1
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Chávez M, Ernst M. Continuous Floquet theory in solid-state NMR. J Chem Phys 2024; 160:244111. [PMID: 38940539 DOI: 10.1063/5.0213078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2024] [Accepted: 06/10/2024] [Indexed: 06/29/2024] Open
Abstract
This article presents the application of continuous Floquet theory in solid-state nuclear magnetic resonance (NMR). Continuous Floquet theory extends the traditional Floquet theory to non-continuous Hamiltonians, enabling the description of observable effects not fully captured by the traditional Floquet theory due to its requirement for a periodic Hamiltonian. We present closed-form expressions for computing first- and second-order effective Hamiltonians, streamlining integration with the traditional Floquet theory and facilitating application in NMR experiments featuring multiple modulation frequencies. Subsequently, we show examples of the practical application of continuous Floquet theory by investigating several solid-state NMR experiments. These examples illustrate the importance of the duration of the pulse scheme regarding the width of the resonance conditions and the near-resonance behavior.
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Affiliation(s)
- Matías Chávez
- Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Matthias Ernst
- Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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2
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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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3
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Sasaki K, Abe E. Suppression of Pulsed Dynamic Nuclear Polarization by Many-Body Spin Dynamics. PHYSICAL REVIEW LETTERS 2024; 132:106904. [PMID: 38518331 DOI: 10.1103/physrevlett.132.106904] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2023] [Accepted: 02/06/2024] [Indexed: 03/24/2024]
Abstract
We study a mechanism by which nuclear hyperpolarization due to the polarization transfer from a microwave-pulse-controlled electron spin is suppressed. From analytical and numerical calculations of the unitary dynamics of multiple nuclear spins, we uncover that, combined with the formation of the dark state within a cluster of nuclei, coherent higher-order nuclear spin dynamics impose limits on the efficiency of the polarization transfer even in the absence of mundane depolarization processes such as nuclear spin diffusion and relaxation. Furthermore, we show that the influence of the dark state can be partly mitigated by introducing a disentangling operation. Our analysis is applied to the nuclear polarizations observed in ^{13}C nuclei coupled with a single nitrogen-vacancy center in diamond [Randall et al., Science 374, 1474 (2021)SCIEAS0036-807510.1126/science.abk0603]. Our Letter sheds light on collective engineering of nuclear spins as well as future designs of pulsed dynamic nuclear polarization protocols.
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Affiliation(s)
- Kento Sasaki
- Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Eisuke Abe
- RIKEN Center for Quantum Computing, Wako, Saitama 351-0198, Japan
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4
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Seetharam K, Biswas D, Noel C, Risinger A, Zhu D, Katz O, Chattopadhyay S, Cetina M, Monroe C, Demler E, Sels D. Digital quantum simulation of NMR experiments. SCIENCE ADVANCES 2023; 9:eadh2594. [PMID: 37976365 PMCID: PMC10656062 DOI: 10.1126/sciadv.adh2594] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 10/18/2023] [Indexed: 11/19/2023]
Abstract
Simulations of nuclear magnetic resonance (NMR) experiments can be an important tool for extracting information about molecular structure and optimizing experimental protocols but are often intractable on classical computers for large molecules such as proteins and for protocols such as zero-field NMR. We demonstrate the first quantum simulation of an NMR spectrum, computing the zero-field spectrum of the methyl group of acetonitrile using four qubits of a trapped-ion quantum computer. We reduce the sampling cost of the quantum simulation by an order of magnitude using compressed sensing techniques. We show how the intrinsic decoherence of NMR systems may enable the zero-field simulation of classically hard molecules on relatively near-term quantum hardware and discuss how the experimentally demonstrated quantum algorithm can be used to efficiently simulate scientifically and technologically relevant solid-state NMR experiments on more mature devices. Our work opens a practical application for quantum computation.
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Affiliation(s)
- Kushal Seetharam
- Department of Electrical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Debopriyo Biswas
- Department of Electrical and Computer Engineering, Department of Physics, Duke Quantum Center, Duke University, Durham, NC 27708, USA
- Joint Quantum Institute, Department of Physics, University of Maryland, College Park, MD 20742, USA
| | - Crystal Noel
- Department of Electrical and Computer Engineering, Department of Physics, Duke Quantum Center, Duke University, Durham, NC 27708, USA
- Joint Quantum Institute, Department of Physics, University of Maryland, College Park, MD 20742, USA
| | - Andrew Risinger
- Joint Quantum Institute, Department of Physics, University of Maryland, College Park, MD 20742, USA
| | - Daiwei Zhu
- Joint Quantum Institute, Department of Physics, University of Maryland, College Park, MD 20742, USA
| | - Or Katz
- Department of Electrical and Computer Engineering, Department of Physics, Duke Quantum Center, Duke University, Durham, NC 27708, USA
| | | | - Marko Cetina
- Joint Quantum Institute, Department of Physics, University of Maryland, College Park, MD 20742, USA
- Department of Physics, Duke Quantum Center, Duke University, Durham, NC 27708, USA
| | - Christopher Monroe
- Department of Electrical and Computer Engineering, Department of Physics, Duke Quantum Center, Duke University, Durham, NC 27708, USA
- Joint Quantum Institute, Department of Physics, University of Maryland, College Park, MD 20742, USA
- IonQ Inc., College Park, MD 20740, USA
| | - Eugene Demler
- Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - Dries Sels
- Department of Physics, New York University, New York, NY 10003, USA
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY 10010, USA
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5
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Ganguly S, Ramachandran R. A critique on the suitability of Fer expansion in time-evolution studies in quantum mechanics. J Chem Phys 2023; 159:184106. [PMID: 37947512 DOI: 10.1063/5.0169532] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2023] [Accepted: 10/23/2023] [Indexed: 11/12/2023] Open
Abstract
The present report examines the utility and exactness of time-propagators derived from Fer expansion (FE). While the mathematical intricacies of the FE scheme are well established, the operational aspects of the same in time-evolution studies remain less explored and authenticated in physical problems of relevance. Through suitable examples, the operational inconsistencies observed in time-evolution studies based on the FE scheme are identified and corroborated through rigorous comparisons with simulations emerging from exact numerical methods. The limitations outlined seriously undermine the advantages associated with the FE scheme over other existing analytic methods.
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Affiliation(s)
- Shreyan Ganguly
- 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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6
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Ganguly S, Ramachandran R. A perspective on the relative merits/demerits of time-propagators based on Floquet theorem. Phys Chem Chem Phys 2023; 25:29747-29773. [PMID: 37885428 DOI: 10.1039/d3cp03801g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2023]
Abstract
The present report examines the nuances of analytic methods employed in the derivation of evolution operators in periodically driven quantum systems based on Floquet theorem. Specifically, time-propagators of the form, U(t) = P(t)e-iH̄t defined in the Hilbert space (of finite dimension), are derived through generalized multimodal expansion of the operators involved. While Floquet methods defined in the extended Hilbert space (of infinite dimension) have remained the method of choice for the description of time-evolution at non-stroboscopic time-intervals, the expansion schemes discussed do present an attractive option for similar studies in the standard Hilbert space. Nevertheless, the convergence criteria and suitability of such methods deserve formal validation in problems of experimental relevance. Employing examples comprising periodic Hamiltonians from magnetic resonance spectroscopy, the exactness of Floquet based time-propagators in the Schrödinger and interaction representation is discussed. Through rigorous comparisons between simulations emerging from analytic and exact numerical methods, the relative merits and demerits of different formulations of Floquet based methods are also discussed.
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Affiliation(s)
- Shreyan Ganguly
- 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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Fregosi A, Marinelli C, Gabbanini C, Bevilacqua G, Biancalana V, Arimondo E, Fioretti A. Floquet space exploration for the dual-dressing of a qubit. Sci Rep 2023; 13:15304. [PMID: 37723191 PMCID: PMC10507086 DOI: 10.1038/s41598-023-41693-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2023] [Accepted: 08/30/2023] [Indexed: 09/20/2023] Open
Abstract
The application of a periodic nonresonant drive to a system allows the Floquet engineering of effective fields described by a broad class of quantum simulated Hamiltonians. The Floquet evolution is based on two different elements. The first one is a time-independent or stroboscopic evolution with an effective Hamiltonian corresponding to the quantum simulation target. The second element is the time evolution at the frequencies of the nonresonant driving and of its harmonics, denoted as micromotion. We examine experimentally and theoretically the harmonic dual-dressing Floquet engineering of a cold atomic two-level sample. Our focus is the dressing operation with small bare energies and large Rabi frequencies, where frequencies and amplitudes of the stroboscopic/micromotion time evolutions are comparable. At the kHz range of our dressed atom oscillations, we probe directly both the stroboscopic and micromotion components of the qubit global time evolution. We develop ad-hoc monitoring tools of the Floquet space evolution. The direct record of the time evolution following a pulsed excitation demonstrates the interplay between the two components of the spin precession in the Floquet space. From the resonant pumping of the dressed system at its evolution frequencies, Floquet eigenenergy spectra up to the fifth order harmonic of the dressing frequency are precisely measured as function of dressing parameters. Dirac points of the Floquet eigenenergies are identified and, correspondingly, a jump in the dynamical phase shift is measured. The stroboscopic Hamiltonian eigenfrequencies are measured also from the probe of the micromotion sidebands.These monitoring tools are appropriate for quantum simulation/computation investigations. Our results evidence that the stroboscopic phase shift of the qubit wavefunction contains an additional information that opens new simulation directions.
