Center for Insoluble Protein Structures (inSpin) and Center for Ultrahigh-Field NMR Spectroscopy, Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, Gustav Wieds Vej 14, DK-8000 Aarhus C, Denmark
| | - Matthias Ernst
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Vipin Agarwal
- TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500 075, India
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14
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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. [PMID: 28111874 PMCID: PMC5396389 DOI: 10.1002/cphc.201601003] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2016] [Revised: 11/07/2016] [Indexed: 12/16/2022]
Abstract
Factors affecting the performance of 1 H heteronuclear decoupling sequences for magic-angle spinning (MAS) NMR spectroscopy of organic solids are explored, as observed by time constants for the decay of nuclear magnetisation under a spin-echo (T2' ). By using a common protocol over a wide range of experimental conditions, including very high magnetic fields and very high radio-frequency (RF) nutation rates, decoupling performance is observed to degrade consistently with increasing magnetic field. Inhomogeneity of the RF field is found to have a significant impact on T2' values, with differences of about 20 % observed between probes with different coil geometries. Increasing RF nutation rates dramatically improve robustness with respect to RF offset, but the performance of phase-modulated sequences degrades at the very high nutation rates achievable in microcoils as a result of RF transients. The insights gained provide better understanding of the factors limiting decoupling performance under different conditions, and the high values of T2' observed (which generally exceed previous literature values) provide reference points for experiments involving spin magnetisation refocussing, such as 2D correlation spectra and measuring small spin couplings.
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Affiliation(s)
- Ilya Frantsuzov
- Department of ChemistryDurham UniversitySouth RoadDurhamDH1 3LEUnited Kingdom
| | - Suresh K. Vasa
- Institute for Molecules and MaterialsRadboud UniversityHeyendaalseweg 1356525 EDNijmegenThe Netherlands
| | - Matthias Ernst
- Laboratory of Physical ChemistryETH ZürichVladimir-Prelog-Weg 28093ZürichSwitzerland
| | - Steven P. Brown
- Department of PhysicsUniversity of WarwickCoventryCV4 7ALUnited Kingdom
| | - Vadim Zorin
- Agilent Technologies (UK) Ltd.6 Mead RoadYarntonOxfordshireOX5 1QUUnited Kingdom
- Mestrelab ResearchS.L Feliciano Barrera 9B—Bajo15706Santiago de CompostelaSpain
| | - Arno P. M. Kentgens
- Institute for Molecules and MaterialsRadboud UniversityHeyendaalseweg 1356525 EDNijmegenThe Netherlands
| | - Paul Hodgkinson
- Department of ChemistryDurham UniversitySouth RoadDurhamDH1 3LEUnited Kingdom
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15
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Sharma K, Madhu PK, Agarwal V. Systematic evaluation of heteronuclear spin decoupling in solid-state NMR at the rotary-resonance conditions in the regime of fast magic-angle spinning. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2016; 270:136-141. [PMID: 27472380 DOI: 10.1016/j.jmr.2016.07.007] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2016] [Revised: 07/15/2016] [Accepted: 07/18/2016] [Indexed: 06/06/2023]
Abstract
The performance of heteronuclear spin decoupling sequences in solid-state NMR severely degrades when the proton radiofrequency (RF) nutation frequencies (ν1) are close to or at multiples of magic-angle spinning (MAS) frequency (νr) that are referred to as rotary-resonance recoupling conditions (ν1=n·νr). Recently, two schemes, namely, PISSARRO and rCW(ApA), have been shown to be less affected by the problem of MAS and RF interference, specifically at the n=2 rotary-resonance recoupling condition, especially in the fast MAS regime. Here, we systematically evaluate the loss in intensity of several heteronuclear spin decoupling sequences at the n=1, 2 conditions compared to high-power decoupling in the fast-MAS regime. We propose that in the fast-MAS regime (above 40kHz) the entire discussion about RF and MAS interference can be avoided by using appropriate low-power decoupling sequences which give comparable performance to decoupling sequences with high-power (1)H irradiation of ca.195kHz.
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Affiliation(s)
- Kshama Sharma
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Narsingi, Hyderabad 500 075, India
| | - P K Madhu
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Narsingi, Hyderabad 500 075, India; Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India.
| | - Vipin Agarwal
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Narsingi, Hyderabad 500 075, India.
