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Bernatowicz P, Shkurenko A, Osior A, Kamieński B, Szymański S. A quantum mechanical alternative to the Arrhenius equation in the interpretation of proton spin-lattice relaxation data for the methyl groups in solids. Phys Chem Chem Phys 2015; 17:28866-78. [PMID: 26451661 DOI: 10.1039/c5cp04924e] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The theory of nuclear spin-lattice relaxation in methyl groups in solids has been a recurring problem in nuclear magnetic resonance (NMR) spectroscopy. The current view is that, except for extreme cases of low torsional barriers where special quantum effects are at stake, the relaxation behaviour of the nuclear spins in methyl groups is controlled by thermally activated classical jumps of the methyl group between its three orientations. The temperature effects on the relaxation rates can be modelled by Arrhenius behaviour of the correlation time of the jump process. The entire variety of relaxation effects in protonated methyl groups have recently been given a consistent quantum mechanical explanation not invoking the jump model regardless of the temperature range. It exploits the damped quantum rotation (DQR) theory originally developed to describe NMR line shape effects for hindered methyl groups. In the DQR model, the incoherent dynamics of the methyl group include two quantum rate (i.e., coherence-damping) processes. For proton relaxation only one of these processes is relevant. In this paper, temperature-dependent proton spin-lattice relaxation data for the methyl groups in polycrystalline methyltriphenyl silane and methyltriphenyl germanium, both deuterated in aromatic positions, are reported and interpreted in terms of the DQR model. A comparison with the conventional approach exploiting the phenomenological Arrhenius equation is made. The present observations provide further indications that incoherent motions of molecular moieties in the condensed phase can retain quantum character over much broader temperature range than is commonly thought.
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Affiliation(s)
- Piotr Bernatowicz
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
| | - Aleksander Shkurenko
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland. and Functional Materials Design, Discovery and Development Research Group (FMD3), Advanced Membranes and Porous Materials Center, Division of Physical Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia
| | - Agnieszka Osior
- Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
| | - Bohdan Kamieński
- Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
| | - Sławomir Szymański
- Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
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Takeda S, Inabe T, Benedict C, Langer U, Limbach HH. Proton Dynamics in Interacting Hydrogen Bonds in the Solid State: Proton Tunneling in the NHO Hydrogen Bonds of N,N′-Di(2-Hydroxy-1-Naphthylmethylene)-p-Phenylenediamine. ACTA ACUST UNITED AC 2014. [DOI: 10.1002/bbpc.199800004] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Szymański S. Spin-lattice relaxation of the methyl group protons in solids revisited: damped quantum rotation approach. J Chem Phys 2012; 137:034513. [PMID: 22830717 DOI: 10.1063/1.4734251] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Proton spin-lattice relaxation of the methyl group in solids had been one of the most thoroughly addressed theoretical problems in nuclear magnetic resonance (NMR) spectroscopy, considered at different levels of sophistication. For systems with substantial quantum tunneling effects, several quantum mechanical treatments were reported, although in practical applications the quantum models were always augmented with or replaced by the classical jump model. However, the latter has recently proved invalid in the description of NMR line shape effects in variable-temperature spectra of hindered methyl groups, while the competing theory of damped quantum rotation (DQR) was shown to be adequate. In this work, the spin-lattice relaxation issue for the methyl protons is readdressed using the latter theory. The main outcome is that, while the existing formulas for the relaxation rates remain unchanged, the crucial parameter entering them, the correlation time of the relevant random process, need to be reinterpreted. It proves to be the inverse of one of the two quantum-rate constants entering the DQR model, neither of which, when taken separately, can be related to the jump process. It can be identified with one describing the life-time broadening of the tunnel peaks in inelastic neutron scattering (INS) spectra of the methyl groups. Such a relationship between the relaxation and INS effects was reported from another laboratory long ago, but only for the low-temperature limit where thermal population of the excited torsional levels of the methyl group can be neglected. The whole spectrum of cases encountered in practical relaxation studies on protonated methyl groups is addressed for the first time. Preliminary experimental confirmation of this novel approach is reported, based on already published NMR data for a single crystal of methylmalonic acid. The once extensively debated issues of quenching of the coherent tunneling and of the classical limit in the dynamics of the methyl groups are readdressed and presented in a consistent manner.
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Affiliation(s)
- S Szymański
- Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland.