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Affiliation(s)
- Alessandro Fregosi
- Istituto Nazionale di Ottica, CNR-INO, Sede Secondaria di Pisa, Via G. Moruzzi 1, 56124, Pisa, Italy
- Dip. di Scienze Fisiche, della Terra e dell'Ambiente, Università degli Studi di Siena, Via Roma 56, 53100, Siena, Italy
| | - Carmela Marinelli
- Istituto Nazionale di Ottica, CNR-INO, Sede Secondaria di Pisa, Via G. Moruzzi 1, 56124, Pisa, Italy
- Dip. di Scienze Fisiche, della Terra e dell'Ambiente, Università degli Studi di Siena, Via Roma 56, 53100, Siena, Italy
| | - Carlo Gabbanini
- Istituto Nazionale di Ottica, CNR-INO, Sede Secondaria di Pisa, Via G. Moruzzi 1, 56124, Pisa, Italy
| | - Giuseppe Bevilacqua
- Dip. di Scienze Fisiche, della Terra e dell'Ambiente, Università degli Studi di Siena, Via Roma 56, 53100, Siena, Italy
| | - Valerio Biancalana
- Dip. di Scienze Fisiche, della Terra e dell'Ambiente, Università degli Studi di Siena, Via Roma 56, 53100, Siena, Italy
| | - Ennio Arimondo
- Istituto Nazionale di Ottica, CNR-INO, Sede Secondaria di Pisa, Via G. Moruzzi 1, 56124, Pisa, Italy
- Dipartimento di Fisica, University of Pisa, Largo Bruno Pontecorvo 3, 56127, Pisa, Italy
| | - Andrea Fioretti
- Istituto Nazionale di Ottica, CNR-INO, Sede Secondaria di Pisa, Via G. Moruzzi 1, 56124, Pisa, Italy.
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8
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Shirai S, Okubo Y, Matsuura K, Osada A, Nakamura Y, Noguchi A. All-Microwave Manipulation of Superconducting Qubits with a Fixed-Frequency Transmon Coupler. PHYSICAL REVIEW LETTERS 2023; 130:260601. [PMID: 37450826 DOI: 10.1103/physrevlett.130.260601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 06/01/2023] [Indexed: 07/18/2023]
Abstract
All-microwave control of fixed-frequency superconducting quantum computing circuits is advantageous for minimizing the noise channels and wiring costs. Here we introduce a swap interaction between two data transmons assisted by the third-order nonlinearity of a coupler transmon under a microwave drive. We model the interaction analytically and numerically and use it to implement an all-microwave controlled-Z gate. The gate based on the coupler-assisted swap transition maintains high drive efficiency and small residual interaction over a wide range of detuning between the data transmons.
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Affiliation(s)
- Shotaro Shirai
- Komaba Institute for Science (KIS), The University of Tokyo, Meguro-ku, Tokyo 153-8902, Japan
| | - Yuta Okubo
- Komaba Institute for Science (KIS), The University of Tokyo, Meguro-ku, Tokyo 153-8902, Japan
| | - Kohei Matsuura
- Department of Applied Physics, Graduate School of Engineering, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Alto Osada
- Komaba Institute for Science (KIS), The University of Tokyo, Meguro-ku, Tokyo 153-8902, Japan
- PRESTO, Japan Science and Technology Agency, Kawaguchi-shi, Saitama 332-0012, Japan
| | - Yasunobu Nakamura
- Department of Applied Physics, Graduate School of Engineering, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
- RIKEN Center for Quantum Computing (RQC), Wako, Saitama 351-0198, Japan
| | - Atsushi Noguchi
- Komaba Institute for Science (KIS), The University of Tokyo, Meguro-ku, Tokyo 153-8902, Japan
- RIKEN Center for Quantum Computing (RQC), Wako, Saitama 351-0198, Japan
- Inamori Research Institute for Science (InaRIS), Kyoto-shi, Kyoto 600-8411, Japan
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9
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Arunachalam V, Sharma K, Mote KR, Madhu PK. Asynchronising five-fold symmetry sequence for better homonuclear polarisation transfer in magic-angle-spinning solid-state NMR. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2023; 124:101858. [PMID: 36796278 DOI: 10.1016/j.ssnmr.2023.101858] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2022] [Revised: 01/28/2023] [Accepted: 01/30/2023] [Indexed: 06/18/2023]
Abstract
Recoupling, decoupling, and multidimensional correlation experiments in magic-angle-spinning (MAS) solid-state NMR can be designed by exploiting the symmetry of internal spin interactions. One such scheme, namely, C521, and its supercycled version SPC521, notated as a five-fold symmetry sequence, is widely used for double-quantum dipole-dipole recoupling. Such schemes are generally rotor synchronised by design. We demonstrate an asynchronous implementation of the SPC521 sequence leading to higher double-quantum homonuclear polarisation transfer efficiency compared to the normal synchronous implementation. Rotor-synchronisation is broken in two different ways: lengthening the duration of one of the pulses, denoted as pulse-width variation (PWV), and mismatching the MAS frequency denoted as MAS variation (MASV). The application of this asynchronous sequence is shown on three different samples, namely, U-13C-alanine and 1,4-13C-labelled ammonium phthalate which include 13Cα-13Cβ, 13Cα-13Co, and 13Co-13Co spin systems, and adenosine 5'- triphosphate disodium salt trihydrate (ATP⋅3H2O). We show that the asynchronous version performs better for spin pairs with small dipole-dipole couplings and large chemical-shift anisotropies, for example, 13Co-13Co. Simulations and experiments are shown to corroborate the results.
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Affiliation(s)
- Vaishali Arunachalam
- Tata Institute of Fundamental Research Hyderabad, 36/P Gopanpally Village, Ranga Reddy District, Hyderabad, 500046, India.
| | - Kshama Sharma
- Tata Institute of Fundamental Research Hyderabad, 36/P Gopanpally Village, Ranga Reddy District, Hyderabad, 500046, India.
| | - Kaustubh R Mote
- Tata Institute of Fundamental Research Hyderabad, 36/P Gopanpally Village, Ranga Reddy District, Hyderabad, 500046, India.
| | - P K Madhu
- Tata Institute of Fundamental Research Hyderabad, 36/P Gopanpally Village, Ranga Reddy District, Hyderabad, 500046, India.
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10
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Aebischer K, Ernst M. Echo modulations under homonuclear decoupling. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2023; 347:107360. [PMID: 36563419 DOI: 10.1016/j.jmr.2022.107360] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2022] [Revised: 12/08/2022] [Accepted: 12/14/2022] [Indexed: 06/17/2023]
Abstract
A simple Hahn echo in a single-spin system with a static Hamiltonian can lead to echo modulations if the static Hamiltonian contains a component along the direction of the echo pulse. These modulations manifest as side bands in the Fourier transform of the echo decay. Experimentally, echo modulations that can be explained by such a model have been observed under homonuclear decoupling in solids where pulse imperfections can lead to residual effective fields in the interaction frame that have arbitrary orientations in space. We show analytically that such echo modulations are significantly reduced in intensity using double-echo sequences in agreement with experimental observations. Using pulse shapes for homonuclear decoupling that mimic and amplify the pulse distortions expected from pulse transients, we show that these effective fields can be one explanation for the observed reduction in echo modulations going from a single to a double Hahn-echo sequence.
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Affiliation(s)
- Kathrin Aebischer
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, Zürich 8093, Switzerland
| | - Matthias Ernst
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, Zürich 8093, Switzerland.