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16
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Equbal A, Leskes M, Nielsen NC, Madhu PK, Vega S. Relative merits of rCW(A) and XiX heteronuclear spin decoupling in solid-state magic-angle-spinning NMR spectroscopy: A bimodal Floquet analysis. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2016; 263:55-64. [PMID: 26773527 DOI: 10.1016/j.jmr.2015.12.019] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2015] [Revised: 12/19/2015] [Accepted: 12/27/2015] [Indexed: 06/05/2023]
Abstract
We present a bimodal Floquet analysis of the recently introduced refocused continuous wave (rCW) solid-state NMR heteronuclear dipolar decoupling method and compare it with the similar looking X-inverse X (XiX) scheme. The description is formulated in the rf interaction frame and is valid for both finite and ideal π pulse rCW irradiation that forms the refocusing element in the rCW scheme. The effective heteronuclear dipolar coupling Hamiltonian up to first order is described. The analysis delineates the difference between the two sequences to different orders of their Hamiltonians for both diagonal and off-diagonal parts. All the resonance conditions observed in experiments and simulations have been characterised and their influence on residual line broadening is highlighted. The theoretical comparison substantiates the numerical simulations and experimental results to a large extent.
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Affiliation(s)
- Asif Equbal
- Center for Insoluble Protein Structures, Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, Gustav Wieds Vej 14, DK-8000 Aarhus C, Denmark
| | - Michal Leskes
- Weizmann Institute of Science, Department of Materials and Interfaces, Rehovot, Israel.
| | - Niels Chr Nielsen
- Center for Insoluble Protein Structures, Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, Gustav Wieds Vej 14, DK-8000 Aarhus C, Denmark.
| | - P K Madhu
- Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India; TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500075, India.
| | - Shimon Vega
- Weizmann Institute of Science, Department of Chemical Physics, Rehovot, Israel.
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17
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18
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Equbal A, Basse K, Nielsen NC. Highly efficient19F heteronuclear decoupling in solid-state NMR spectroscopy using supercycled refocused-CW irradiation. Phys Chem Chem Phys 2016; 18:30990-30997. [DOI: 10.1039/c6cp06574k] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present heteronuclear19F refocused CW (rCW) decoupling pulse sequences for solid-state magic-angle-spinning NMR applications.
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Affiliation(s)
- Asif Equbal
- Center for Insoluble Protein Structures (inSPIN)
- Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry
- Aarhus University
- Denmark
| | - Kristoffer Basse
- Center for Insoluble Protein Structures (inSPIN)
- Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry
- Aarhus University
- Denmark
| | - Niels Chr. Nielsen
- Center for Insoluble Protein Structures (inSPIN)
- Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry
- Aarhus University
- Denmark
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19
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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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20
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Frantsuzov I, Ernst M, Brown SP, Hodgkinson P. Simulating spin dynamics in organic solids under heteronuclear decoupling. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2015; 70:28-37. [PMID: 26073419 DOI: 10.1016/j.ssnmr.2015.05.003] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2014] [Revised: 04/14/2015] [Accepted: 05/07/2015] [Indexed: 06/04/2023]
Abstract
Although considerable progress has been made in simulating the dynamics of multiple coupled nuclear spins, predicting the evolution of nuclear magnetisation in the presence of radio-frequency decoupling remains challenging. We use exact numerical simulations of the spin dynamics under simultaneous magic-angle spinning and RF decoupling to determine the extent to which numerical simulations can be used to predict the experimental performance of heteronuclear decoupling for the CW, TPPM and XiX sequences, using the methylene group of glycine as a model system. The signal decay times are shown to be strongly dependent on the largest spin order simulated. Unexpectedly large differences are observed between the dynamics with and without spin echoes. Qualitative trends are well reproduced by modestly sized spin system simulations, and the effects of finite spin-system size can, in favourable cases, be mitigated by extrapolation. Quantitative prediction of the behaviour in complex parameter spaces is found, however, to be very challenging, suggesting that there are significant limits to the role of numerical simulations in RF decoupling problems, even when specialist techniques, such as state-space restriction, are used.
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Affiliation(s)
- Ilya Frantsuzov
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
| | - Matthias Ernst
- Laboratory of Physical Chemistry, ETH Zürich, Wolfgang-Pauli-Strasse 10, 8093 Zürich, Switzerland
| | - Steven P Brown
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Paul Hodgkinson
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom.
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21
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Mananga ES, Charpentier T. Floquet–Magnus expansion for general N-coupled spins systems in magic-angle spinning nuclear magnetic resonance spectra. Chem Phys 2015. [DOI: 10.1016/j.chemphys.2015.02.006] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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22
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Abstract
We describe a more broad-banded version of the DREAM double-quantum dipolar-recoupling sequence, which is devised by superimposing a phase-alternating RF irradiation scheme, that is, XiX pulses, on top of the original DREAM sequence. We call this sequence XiX(CW) DREAM. The recoupling conditions and the corresponding first-order effective Hamiltonian are analyzed using triple-mode Floquet theory. The performance of the XiX(CW) DREAM sequence is compared to the original DREAM sequence by numerical simulations and experiments on small model substances and the model protein ubiquitin. The results confirm that XiX(CW) DREAM shows a wider recoupling bandwidth compared to that of DREAM, therefore making the choice for the position of the carrier frequency less critical.
