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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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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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Ganapathy V, Ramachandran R. Effective Floquet Hamiltonian theory of multiple-quantum NMR in anisotropic solids involving quadrupolar spins: Challenges and Perspectives. J Chem Phys 2017; 147:144202. [DOI: 10.1063/1.4993313] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Vinay Ganapathy
- Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, Mohali 140306, Punjab, India
| | - Ramesh Ramachandran
- Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, Mohali 140306, Punjab, India
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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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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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SivaRanjan U, Ramachandran R. Unraveling multi-spin effects in rotational resonance nuclear magnetic resonance using effective reduced density matrix theory. J Chem Phys 2014; 140:054101. [DOI: 10.1063/1.4863212] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Pandey MK, Qadri Z, Ramachandran R. Understanding cross-polarization (CP) NMR experiments through dipolar truncation. J Chem Phys 2013; 138:114108. [PMID: 23534628 DOI: 10.1063/1.4794856] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A theoretical model based on the phenomenon of dipolar truncation is proposed to explain the nuances of polarization transfer from abundant to less-abundant nuclei in cross-polarization (CP) NMR experiments. Specifically, the transfer of polarization from protons to carbons (in solids) in strongly coupled systems is described in terms of effective Hamiltonians based on dipolar truncation. Through suitable model spin systems, the important role of dipolar truncation in the propagation of spin polarization in CP experiments is outlined. We believe that the analytic theory presented herein provides a convenient framework for modeling polarization transfer in strongly coupled systems.
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Affiliation(s)
- Manoj Kumar Pandey
- Department of Chemical Sciences, Indian Institute of Science Education and Research Mohali, Sector 81, Manauli P.O. Box-140306, Mohali, Punjab, India
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