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11
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Sajith SV, Jayanthi S, Lupulescu A. Effective Hamiltonian and spin dynamics in fast MAS TRAPDOR-HMQC experiments involving spin-3/2 quadrupolar nuclei. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2022; 122:101821. [PMID: 36191580 DOI: 10.1016/j.ssnmr.2022.101821] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2022] [Revised: 08/21/2022] [Accepted: 08/26/2022] [Indexed: 06/16/2023]
Abstract
We present a theoretical and numerical description of the spin dynamics associated with TRAPDOR-HMQC (T-HMQC) experiment for a 1H (I) - 35Cl (S) spin system under fast magic angle spinning (MAS). Towards this an exact effective Hamiltonian describing the system is numerically evaluated with matrix logarithm approach. The different magnitudes of the heteronuclear and pure S terms in the effective Hamiltonian allow us to suggest a truncation approximation, which is shown to be in excellent agreement with the exact time evolution. Limitations of this approximation, especially at the rotary resonance condition, are discussed. The truncated effective Hamiltonian is further employed to monitor the buildup of various coherences during TRAPDOR irradiation. We observe and explain a functional resemblance between the magnitude of different terms in the truncated effective Hamiltonian and the amplitudes of various coherences during TRAPDOR irradiation, as function of crystallite orientation. Subsequently, the dependence of the sign (phase) of the T-HMQC signal on the coherence type generated is investigated numerically and analytically. We examine the continuous creation and evolution of various coherences at arbitrary times, i.e., at and between avoided level crossings. Behavior between consecutive crossings is described analytically and reveals 'quadrature' evolution of pairs of coherences and coherence interconversions. The adiabatic, sudden, and intermediate regimes for T-HMQC experiments are discussed within the approach established by A. J. Vega. Equations as well as numerical simulations suggest the existence of a driving coherence which builds up between consecutive crossings and then gets distributed at crossings among other coherences. In the intermediate regime, redistribution of the driving coherence to other coherences is almost uniform such that coherences involving S-spin double-quantum terms may be efficiently produced.
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Affiliation(s)
- Sadasivan V Sajith
- Department of Physics, Indian Institute of Space Science and Technology, Valiamala, Thiruvananthapuram, 695 547, Kerala, India
| | - Sundaresan Jayanthi
- Department of Physics, Indian Institute of Space Science and Technology, Valiamala, Thiruvananthapuram, 695 547, Kerala, India.
| | - Adonis Lupulescu
- Extreme Light Infrastructure-Nuclear Physics ELI-NP, Laser Gamma Experiments Department (LGED), "Horia Hulubei" National Institute for Physics and Nuclear Engineering IFIN-HH, 30 Reactorului Street, 077125, Bucharest, Măgurele, Romania.
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12
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Chávez M, Ernst M. A continuous approach to Floquet theory for pulse-sequence optimization in solid-state NMR. J Chem Phys 2022; 157:184103. [DOI: 10.1063/5.0109229] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
We present a framework that uses a continuous frequency space to describe and design solid-state nuclear magnetic resonance (NMR) experiments. The approach is similar to the well-established Floquet treatment for NMR, but it is not restricted to periodic Hamiltonians and allows the design of experiments in a reverse fashion. The framework is based on perturbation theory on a continuous Fourier space, which leads to effective, i.e., time-independent, Hamiltonians. It allows the back-calculation of the pulse scheme from the desired effective Hamiltonian as a function of spin-system parameters. We show as an example how to back-calculate the rf irradiation in the MIRROR experiment from the desired chemical-shift offset behavior of the sequence.
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Affiliation(s)
- Matías Chávez
- 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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13
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Bayzou R, Trébosc J, Hung I, Gan Z, Lafon O, Amoureux JP. Indirect NMR detection via proton of nuclei subject to large anisotropic interactions, such as 14N, 195Pt, and 35Cl, using the T-HMQC sequence. J Chem Phys 2022; 156:064202. [DOI: 10.1063/5.0082700] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Affiliation(s)
- Racha Bayzou
- Univ. Lille, CNRS, Centrale Lille, Univ. Artois, UMR 8181–UCCS–Unité de Catalyse et Chimie du Solide, 59000 Lille, France
| | - Julien Trébosc
- Univ. Lille, CNRS, INRAE, Centrale Lille, Univ. Artois, FR 2638–IMEC–Fédération Chevreul, 59000 Lille, France
| | - Ivan Hung
- National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, Florida 32310, USA
| | - Zhehong Gan
- National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, Florida 32310, USA
| | - Olivier Lafon
- Univ. Lille, CNRS, Centrale Lille, Univ. Artois, UMR 8181–UCCS–Unité de Catalyse et Chimie du Solide, 59000 Lille, France
| | - Jean-Paul Amoureux
- Univ. Lille, CNRS, Centrale Lille, Univ. Artois, UMR 8181–UCCS–Unité de Catalyse et Chimie du Solide, 59000 Lille, France
- Riken NMR Science and Development Division, Yokohama-shi 230-0045, Kanagawa, Japan
- Bruker Biospin, 34 rue de l’industrie, 67166 Wissembourg, France
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14
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Bansal M, Ramachandran R. Theory of radio-frequency pulses on periodically driven three-level systems: challenges and perspectives. Phys Chem Chem Phys 2022; 24:29092-29111. [DOI: 10.1039/d2cp03906k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Nuances of multiple-quantum transitions in periodically driven systems is discussed through analytical methods based on time propagators derived from Floquet theory.
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Affiliation(s)
- Mohit Bansal
- 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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15
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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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Wang G, Li C, Cappellaro P. Observation of Symmetry-Protected Selection Rules in Periodically Driven Quantum Systems. PHYSICAL REVIEW LETTERS 2021; 127:140604. [PMID: 34652183 DOI: 10.1103/physrevlett.127.140604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2021] [Revised: 08/09/2021] [Accepted: 09/09/2021] [Indexed: 06/13/2023]
Abstract
Periodically driven (Floquet) quantum systems have recently been a focus of nonequilibrium physics by virtue of their rich dynamics. Time-periodic systems not only exhibit symmetries that resemble those in spatially periodic systems, but also display novel behavior that arises from symmetry breaking. Characterization of such dynamical symmetries is crucial, but often challenging due to limited driving strength and lack of an experimentally accessible characterization technique. Here, we show how to reveal dynamical symmetries, namely, parity, rotation, and particle-hole symmetries, by observing symmetry-induced Floquet selection rules. Notably, we exploit modulated driving to reach the strong light-matter coupling regime, and we introduce a protocol to experimentally extract the transition matrix elements between Floquet states from the system coherent evolution. By using nitrogen-vacancy centers in diamond as an experimental test bed, we execute our protocol to observe symmetry-protected dark states and dark bands, and coherent destruction of tunneling. Our work shows how one can exploit the quantum control toolkit to study dynamical symmetries that arise in the topological phases of strongly driven Floquet systems.
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Affiliation(s)
- Guoqing Wang
- Research Laboratory of Electronics and Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Changhao Li
- Research Laboratory of Electronics and Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Paola Cappellaro
- Research Laboratory of Electronics and Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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17
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Aebischer K, Tošner Z, Ernst M. Effects of radial radio-frequency field inhomogeneity on MAS solid-state NMR experiments. MAGNETIC RESONANCE (GOTTINGEN, GERMANY) 2021; 2:523-543. [PMID: 37904774 PMCID: PMC10539735 DOI: 10.5194/mr-2-523-2021] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/06/2021] [Accepted: 06/14/2021] [Indexed: 11/01/2023]
Abstract
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.
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Affiliation(s)
- Kathrin Aebischer
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Zdeněk Tošner
- Department of Chemistry, Faculty of Science, Charles University, Hlavova 8, 12842 Prague 2, Czech Republic
| | - Matthias Ernst
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
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18
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Chávez M, Wiegand T, Malär A, Meier B, Ernst M. Residual dipolar line width in magic-angle spinning proton solid-state NMR. MAGNETIC RESONANCE (GOTTINGEN, GERMANY) 2021; 2:499-509. [PMID: 37904755 PMCID: PMC10539731 DOI: 10.5194/mr-2-499-2021] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Accepted: 06/24/2021] [Indexed: 11/01/2023]
Abstract
Magic-angle spinning is routinely used to average anisotropic interactions in solid-state nuclear magnetic resonance (NMR). Due to the fact that the homonuclear dipolar Hamiltonian of a strongly coupled spin system does not commute with itself at different time points during the rotation, second-order and higher-order terms lead to a residual dipolar line broadening in the observed resonances. Additional truncation of the residual broadening due to isotropic chemical-shift differences can be observed. We analyze the residual line broadening in coupled proton spin systems based on theoretical calculations of effective Hamiltonians up to third order using Floquet theory and compare these results to numerically obtained effective Hamiltonians in small spin systems. We show that at spinning frequencies beyond 75 kHz, second-order terms dominate the residual line width, leading to a 1 / ω r dependence of the second moment which we use to characterize the line width. However, chemical-shift truncation leads to a partial ω r - 2 dependence of the line width which looks as if third-order effective Hamiltonian terms are contributing significantly. At slower spinning frequencies, cross terms between the chemical shift and the dipolar coupling can contribute in third-order effective Hamiltonians. We show that second-order contributions not only broaden the line, but also lead to a shift of the center of gravity of the line. Experimental data reveal such spinning-frequency-dependent line shifts in proton spectra in model substances that can be explained by line shifts induced by the second-order dipolar Hamiltonian.
