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Title: Comparison among Magnus/Floquet/Fer expansion schemes in solid-state NMR

Abstract

We here revisit expansion schemes used in nuclear magnetic resonance (NMR) for the calculation of effective Hamiltonians and propagators, namely, Magnus, Floquet, and Fer expansions. While all the expansion schemes are powerful methods there are subtle differences among them. To understand the differences, we performed explicit calculation for heteronuclear dipolar decoupling, cross-polarization, and rotary-resonance experiments in solid-state NMR. As the propagator from the Fer expansion takes the form of a product of sub-propagators, it enables us to appreciate effects of time-evolution under Hamiltonians with different orders separately. While 0th-order average Hamiltonian is the same for the three expansion schemes with the three cases examined, there is a case that the 2nd-order term for the Magnus/Floquet expansion is different from that obtained with the Fer expansion. The difference arises due to the separation of the 0th-order term in the Fer expansion. The separation enables us to appreciate time-evolution under the 0th-order average Hamiltonian, however, for that purpose, we use a so-called left-running Fer expansion. Comparison between the left-running Fer expansion and the Magnus expansion indicates that the sign of the odd orders in Magnus may better be reversed if one would like to consider its effect in order.

Authors:
 [1];  [2];  [2]
  1. Division of Chemistry, Graduate School of Science, Kyoto University, 606-8502 Kyoto (Japan)
  2. TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500 075 (India)
Publication Date:
OSTI Identifier:
22415603
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 142; Journal Issue: 13; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; COMPARATIVE EVALUATIONS; DECOUPLING; EXPANSION; FLOQUET FUNCTION; HAMILTONIANS; NUCLEAR MAGNETIC RESONANCE; POLARIZATION; PROPAGATOR; SOLIDS

Citation Formats

Takegoshi, K., E-mail: takeyan@kuchem.kyoto-u.ac.jp, Miyazawa, Norihiro, Sharma, Kshama, Madhu, P. K., and Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005. Comparison among Magnus/Floquet/Fer expansion schemes in solid-state NMR. United States: N. p., 2015. Web. doi:10.1063/1.4916324.
Takegoshi, K., E-mail: takeyan@kuchem.kyoto-u.ac.jp, Miyazawa, Norihiro, Sharma, Kshama, Madhu, P. K., & Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005. Comparison among Magnus/Floquet/Fer expansion schemes in solid-state NMR. United States. https://doi.org/10.1063/1.4916324
Takegoshi, K., E-mail: takeyan@kuchem.kyoto-u.ac.jp, Miyazawa, Norihiro, Sharma, Kshama, Madhu, P. K., and Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005. 2015. "Comparison among Magnus/Floquet/Fer expansion schemes in solid-state NMR". United States. https://doi.org/10.1063/1.4916324.
@article{osti_22415603,
title = {Comparison among Magnus/Floquet/Fer expansion schemes in solid-state NMR},
author = {Takegoshi, K., E-mail: takeyan@kuchem.kyoto-u.ac.jp and Miyazawa, Norihiro and Sharma, Kshama and Madhu, P. K. and Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005},
abstractNote = {We here revisit expansion schemes used in nuclear magnetic resonance (NMR) for the calculation of effective Hamiltonians and propagators, namely, Magnus, Floquet, and Fer expansions. While all the expansion schemes are powerful methods there are subtle differences among them. To understand the differences, we performed explicit calculation for heteronuclear dipolar decoupling, cross-polarization, and rotary-resonance experiments in solid-state NMR. As the propagator from the Fer expansion takes the form of a product of sub-propagators, it enables us to appreciate effects of time-evolution under Hamiltonians with different orders separately. While 0th-order average Hamiltonian is the same for the three expansion schemes with the three cases examined, there is a case that the 2nd-order term for the Magnus/Floquet expansion is different from that obtained with the Fer expansion. The difference arises due to the separation of the 0th-order term in the Fer expansion. The separation enables us to appreciate time-evolution under the 0th-order average Hamiltonian, however, for that purpose, we use a so-called left-running Fer expansion. Comparison between the left-running Fer expansion and the Magnus expansion indicates that the sign of the odd orders in Magnus may better be reversed if one would like to consider its effect in order.},
doi = {10.1063/1.4916324},
url = {https://www.osti.gov/biblio/22415603}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 13,
volume = 142,
place = {United States},
year = {Tue Apr 07 00:00:00 EDT 2015},
month = {Tue Apr 07 00:00:00 EDT 2015}
}