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Affiliation(s)
- Kong Ooi Tan
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Anders B Nielsen
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Beat H Meier
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Matthias Ernst
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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23
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Equbal A, Paul S, Mithu VS, Madhu PK, Nielsen NC. Efficient heteronuclear decoupling in MAS solid-state NMR using non-rotor-synchronized rCW irradiation. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2014; 246:104-109. [PMID: 25123538 DOI: 10.1016/j.jmr.2014.07.006] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2014] [Revised: 06/30/2014] [Accepted: 07/09/2014] [Indexed: 06/03/2023]
Abstract
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-(13)C-glycine and U-(13)C-L-histidine·HCl·H2O.
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Affiliation(s)
- Asif Equbal
- 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
| | - Subhradip Paul
- 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
| | - Venus Singh Mithu
- Department of Chemistry, Guru Nanak Dev University, Amritsar 143005, India
| | - P K Madhu
- Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India; TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500 075, India.
| | - Niels Chr Nielsen
- 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.
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24
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Tan KO, Scholz I, van Beek JD, Meier BH, Ernst M. Improved decoupling during symmetry-based C9-TOBSY sequences. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2014; 239:61-68. [PMID: 24384065 DOI: 10.1016/j.jmr.2013.11.017] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2013] [Revised: 11/26/2013] [Accepted: 11/29/2013] [Indexed: 06/03/2023]
Abstract
We show that heteronuclear decoupling during symmetry-based C9 TOBSY sequences can be improved by using phase-alternating pulse sequences (XiX) instead of cw irradiation. The use of XiX sequences makes the optimization of the decoupling rf-field amplitude simpler and lowers the decoupling rf-field requirements to attain a comparable performance. A Floquet analysis of the first-order resonance conditions was used to determine the correct timing of the XiX sequence to avoid interference between the C sequence and the decoupling. The decoupling performance is analyzed analytically using Floquet theory and verified using numerical simulations as well as experimental results.
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Affiliation(s)
- Kong Ooi Tan
- Physical Chemistry, ETH Zürich, Wolfgang-Pauli-Strasse 10, 8093 Zürich, Switzerland
| | - Ingo Scholz
- Physical Chemistry, ETH Zürich, Wolfgang-Pauli-Strasse 10, 8093 Zürich, Switzerland
| | - Jacco D van Beek
- Physical Chemistry, ETH Zürich, Wolfgang-Pauli-Strasse 10, 8093 Zürich, Switzerland
| | - Beat H Meier
- Physical Chemistry, ETH Zürich, Wolfgang-Pauli-Strasse 10, 8093 Zürich, Switzerland.
| | - Matthias Ernst
- Physical Chemistry, ETH Zürich, Wolfgang-Pauli-Strasse 10, 8093 Zürich, Switzerland.
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25
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Madhu PK. Heteronuclear Spin Decoupling in Solid-State Nuclear Magnetic Resonance: Overview and Outlook. Isr J Chem 2013. [DOI: 10.1002/ijch.201300097] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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26
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Mananga ES. Applications of Floquet-Magnus expansion, average Hamiltonian theory and Fer expansion to study interactions in solid state NMR when irradiated with the magic-echo sequence. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2013; 55-56:54-62. [PMID: 24034855 PMCID: PMC5378413 DOI: 10.1016/j.ssnmr.2013.08.002] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2013] [Revised: 06/21/2013] [Accepted: 08/13/2013] [Indexed: 06/02/2023]
Abstract
This work presents the possibility of applying the Floquet-Magnus expansion and the Fer expansion approaches to the most useful interactions known in solid-state nuclear magnetic resonance using the magic-echo scheme. The results of the effective Hamiltonians of these theories and average Hamiltonian theory are presented.
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Affiliation(s)
- Eugene Stephane Mananga
- Harvard Medical School and Massachusetts General Hospital, Center for Advanced Medical Imaging Sciences, Division of Nuclear Medicine and Molecular Imaging Physics, Department of Radiology, 55 Fruit Street, Boston, MA 02114, United States.