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Affiliation(s)
- Matías Chávez
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Thomas Wiegand
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Alexander A. Malär
- 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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19
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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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20
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Carvalho JP, Pell AJ. Frequency-swept adiabatic pulses for broadband solid-state MAS NMR. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2021; 324:106911. [PMID: 33482528 DOI: 10.1016/j.jmr.2020.106911] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2020] [Revised: 12/17/2020] [Accepted: 12/25/2020] [Indexed: 06/12/2023]
Abstract
We present a complete description of frequency-swept adiabatic pulses applied to isolated spin-1/2 nuclei with a shift anisotropy in solid materials under magic-angle spinning. Our theoretical framework unifies the existing descriptions of adiabatic pulses in the high-power regime, where the radiofrequency (RF) amplitude is greater than twice the spinning frequency, and the low-power regime, where the RF power is less than the spinning frequency, and so links the short high-powered adiabatic pulse (SHAP) and single-sideband-selective adiabatic pulses (S3AP) schemes used in paramagnetic solid-state NMR. We also identify a hitherto unidentified third regime intermediate between the low- and high-power regimes, and separated from them by rotary resonance conditions. We show that the prevailing benchmark of inversion performance based on (super) adiabatic factors is only applicable in the high- and intermediate-power regimes, but fails to account both for the poor performance at rotary resonance, and the impressive inversion seen in the low-power regime. For low-power pulses, which are non-adiabatic according to this definition of (super) adiabaticity, the effective Floquet Hamiltonian in the jolting frame reveals "hidden" (super) adiabaticity. The theory is demonstrated using a combination of simulation and experiment, and is used to refine the practical recommendations for the experimentalist who wishes to use these pulses.
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Affiliation(s)
- José P Carvalho
- Materials and Environmental Chemistry, Stockholm University, Svänte Arrhenius väg 16 C 106 91, Stockholm, Sweden
| | - Andrew J Pell
- Materials and Environmental Chemistry, Stockholm University, Svänte Arrhenius väg 16 C 106 91, Stockholm, Sweden; Centre de RMN Trés Hauts Champs de Lyon (FRE 2034 - CNRS, ENS Lyon, UCB Lyon 1), Université de Lyon, 5 rue de la Doua, 69100 Villeurbanne, France.
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21
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Aleksis R, Pell AJ. Low-power synchronous helical pulse sequences for large anisotropic interactions in MAS NMR: Double-quantum excitation of 14N. J Chem Phys 2020; 153:244202. [PMID: 33380069 DOI: 10.1063/5.0030604] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We develop a theoretical framework for a class of pulse sequences in the nuclear magnetic resonance (NMR) of rotating solids, which are applicable to nuclear spins with anisotropic interactions substantially larger than the spinning frequency, under conditions where the radiofrequency amplitude is smaller than or comparable to the spinning frequency. The treatment is based on average Hamiltonian theory and allows us to derive pulse sequences with well-defined relationships between the pulse parameters and spinning frequency for exciting specific coherences without the need for any detailed calculations. This framework is applied to the excitation of double-quantum spectra of 14N and is used both to evaluate the existing low-power pulse schemes and to predict the new ones, which we present here. It is shown that these sequences can be designed to be γ-encoded and therefore allow the acquisition of sideband-free spectra. It is also shown how these new double-quantum excitation sequences are incorporated into heteronuclear correlation NMR, such as 1H-14N dipolar double-quantum heteronuclear multiple-quantum correlation spectroscopy. The new experiments are evaluated both with numerical simulations and experiments on glycine and N-acetylvaline, which represent cases with "moderate" and "large" quadrupolar interactions, respectively. The analyzed pulse sequences perform well for the case of a "moderate" quadrupolar interaction, however poorly with a "large" quadrupolar interaction, for which future work on pulse sequence development is necessary.
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Affiliation(s)
- Rihards Aleksis
- Department of Materials and Environmental Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden
| | - Andrew J Pell
- Department of Materials and Environmental Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden
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Sajith SV, Jayanthi S, Lupulescu A. Effective Hamiltonian and 1H- 14N cross polarization/double cross polarization at fast MAS. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2020; 320:106832. [PMID: 33011464 DOI: 10.1016/j.jmr.2020.106832] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Revised: 09/15/2020] [Accepted: 09/18/2020] [Indexed: 06/11/2023]
Abstract
In this work we investigate in detail the underlying spin-dynamics associated with 1H-14N double CP experiments under fast MAS, recently demonstrated by Carnevale et al. We employ matrix logarithm and Floquet theory to compute numerically the effective Hamiltonian associated to the time-dependent problem. Certain common features related to construction of effective Hamiltonians by both approaches are discussed. The main observations related to 1H-14N CPMAS/double CP transfer are: (a) various spin terms of the effective Hamiltonian strongly depend on the crystallite orientation; (b) significant CP transfer occurs only when the magnitudes of the effective1H and 14N RF strengths are comparable, and simultaneously all pure 14N terms in the effective Hamiltonian are small, except for the longitudinal and the RF terms; (c) the sign of 14N CPMAS signal follows the sign of 14N effective RF strength; (d) sign of the double CP signal is largely independent of crystallite orientation. We predict and verify matching conditions employing multiples of the spinning frequency or involving different 14N RF strengths. We provide an analytical proof for (d). The proof also provides an estimate for the ratio of 1H-14N and 14N-1H transfer amplitudes which is further substantiated through simulations. In addition, we find that double CP signals include contributions from several single-quantum coherences present after the first CP process. The uneven contribution from different coherences leads to a reversal of signal at very short contact times, a feature noted experimentally by Carnevale et al. The connection between CPMAS transfer and efficient spin-lock is discussed and illustrated. The factors affecting second-order quadrupolar lineshapes in double CP experiment are examined. With a linear ramp of 1H RF amplitude we have observed that significant CP transfer occurs for more crystallite orientations resulting in improved sensitivity.
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Affiliation(s)
- Sadasivan V Sajith
- Department of Physics, Indian Institute of Space Science and Technology, Valiamala, Thiruvananthapuram 695 547, Kerala, India
| | - Sundaresan Jayanthi
- Department of Physics, Indian Institute of Space Science and Technology, Valiamala, Thiruvananthapuram 695 547, Kerala, India.
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23
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Ganguly S, Garg R, Ramachandran R. On the equivalence between different averaging schemes in magnetic resonance. J Chem Phys 2020; 153:094103. [PMID: 32891089 DOI: 10.1063/5.0018753] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Evolution of quantum mechanical systems under time-dependent Hamiltonians has remained a challenging problem of interest across all disciplines. Through suitable approximations, different averaging methods have emerged in the past for modeling the time-evolution under time-dependent Hamiltonians. To this end, the development of analytic methods in the form of time-averaged effective Hamiltonians has gained prominence over other methods. In particular, the advancement of spectroscopic methods for probing molecular structures has benefited enormously from such theoretical pursuits. Nonetheless, the validity of the approximations and the exactness of the proposed effective Hamiltonians have always remained a contentious issue. Here, in this report, we reexamine the equivalence between the effective Hamiltonians derived from the Magnus formula and Floquet theory through suitable examples in magnetic resonance.