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Dahlberg C, Dvinskikh SV, Schuleit M, Furó I. Polymer Swelling, Drug Mobilization and Drug Recrystallization in Hydrating Solid Dispersion Tablets Studied by Multinuclear NMR Microimaging and Spectroscopy. Mol Pharm 2011; 8:1247-56. [DOI: 10.1021/mp200051e] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Carina Dahlberg
- Division of Physical Chemistry and Industrial NMR Centre, Department of Chemistry, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
- YKI, Institute for Surface Chemistry, Box 5607, SE-114 86 Stockholm, Sweden
| | - Sergey V. Dvinskikh
- Division of Physical Chemistry and Industrial NMR Centre, Department of Chemistry, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
| | - Michael Schuleit
- Forum 1, Pharmaceutical & Analytical Development, Novartis Pharma AG, Novartis Campus, CH 4056 Basel, Switzerland
| | - István Furó
- Division of Physical Chemistry and Industrial NMR Centre, Department of Chemistry, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
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Affiliation(s)
- Barbara Gabryś
- a Laboratorium voor Vaste Stof-Fysika en Magnetisme , Katholieke Universiteit Leuven , B-3030 , Leuven , Belgium
- b Department of Chemical Engineering and Chemical Technology , Imperial College , Prince Consort Road, London , SW7 2BY , England
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Kimura N, Yamashita M, Ikeda R. Metallic behaviour and molecular motions in a 1-D –Pt–Pt–I– type complex, Pt2(CH3CS2)4I, studied by solid-state 13C and 1H NMR. Chem Phys Lett 2005. [DOI: 10.1016/j.cplett.2005.02.104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Gutsche P, Haeberlen U. The low-temperature 13C and 2H spectra and relaxation rates of methyl groups depend on the azimuth of B0 in the molecular frame. Those of 1H do not. Why? SOLID STATE NUCLEAR MAGNETIC RESONANCE 2004; 26:46-50. [PMID: 15157538 DOI: 10.1016/j.ssnmr.2003.11.002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2003] [Indexed: 05/24/2023]
Abstract
It is shown that the answer to the question asked in the title is: Because the axial symmetry axes of the H-H dipolar coupling tensors in a -CH3 group are perpendicular to the (assumed) threefold axis of the group. By contrast, those of the 13C-H dipolar and 2H quadrupolar coupling tensors are not. The use of "symmetry adapted" spin functions and of a symmetry adapted form of the (dipolar) coupling Hamiltonian greatly simplifies the analysis.
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Affiliation(s)
- P Gutsche
- SAP AG, Neurottstr. 16, 69190 Walldorf, Germany
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Gabrys B, Gerven LV. Coupling between the Zeeman and tunnel energies in pentamethylbenzene: measurements of the proton spin-lattice relaxation rate T1-1. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/18/6/018] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Šepa J, Gorte R, Suits B, White D. Molecular motion of methyl rotor in a zeolite: proton NMR lineshapes of CH3CN-2HZSM-5 adsorption complex. Chem Phys Lett 1998. [DOI: 10.1016/s0009-2614(98)00430-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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Kubo A, Dubey AK, McDowell CA. Proton two-dimensional exchange nuclear magnetic resonance study of a p-xylene-d6zeolite inclusion compound. Mol Phys 1994. [DOI: 10.1080/00268979400100751] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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CONNOR C. Low-Frequency Magnetic Resonance with a dc SQUID. ADVANCES IN MAGNETIC AND OPTICAL RESONANCE 1990. [DOI: 10.1016/s1057-2732(13)70009-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
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Murphy M, White D. Matrix isolation nuclear magnetic resonance studies of methyl group spin–rotation coupling. J Chem Phys 1989. [DOI: 10.1063/1.456789] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Murphy M, Semack MG, White D. Zeeman and dipolar coherences in dilute spin powders. matrix-isolated CH3CN. ACTA ACUST UNITED AC 1987. [DOI: 10.1016/0022-2364(87)90181-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Takeda S, Chihara H. Methyl rotation in 1,2,4,5-tetramethylbenzene and tetramethylpyrazine in the solid state. Tunneling spectra by proton NMR. ACTA ACUST UNITED AC 1983. [DOI: 10.1016/0022-2364(83)90050-1] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Morimoto K, Shimomura K, Ueki A. Spin-lattice relaxation of methyl groups in the rotating frame. ACTA ACUST UNITED AC 1982. [DOI: 10.1016/0022-2364(82)90271-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Application of the Jeener-Broekaert pulse sequence to molecular dynamics studies in liquid crystals. ACTA ACUST UNITED AC 1981. [DOI: 10.1016/0022-2364(81)90032-9] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Tang J, Sterna L, Pines A. Anisotropic spin-lattice relaxation of deuterated hexamethylbenzene. ACTA ACUST UNITED AC 1980. [DOI: 10.1016/0022-2364(80)90294-2] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Tang J, Pines A, Emid S. Spin–lattice relaxation of reorienting or tunneling deuterated methyl groups. J Chem Phys 1980. [DOI: 10.1063/1.439903] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Albert S, Ripmeester JA. Methyl group rotation and bonding in solid hexamethyldialuminum, Al2(CH3)6. J Chem Phys 1979. [DOI: 10.1063/1.437500] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Banks G, Wei IY, Johnson CS. Selective deuteration and the anomalous temperature dependence of proton spin–lattice relaxation in polycrystalline p-tert-butyltoluene. J Chem Phys 1978. [DOI: 10.1063/1.436887] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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