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27
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Agarwal V, Tuherm T, Reinhold A, Past J, Samoson A, Ernst M, Meier BH. Amplitude-modulated low-power decoupling sequences for fast magic-angle spinning NMR. Chem Phys Lett 2013. [DOI: 10.1016/j.cplett.2013.07.073] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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28
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Agarwal V, Sardo M, Scholz I, Böckmann A, Ernst M, Meier BH. PAIN with and without PAR: variants for third-spin assisted heteronuclear polarization transfer. JOURNAL OF BIOMOLECULAR NMR 2013; 56:365-377. [PMID: 23807391 DOI: 10.1007/s10858-013-9756-4] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2013] [Accepted: 06/17/2013] [Indexed: 06/02/2023]
Abstract
In this article, we describe third-spin assisted heteronuclear recoupling experiments, which play an increasingly important role in measuring long-range heteronuclear couplings, in particular (15)N-(13)C, in proteins. In the proton-assisted insensitive nuclei cross polarization (PAIN-CP) experiment (de Paëpe et al. in J Chem Phys 134:095101, 2011), heteronuclear polarization transfer is always accompanied by homonuclear transfer of the proton-assisted recoupling (PAR) type. We present a phase-alternating experiment that promotes heteronuclear (e.g. (15)N → (13)C) polarization transfer while simultaneously minimizing homonuclear (e.g.(13)C → (13)C) transfer (PAIN without PAR). This minimization of homonuclear polarization transfer is based on the principle of the resonant second-order transfer (RESORT) recoupling scheme where the passive proton spins are irradiated by a phase-alternating sequence and the modulation frequency is matched to an integer multiple of the spinning frequency. The similarities and differences between the PAIN-CP and this het-RESORT experiment are discussed here.
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Affiliation(s)
- Vipin Agarwal
- Physical Chemistry, ETH Zurich, 8093 Zurich, Switzerland
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29
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Mananga ES. Progress in spin dynamics solid-state nuclear magnetic resonance with the application of Floquet-Magnus expansion to chemical shift anisotropy. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2013; 54:1-7. [PMID: 23711337 PMCID: PMC3759595 DOI: 10.1016/j.ssnmr.2013.04.001] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2013] [Revised: 04/09/2013] [Accepted: 04/22/2013] [Indexed: 06/02/2023]
Abstract
The purpose of this article is to present an historical overview of theoretical approaches used for describing spin dynamics under static or rotating experiments in solid state nuclear magnetic resonance. The article gives a brief historical overview for major theories in nuclear magnetic resonance and the promising theories. We present the first application of Floquet-Magnus expansion to chemical shift anisotropy when irradiated by BABA pulse sequence.
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Affiliation(s)
- Eugene Stephane Mananga
- Harvard University, Harvard Medical School, and Massachusetts General Hospital, Center for Advanced Radiological Sciences, Division of Nuclear Medicine and Molecular Imaging Physics, Department of Radiology, 55 Fruit Street, Boston, MA 02114, USA.
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30
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Schanda P, Meier BH, Ernst M. Accurate measurement of one-bond H-X heteronuclear dipolar couplings in MAS solid-state NMR. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2011; 210:246-59. [PMID: 21482161 DOI: 10.1016/j.jmr.2011.03.015] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2011] [Revised: 03/08/2011] [Accepted: 03/14/2011] [Indexed: 05/13/2023]
Abstract
The accurate experimental determination of dipolar-coupling constants for one-bond heteronuclear dipolar couplings in solids is a key for the quantification of the amplitudes of motional processes. Averaging of the dipolar coupling reports on motions on time scales up to the inverse of the coupling constant, in our case tens of microseconds. Combining dipolar-coupling derived order parameters that characterize the amplitudes of the motion with relaxation data leads to a more precise characterization of the dynamical parameters and helps to disentangle the amplitudes and the time scales of the motional processes, which impact relaxation rates in a highly correlated way. Here. we describe and characterize an improved experimental protocol--based on REDOR--to measure these couplings in perdeuterated proteins with a reduced sensitivity to experimental missettings. Because such effects are presently the dominant source of systematic errors in experimental dipolar-coupling measurements, these compensated experiments should help to significantly improve the precision of such data. A detailed comparison with other commonly used pulse sequences (T-MREV, phase-inverted CP, R18(2)(5), and R18(1)(7)) is provided.
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Affiliation(s)
- Paul Schanda
- Physical Chemistry, ETH Zürich, Wolfgang-Pauli-Strasse 10, 8093 Zürich, Switzerland
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31
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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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32
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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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33
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34
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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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35
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Lesage A. Recent advances in solid-state NMR spectroscopy of spin I = 1/2 nuclei. Phys Chem Chem Phys 2009; 11:6876-91. [DOI: 10.1039/b907733m] [Citation(s) in RCA: 81] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
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36
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Scholz I, Huber M, Manolikas T, Meier BH, Ernst M. MIRROR recoupling and its application to spin diffusion under fast magic-angle spinning. Chem Phys Lett 2008. [DOI: 10.1016/j.cplett.2008.05.058] [Citation(s) in RCA: 92] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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37
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Affiliation(s)
- Cecil Dybowski*
- Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716
| | - Shi Bai
- Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716
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38
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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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39
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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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40
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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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41
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Swept-frequency two-pulse phase modulation for heteronuclear dipolar decoupling in solid-state NMR. Chem Phys Lett 2006. [DOI: 10.1016/j.cplett.2006.06.007] [Citation(s) in RCA: 175] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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