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Affiliation(s)
- Shreyan Ganguly
- Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, Manauli P.O. Box-140306, Mohali, Punjab, India
| | - 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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24
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Potnuru LR, Duong NT, Ahlawat S, Raran-Kurussi S, Ernst M, Nishiyama Y, Agarwal V. Accuracy of 1H- 1H distances measured using frequency selective recoupling and fast magic-angle spinning. J Chem Phys 2020; 153:084202. [PMID: 32872876 DOI: 10.1063/5.0019717] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
Selective recoupling of protons (SERP) is a method to selectively and quantitatively measure magnetic dipole-dipole interaction between protons and, in turn, the proton-proton distance in solid-state samples at fast magic-angle spinning. We present a bimodal operator-based Floquet approach to describe the numerically optimized SERP recoupling sequence. The description calculates the allowed terms in the first-order effective Hamiltonian, explains the origin of selectivity during recoupling, and shows how different terms are modulated as a function of the radio frequency amplitude and the phase of the sequence. Analytical and numerical simulations have been used to evaluate the effect of higher-order terms and offsets on the polarization transfer efficiency and quantitative distance measurement. The experimentally measured 1H-1H distances on a fully protonated thymol sample are ∼10%-15% shorter than those reported from diffraction studies. A semi-quantitative model combined with extensive numerical simulations is used to rationalize the effect of the third-spin and the role of different parameters in the experimentally observed shorter distances. Measurements at high magnetic fields improve the match between experimental and diffraction distances. The measurement of 1H-1H couplings at offsets different from the SERP-offset has also been explored. Experiments were also performed on a perdeuterated ubiquitin sample to demonstrate the feasibility of simultaneously measuring multiple quantitative distances and to evaluate the accuracy of the measured distance in the absence of multispin effects. The estimation of proton-proton distances provides a boost to structural characterization of small pharmaceuticals and biomolecules, given that the positions of protons are generally not well defined in x-ray structures.
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Affiliation(s)
- Lokeswara Rao Potnuru
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research Hyderabad, Survey No. 36/P, Gopanpally, Ranga Reddy District, Hyderabad 500 107, India
| | - Nghia Tuan Duong
- NMR Science and Development Division, RIKEN SPring-8 Center, and Nano-Crystallography Unit, RIKEN-JEOL Collaboration Center, Yokohama, Kanagawa 230-0045, Japan
| | - Sahil Ahlawat
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research Hyderabad, Survey No. 36/P, Gopanpally, Ranga Reddy District, Hyderabad 500 107, India
| | - Sreejith Raran-Kurussi
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research Hyderabad, Survey No. 36/P, Gopanpally, Ranga Reddy District, Hyderabad 500 107, India
| | - Matthias Ernst
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Yusuke Nishiyama
- NMR Science and Development Division, RIKEN SPring-8 Center, and Nano-Crystallography Unit, RIKEN-JEOL Collaboration Center, Yokohama, Kanagawa 230-0045, Japan
| | - Vipin Agarwal
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research Hyderabad, Survey No. 36/P, Gopanpally, Ranga Reddy District, Hyderabad 500 107, India
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Concilio MG. Large-scale magnetic resonance simulations: A tutorial. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2020; 58:691-717. [PMID: 32173898 DOI: 10.1002/mrc.5018] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2019] [Revised: 02/14/2020] [Accepted: 03/09/2020] [Indexed: 06/10/2023]
Abstract
Computational modeling is becoming an essential tool in magnetic resonance to design and optimize experiments, test the performance of theoretical models, and interpret experimental data. Recent theoretical research and software development made possible simulations of large spin systems, for example, proteins with thousands of spins, in reasonable time. In the last few years, the Fokker-Planck formalism also re-emerged due to its ability to handle spatial dynamics. The purpose of this tutorial is to describe advantages and disadvantages of the most common formalisms, the latest developments and strategies to improve the computational efficiency, and to guide users in the setting up of a simulation using the Spinach software.
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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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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. MAGNETIC RESONANCE (GOTTINGEN, GERMANY) 2020; 1:13-25. [PMID: 37904890 PMCID: PMC10500695 DOI: 10.5194/mr-1-13-2020] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2019] [Accepted: 01/21/2020] [Indexed: 11/01/2023]
Abstract
Homonuclear decoupling sequences in solid-state nuclear magnetic resonance (NMR) under magic-angle spinning (MAS) show experimentally significantly larger residual line width than expected from Floquet theory to second order. We present an in-depth theoretical and experimental analysis of the origin of the residual line width under decoupling based on frequency-switched Lee-Goldburg (FSLG) sequences. We analyze the effect of experimental pulse-shape errors (e.g., pulse transients and B 1 -field inhomogeneities) and use a Floquet-theory-based description of higher-order error terms that arise from the interference between the MAS rotation and the pulse sequence. It is shown that the magnitude of the third-order auto term of a single homo- or heteronuclear coupled spin pair is important and leads to significant line broadening under FSLG decoupling. Furthermore, we show the dependence of these third-order error terms on the angle of the effective field with the B 0 field. An analysis of second-order cross terms is presented that shows that the influence of three-spin terms is small since they are averaged by the pulse sequence. The importance of the inhomogeneity of the radio-frequency (rf) field is discussed and shown to be the main source of residual line broadening while pulse transients do not seem to play an important role. Experimentally, the influence of the combination of these error terms is shown by using restricted samples and pulse-transient compensation. The results show that all terms are additive but the major contribution to the residual line width comes from the rf-field inhomogeneity for the standard implementation of FSLG sequences, which is significant even for samples with a restricted volume.
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Affiliation(s)
| | - Liam Grunwald
- Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Manuel Ochsner
- Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Daniel Zindel
- Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Beat H. Meier
- Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Matthias Ernst
- Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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Agarwal V. The origin of negative cross-peaks in proton-spin diffusion spectrum of fully protonated solids at fast MAS: Coherent or incoherent effect? JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2020; 311:106661. [PMID: 31869741 DOI: 10.1016/j.jmr.2019.106661] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2019] [Revised: 11/13/2019] [Accepted: 11/23/2019] [Indexed: 06/10/2023]
Abstract
Spin-diffusion (SD) is amongst the first methods proposed to spatially transfer polarization between dipolar-coupled nuclear spins. Lab-frame SD has proved particularly useful in structural characterization of a large variety of molecules. During SD, the rate of magnetization transfer between the two nuclei depends on the square of the dipolar coupling and the zero-quantum lineshape of the two spins. The relative sign of the diagonal and cross-peaks is determined by the spin part of the dipolar Hamiltonian. Practically, SD experiments are used in two ways: (a) SD transfer amongst only the protons (known as proton spin-diffusion or PSD) and b) SD amongst rare nuclei, coupled to a strong proton bath, known as proton driven spin-diffusion (PDSD). It is well established that the diagonal and cross-peaks have the same sign during SD based polarization transfer. 2D PSD experiments recorded on Histidine.HCl.H2O sample at fast magic angle spinning (MAS) show that some of the cross-peaks in the 2D spectrum are negative with respect to the diagonal peaks. Cross-relaxation due to stochastic motion is generally believed to give rise to such negative peaks. Herein, we use theoretical calculations, numerical simulations and experiments to show that the origin of the negative cross-peaks in PSD spectrum is due to coherent interactions. The origin of negative peaks can be specifically ascribed to a four spin, double-flip-double flop term, in the third-order Hamiltonian. These terms become the dominant terms at fast spinning when additional - conditions are satisfied.
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Affiliation(s)
- Vipin Agarwal
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad, Sy. No. 36/P, Gopanpally, Ranga Reddy District, Hyderabad 500 107, India.
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Lapin J, Nevzorov AA. De novo NMR pulse sequence design using Monte-Carlo optimization techniques. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2020; 310:106641. [PMID: 31734619 DOI: 10.1016/j.jmr.2019.106641] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2019] [Revised: 11/03/2019] [Accepted: 11/04/2019] [Indexed: 06/10/2023]
Abstract
Separated Local Field (SLF) experiments have been routinely used for measuring 1H-15N heteronuclear dipolar couplings in oriented-sample solid-state NMR for structure determination of proteins. In the on-going pursuit of designing better-performing SLF pulse sequences (e.g. by increasing the number of subdwells, and varying the rf amplitudes and phases), analytical treatment of the relevant average Hamiltonian terms may become cumbersome and/or nearly impossible. Numerical simulations of NMR experiments using GPU processors can be employed to rapidly calculate spectra for moderately sized spin systems, which permit an efficient numeric optimization of pulse sequences by the Monte Carlo Simulated Annealing protocol. In this work, a computational strategy was developed to find the optimal phases and timings that substantially improve the 1H-15N dipolar linewidths over a broad range of dipolar couplings as compared to SAMPI4. More than 100 pulse sequences were developed de novo and tested on an N-acetyl Leucine crystal. Seventeen distinct pulse sequences were shown to produce sharper mean linewidths than SAMPI4. Overall, these pulse sequences have more variable parameters (involving non-quadrature phases) and do not involve symmetry between the odd and even dwells, which would likely preclude their rigorous analytical treatment. The top performing pulse sequence, termed ROULETTE-1, has 18% sharper mean linewidths than SAMPI4 when run on an N-acetyl Leucine crystal. This sequence was also shown to be robust over a broad range of 1H carrier frequencies and various crystal orientations. The performance of such an optimized pulse sequence was also illustrated on 15N Leucine-labeled Pf1 coat protein reconstituted in magnetically aligned bicelles. For the optimized pulse sequence the mean peak width was 14% sharper than SAMPI4, which in turn yielded a better signal to noise ratio, 20:1 vs. 17:1. This method is potentially extendable to de novo development of a variety of NMR experiments.
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Affiliation(s)
- Joel Lapin
- Department of Chemistry, North Carolina State University, 2620 Yarbrough Drive, Raleigh, NC 27695-8204, United States
| | - Alexander A Nevzorov
- Department of Chemistry, North Carolina State University, 2620 Yarbrough Drive, Raleigh, NC 27695-8204, United States.
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30
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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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31
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Malär AA, Smith-Penzel S, Camenisch GM, Wiegand T, Samoson A, Böckmann A, Ernst M, Meier BH. Quantifying proton NMR coherent linewidth in proteins under fast MAS conditions: a second moment approach. Phys Chem Chem Phys 2019; 21:18850-18865. [PMID: 31432055 DOI: 10.1039/c9cp03414e] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
Proton detected solid-state NMR under fast magic-angle-spinning (MAS) conditions is currently redefining the applications of solid-state NMR, in particular in structural biology. Understanding the contributions to the spectral linewidth is thereby of paramount importance. When disregarding the sample-dependent inhomogeneous contributions, the NMR proton linewidth is defined by homogeneous broadening, which has incoherent and coherent contributions. Understanding and disentangling these different contributions in multi-spin systems like proteins is still an open issue. The coherent contribution is mainly caused by the dipolar interaction under MAS and is determined by the molecular structure and the proton chemical shifts. Numerical simulation approaches based on numerically exact direct integration of the Liouville-von Neumann equation can give valuable information about the lineshape, but are limited to small spin systems (<12 spins). We present an alternative simulation method for the coherent contributions based on the rapid and partially analytic calculation of the second moments of large spin systems. We first validate the method on a simple system by predicting the 19F linewidth in CaF2 under MAS. We compare simulation results to experimental data for microcrystalline ubiquitin (deuterated 100% back-exchanged at 110 kHz and fully-protonated at 125 kHz). Our results quantitatively explain the observed linewidth per-residue basis for the vast majority of residues.
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Affiliation(s)
- Alexander A Malär
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland.
| | - Susanne Smith-Penzel
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland.
| | - Gian-Marco Camenisch
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland.
| | - Thomas Wiegand
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland.
| | - Ago Samoson
- School of Information Technologies, Tallinn University of Technology, Tallinn, Estonia. and NMR Institute MTÜ, Tallinn, Estonia
| | - Anja Böckmann
- Institut de Biologie et Chimie des Protéines, Bases Moléculaires et Structurales des Systèmes Infectieux, Labex Ecofect, UMR 5086 CNRS, Université de Lyon, 7 passage du Vercors, 69367 Lyon, France.
| | - Matthias Ernst
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland.
| | - Beat H Meier
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland.
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32
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Pell AJ, Pintacuda G, Grey CP. Paramagnetic NMR in solution and the solid state. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2019; 111:1-271. [PMID: 31146806 DOI: 10.1016/j.pnmrs.2018.05.001] [Citation(s) in RCA: 210] [Impact Index Per Article: 42.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2017] [Revised: 05/11/2018] [Accepted: 05/12/2018] [Indexed: 05/22/2023]
Abstract
The field of paramagnetic NMR has expanded considerably in recent years. This review addresses both the theoretical description of paramagnetic NMR, and the way in which it is currently practised. We provide a review of the theory of the NMR parameters of systems in both solution and the solid state. Here we unify the different languages used by the NMR, EPR, quantum chemistry/DFT, and magnetism communities to provide a comprehensive and coherent theoretical description. We cover the theory of the paramagnetic shift and shift anisotropy in solution both in the traditional formalism in terms of the magnetic susceptibility tensor, and using a more modern formalism employing the relevant EPR parameters, such as are used in first-principles calculations. In addition we examine the theory first in the simple non-relativistic picture, and then in the presence of spin-orbit coupling. These ideas are then extended to a description of the paramagnetic shift in periodic solids, where it is necessary to include the bulk magnetic properties, such as magnetic ordering at low temperatures. The description of the paramagnetic shift is completed by describing the current understanding of such shifts due to lanthanide and actinide ions. We then examine the paramagnetic relaxation enhancement, using a simple model employing a phenomenological picture of the electronic relaxation, and again using a more complex state-of-the-art theory which incorporates electronic relaxation explicitly. An additional important consideration in the solid state is the impact of bulk magnetic susceptibility effects on the form of the spectrum, where we include some ideas from the field of classical electrodynamics. We then continue by describing in detail the solution and solid-state NMR methods that have been deployed in the study of paramagnetic systems in chemistry, biology, and the materials sciences. Finally we describe a number of case studies in paramagnetic NMR that have been specifically chosen to highlight how the theory in part one, and the methods in part two, can be used in practice. The systems chosen include small organometallic complexes in solution, solid battery electrode materials, metalloproteins in both solution and the solid state, systems containing lanthanide ions, and multi-component materials used in pharmaceutical controlled-release formulations that have been doped with paramagnetic species to measure the component domain sizes.
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Affiliation(s)
- Andrew J Pell
- Department of Materials and Environmental Chemistry, Arrhenius Laboratory, Stockholm University, Svante Arrhenius väg 16 C, SE-106 91 Stockholm, Sweden.
| | - Guido Pintacuda
- Institut des Sciences Analytiques (CNRS UMR 5280, ENS de Lyon, UCB Lyon 1), Université de Lyon, 5 rue de la Doua, 69100 Villeurbanne, France
| | - Clare P Grey
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
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33
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Equbal A, Leavesley A, Jain SK, Han S. Cross-Effect Dynamic Nuclear Polarization Explained: Polarization, Depolarization, and Oversaturation. J Phys Chem Lett 2019; 10:548-558. [PMID: 30645130 DOI: 10.1021/acs.jpclett.8b02834] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
The scope of this Perspective is to analytically describe NMR hyperpolarization by the three-spin cross effect (CE) dynamic nuclear polarization (DNP) using an effective Hamiltonian concept. We apply, for the first time, the bimodal operator-based Floquet theory in the Zeeman-interaction frame for two and three coupled spins to derive the known interaction Hamiltonian for CE-DNP. With a unified understanding of CE-DNP, and supported by empirical observation of the state of electron spin polarization under the given experimental conditions, we explain diverse manifestations of CE from oversaturation, enhanced hyperpolarization by broad-band saturation, to nuclear spin depolarization under magic-angle spinning.
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Affiliation(s)
- Asif Equbal
- Department of Chemistry and Biochemistry , University of California, Santa Barbara , Santa Barbara , California 93106 , United States
| | - Alisa Leavesley
- Department of Chemistry and Biochemistry , University of California, Santa Barbara , Santa Barbara , California 93106 , United States
| | - Sheetal Kumar Jain
- Department of Chemistry and Biochemistry , University of California, Santa Barbara , Santa Barbara , California 93106 , United States
| | - Songi Han
- Department of Chemistry and Biochemistry , University of California, Santa Barbara , Santa Barbara , California 93106 , United States
- Department of Chemical Engineering , University of California, Santa Barbara , Santa Barbara , California 93106 , United States
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34
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Sheberstov KF, Kiryutin AS, Bengs C, Hill-Cousins JT, Brown LJ, Brown RCD, Pileio G, Levitt MH, Yurkovskaya AV, Ivanov KL. Excitation of singlet–triplet coherences in pairs of nearly-equivalent spins. Phys Chem Chem Phys 2019; 21:6087-6100. [DOI: 10.1039/c9cp00451c] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
We present approaches for an efficient excitation of singlet–triplet coherences in pairs of nearly-equivalent spins.
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Affiliation(s)
- Kirill F. Sheberstov
- International Tomography Center
- Siberian Branch of the Russian Academy of Science
- Novosibirsk
- Russia
- Johannes Gutenberg-Universität
| | - Alexey S. Kiryutin
- International Tomography Center
- Siberian Branch of the Russian Academy of Science
- Novosibirsk
- Russia
- Novosibirsk State University
| | | | | | - Lynda J. Brown
- School of Chemistry
- University of Southampton
- Southampton
- UK
| | | | | | | | - Alexandra V. Yurkovskaya
- International Tomography Center
- Siberian Branch of the Russian Academy of Science
- Novosibirsk
- Russia
- Novosibirsk State University
| | - Konstantin L. Ivanov
- International Tomography Center
- Siberian Branch of the Russian Academy of Science
- Novosibirsk
- Russia
- Novosibirsk State University
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35
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Tan KO, Yang C, Weber RT, Mathies G, Griffin RG. Time-optimized pulsed dynamic nuclear polarization. SCIENCE ADVANCES 2019; 5:eaav6909. [PMID: 30746482 PMCID: PMC6357739 DOI: 10.1126/sciadv.aav6909] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2018] [Accepted: 12/05/2018] [Indexed: 05/05/2023]
Abstract
Pulsed dynamic nuclear polarization (DNP) techniques can accomplish electron-nuclear polarization transfer efficiently with an enhancement factor that is independent of the Zeeman field. However, they often require large Rabi frequencies and, therefore, high-power microwave irradiation. Here, we propose a new low-power DNP sequence for static samples that is composed of a train of microwave pulses of length τp spaced with delays d. A particularly robust DNP condition using a period τm = τp + d set to ~1.25 times the Larmor period τLarmor is investigated which is a time-optimized pulsed DNP sequence (TOP-DNP). At 0.35 T, we obtained an enhancement of ~200 using TOP-DNP compared to ~172 with nuclear spin orientation via electron spin locking (NOVEL), a commonly used pulsed DNP sequence, while using only ~7% microwave power required for NOVEL. Experimental data and simulations at higher fields suggest a field-independent enhancement factor, as predicted by the effective Hamiltonian.
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Affiliation(s)
- Kong Ooi Tan
- Francis Bitter Magnet Laboratory and Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Chen Yang
- Francis Bitter Magnet Laboratory and Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | | | - Guinevere Mathies
- Francis Bitter Magnet Laboratory and Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Robert G. Griffin
- Francis Bitter Magnet Laboratory and Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Corresponding author.
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36
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Gan Z, Hung I, Nishiyama Y, Amoureux JP, Lafon O, Nagashima H, Trébosc J, Hu B. 14N overtone nuclear magnetic resonance of rotating solids. J Chem Phys 2018; 149:064201. [PMID: 30111134 PMCID: PMC8808743 DOI: 10.1063/1.5044653] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2018] [Accepted: 07/17/2018] [Indexed: 11/14/2022] Open
Abstract
By irradiating and observing at twice the 14N Larmor frequency, overtone (OT) nuclear magnetic resonance (NMR) is capable of obtaining 14NOT spectra without first-order quadrupolar broadening. Direct excitation and detection of the usually "forbidden" double-quantum transition is mediated by the perturbation from the large quadrupole interaction to the spin states quantized by the Zeeman interaction. A recent study [L. A. O'Dell and C. I. Ratcliffe, Chem. Phys. Lett. 514, 168 (2011)] has shown that 14NOT NMR under magic-angle spinning (MAS) can yield high-resolution spectra with typical second-order quadrupolar line shapes allowing the measurement of 14N chemical shift and quadrupolar coupling parameters. This article has also shown that under MAS the main 14NOT peak is shifted by twice the sample spinning frequency with respect to its static position. We present the theory of 14NOT NMR of static or rotating samples and the physical picture of the intriguing spinning-induced shift in the second case. We use perturbation theory for the case of static samples and Floquet theory for rotating samples. In both cases, the results can be described by a so-called OT parameter that scales down the 14NOT radio-frequency (rf) excitation and signal detection. This OT parameter shows that the components of the rf field, which are transverse and longitudinal with respect to the magnetic field, are both effective for 14NOTrf excitation and signal detection. In the case of MAS at angular frequency ωr , the superposition of the excitation and detection components in the OT parameter makes either the +2ωr or -2ωr term the dominant 14NOT signal, depending on the sense of sample spinning with respect to the magnetic field. This leads to an apparent 14NOT signal shifted at twice the spinning frequency. The features of 14NOT NMR spectra for both static and rotating samples are illustrated with simulations. The spinning induced shift and its dependence on the spinning direction are confirmed experimentally by reversing the spinning direction and the field of the 36 T series-connected hybrid magnet at the US National High Magnetic Field Laboratory.
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Affiliation(s)
- Zhehong Gan
- Center of Interdisciplinary Magnetic Resonance, National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, Florida 32310, USA
| | - Ivan Hung
- Center of Interdisciplinary Magnetic Resonance, National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, Florida 32310, USA
| | | | | | | | - Hiroki Nagashima
- Univ. Lille, CNRS UMR 8181, UCCS Unit of Catalysis and Chemistry of Solids, F-59000 Lille, France
| | - Julien Trébosc
- Univ. Lille, CNRS UMR 8181, UCCS Unit of Catalysis and Chemistry of Solids, F-59000 Lille, France
| | - Bingwen Hu
- Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Materials Science, East China Normal University, Shanghai 200062, China
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37
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Pell AJ, Sanders KJ, Wegner S, Pintacuda G, Grey CP. Low-power broadband solid-state MAS NMR of 14N. J Chem Phys 2018; 146:194202. [PMID: 28527462 DOI: 10.1063/1.4983220] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose two broadband pulse schemes for 14N solid-state magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) that achieves (i) complete population inversion and (ii) efficient excitation of the double-quantum spectrum using low-power single-sideband-selective pulses. We give a comprehensive theoretical description of both schemes using a common framework that is based on the jolting-frame formalism of Caravatti et al. [J. Magn. Reson. 55, 88 (1983)]. This formalism is used to determine for the first time that we can obtain complete population inversion of 14N under low-power conditions, which we do here using single-sideband-selective adiabatic pulses. It is then used to predict that double-quantum coherences can be excited using low-power single-sideband-selective pulses. We then proceed to design a new experimental scheme for double-quantum excitation. The final double-quantum excitation pulse scheme is easily incorporated into other NMR experiments, as demonstrated here for double quantum-single quantum 14N correlation spectroscopy, and 1H-14N dipolar heteronuclear multiple-quantum correlation experiments. These pulses and irradiation schemes are evaluated numerically using simulations on single crystals and full powders, as well as experimentally on ammonium oxalate ((NH4)2C2O4) at moderate MAS and glycine at ultra-fast MAS. The performance of these new NMR methods is found to be very high, with population inversion efficiencies of 100% and double-quantum excitation efficiencies of 30%-50%, which are hitherto unprecedented for the low radiofrequency field amplitudes, up to the spinning frequency, that are used here.
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Affiliation(s)
- Andrew J Pell
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Kevin J Sanders
- Centre de RMN à Très Hauts Champs, Institut des Sciences Analytiques (CNRS, ENS Lyon, UCB Lyon 1), Université de Lyon, 69100 Villeurbanne, France
| | | | - Guido Pintacuda
- Centre de RMN à Très Hauts Champs, Institut des Sciences Analytiques (CNRS, ENS Lyon, UCB Lyon 1), Université de Lyon, 69100 Villeurbanne, France
| | - Clare P Grey
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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38
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Bengs C, Levitt MH. SpinDynamica: Symbolic and numerical magnetic resonance in a Mathematica environment. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2018; 56:374-414. [PMID: 28809056 PMCID: PMC6001486 DOI: 10.1002/mrc.4642] [Citation(s) in RCA: 76] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2017] [Accepted: 08/03/2017] [Indexed: 05/11/2023]
Abstract
SpinDynamica is a set of Mathematica packages for performing numerical and symbolic analysis of a wide range of magnetic resonance experiments and phenomena. An overview of the SpinDynamica architecture and functionality is given, with some simple representative examples.
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Affiliation(s)
- Christian Bengs
- School of ChemistryUniversity of SouthamptonSouthamptonSO17 1BJUK
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39
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Mote KR, Madhu PK. Simultaneous homonuclear and heteronuclear spin decoupling in magic-angle spinning solid-state NMR. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2018; 90:7-12. [PMID: 29370958 DOI: 10.1016/j.ssnmr.2018.01.001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2017] [Revised: 01/08/2018] [Accepted: 01/09/2018] [Indexed: 06/07/2023]
Abstract
We show here an effective way of implementing simultaneously homonuclear and heteronuclear dipolar decoupling in magic-angle spinning (MAS) solid-state NMR. Whilst the homonuclear spin decoupling is applied on the 1H channel, heteronuclear spin decoupling is applied on the 13C channel. The 1H spins are observed in a windowed fashion in this case. The resultant 1H spectrum has higher resolution due to the attenuation of broadening arising from both homonuclear 1H-1H and heteronuclear 1H-13C interactions, with the latter normally leading to additional line broadening in 13C labelled samples. The experiments are performed at MAS frequencies of ca. 60 kHz.
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Affiliation(s)
- Kaustubh R Mote
- Tata Institute of Fundamental Research Hyderabad, Survey No. 36/P, Gopanapally Village, Serilingampally Mandal, Ranga Reddy District, Hyderabad, 500 107, India.
| | - Perunthiruthy K Madhu
- Tata Institute of Fundamental Research Hyderabad, Survey No. 36/P, Gopanapally Village, Serilingampally Mandal, Ranga Reddy District, Hyderabad, 500 107, India; Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, 400 005, India.
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40
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Tan KO, Agarwal V, Lakomek NA, Penzel S, Meier BH, Ernst M. Efficient low-power TOBSY sequences for fast MAS. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2018; 89:27-34. [PMID: 29233617 DOI: 10.1016/j.ssnmr.2017.11.003] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2017] [Revised: 11/28/2017] [Accepted: 11/28/2017] [Indexed: 06/07/2023]
Abstract
Through-bond J-coupling based experiments in solid-state NMR spectroscopy are challenging because the J couplings are typically much smaller than the dipolar couplings. This often leads to a lower transfer efficiency compared to dipolar-coupling based sequences. One of the reasons for the low transfer efficiency are the second-order cross terms involving the strong heteronuclear dipolar couplings leading to fast magnetization decay. Here, we show that by employing a symmetry-based C9 sequence, which was carefully selected to suppress second-order terms, efficient polarization transfers of up to 80% can be achieved without decoupling on fully protonated two-spin model systems at a MAS frequency of 55.5 kHz with rf-field amplitudes of about 25 kHz. In addition, we analyse the effects of rf inhomogeneity and crystallites selection due to the polarization preparation method on the TOBSY transfer efficiency. We demonstrate on small model substances as well as on deuterated and 100% back-exchanged ubiquitin that C9391 and C9481 are efficient and practical TOBSY sequences at experimental conditions ranging from proton Larmor frequencies of 400-850 MHz, and MAS frequencies ranging from 55.5 to 111.1 kHz.
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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
| | | | - Susanne Penzel
- 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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41
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Tunable two-phonon higher-order sideband amplification in a quadratically coupled optomechanical system. Sci Rep 2017; 7:17637. [PMID: 29247232 PMCID: PMC5732222 DOI: 10.1038/s41598-017-17974-y] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2017] [Accepted: 12/04/2017] [Indexed: 11/20/2022] Open
Abstract
We propose an efficient scheme for the controllable amplification of two-phonon higher-order sidebands in a quadratically coupled optomechanical system. In this scheme, a strong control field and a weak probe pulse are injected into the cavity, and the membrane located at the middle position of the cavity is driven resonantly by a weak coherent mechanical pump. Beyond the conventional linearized approximation, we derive analytical expressions for the output transmission of probe pulse and the amplitude of second-order sideband by adding the nonlinear coefficients into the Heisenberg-Langevin formalism. Using experimentally achievable parameters, we identify the conditions under which the mechanical pump and the frequency detuning of control field allow us to modify the transmission of probe pulse and improve the amplitude of two-phonon higher-order sideband generation beyond what is achievable in absence of the mechanical pump. Furthermore, we also find that the higher-order sideband generation depends sensitively on the phase of mechanical pump when the control field becomes strong. The present proposal offers a practical opportunity to design chip-scale optical communications and optical frequency combs.
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42
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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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43
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Mananga ES. Equivalence of the Floquet–Magnus and Fer Expansions to Investigate the Dynamics of a Spin System in the Three-Level System. J Phys Chem A 2017; 121:6063-6078. [DOI: 10.1021/acs.jpca.7b01723] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Eugene Stephane Mananga
- Ph.D. Program in
Physics and Ph.D. Program in Chemistry, The Graduate Center, The City University of New York, 365 Fifth Avenue, New York, New York 10016, United States
- Department of Applied Physics, New York University, 6 Metrotech Center, Brooklyn, New York 11201, United States
- Department of Engineering, Physics, and Technology, The City University of New York, BCC, 2155 University Avenue, CPH 118, Bronx, New York 10453, United States
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44
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Cirio M, Debnath K, Lambert N, Nori F. Amplified Optomechanical Transduction of Virtual Radiation Pressure. PHYSICAL REVIEW LETTERS 2017; 119:053601. [PMID: 28949752 DOI: 10.1103/physrevlett.119.053601] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2017] [Indexed: 06/07/2023]
Abstract
Here we describe how, utilizing a time-dependent optomechanical interaction, a mechanical probe can provide an amplified measurement of the virtual photons dressing the quantum ground state of an ultrastrongly coupled light-matter system. We calculate the thermal noise tolerated by this measurement scheme and discuss an experimental setup in which it could be realized.
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Affiliation(s)
- Mauro Cirio
- CEMS, RIKEN, Wako-shi, Saitama 351-0198, Japan
| | - Kamanasish Debnath
- CEMS, RIKEN, Wako-shi, Saitama 351-0198, Japan
- EPFL, CH-1015 Lausanne, Switzerland
| | | | - Franco Nori
- CEMS, RIKEN, Wako-shi, Saitama 351-0198, Japan
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
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45
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Coote P, Anklin C, Massefski W, Wagner G, Arthanari H. Rapid convergence of optimal control in NMR using numerically-constructed toggling frames. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2017; 281:94-103. [PMID: 28578162 PMCID: PMC5541913 DOI: 10.1016/j.jmr.2017.05.011] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2017] [Revised: 05/18/2017] [Accepted: 05/22/2017] [Indexed: 05/23/2023]
Abstract
We present a numerical method for rapidly solving the Bloch equation for an arbitrary time-varying spin-1/2 Hamiltonian. The method relies on fast, vectorized computations such as summation and quaternion multiplication, rather than slow computations such as matrix exponentiation. A toggling frame is constructed in which the Hamiltonian is time-invariant, and therefore has a simple analytical solution. The key insight is that constructing this frame is faster than solving the system dynamics in the original frame. Rapidly solving the Bloch equations for an arbitrary Hamiltonian is particularly useful in the context of NMR optimal control. Optimal control theory can be used to design pulse shapes for a range of tasks in NMR spectroscopy. However, it requires multiple simulations of the Bloch equations at each stage of the algorithm, and for each relevant set of parameters (e.g. chemical shift frequencies). This is typically time consuming. We demonstrate that by working in an appropriate toggling frame, optimal control pulses can be generated much faster. We present a new alternative to the well-known GRAPE algorithm to continuously update the toggling-frame as the optimal pulse is generated, and demonstrate that this approach is extremely fast. The use and benefit of rapid optimal pulse generation is demonstrated for 19F fragment screening experiments.
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Affiliation(s)
- Paul Coote
- Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, Boston, MA, USA.
| | | | | | - Gerhard Wagner
- Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, Boston, MA, USA
| | - Haribabu Arthanari
- Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, Boston, MA, USA; Dana Farber Cancer Institute, Boston, MA, USA.
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46
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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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47
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Shankar R, Ernst M, Madhu PK, Vosegaard T, Nielsen NC, Nielsen AB. A general theoretical description of the influence of isotropic chemical shift in dipolar recoupling experiments for solid-state NMR. J Chem Phys 2017; 146:134105. [DOI: 10.1063/1.4979123] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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48
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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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49
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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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50
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Mote KR, Agarwal V, Madhu PK. Five decades of homonuclear dipolar decoupling in solid-state NMR: Status and outlook. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2016; 97:1-39. [PMID: 27888838 DOI: 10.1016/j.pnmrs.2016.08.001] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2016] [Revised: 07/11/2016] [Accepted: 08/02/2016] [Indexed: 06/06/2023]
Abstract
It has been slightly more than fifty years since the first homonuclear spin decoupling scheme, Lee-Goldburg decoupling, was proposed for removing homonuclear dipolar interactions in solid-state nuclear magnetic resonance. A family of such schemes has made observation of high-resolution NMR spectra of abundant spins possible in various applications in solid state. This review outlines the strategies used in this field and the future prospects of homonuclear spin decoupling in solid-state NMR.
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Affiliation(s)
- Kaustubh R Mote
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Narsingi, Hyderabad 500 075, India
| | - Vipin Agarwal
- 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 400 005, India
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