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Title: Simple expressions of the nuclear relaxation rate enhancement due to quadrupole nuclei in slowly tumbling molecules

Abstract

For slowly tumbling entities or quasi-rigid lattices, we derive very simple analytical expressions of the quadrupole relaxation enhancement (QRE) of the longitudinal relaxation rate R{sub 1} of nuclear spins I due to their intramolecular magnetic dipolar coupling with quadrupole nuclei of arbitrary spins S ≥ 1. These expressions are obtained by using the adiabatic approximation for evaluating the time evolution operator of the quantum states of the quadrupole nuclei S. They are valid when the gyromagnetic ratio of the spin S is much smaller than that of the spin I. The theory predicts quadrupole resonant peaks in the dispersion curve of R{sub 1} vs magnetic field. The number, positions, relative intensities, Lorentzian shapes, and widths of these peaks are explained in terms of the following properties: the magnitude of the quadrupole Hamiltonian and the asymmetry parameter of the electric field gradient (EFG) acting on the spin S, the S-I inter-spin orientation with respect to the EFG principal axes, the rotational correlation time of the entity carrying the S–I pair, and/or the proper relaxation time of the spin S. The theory is first applied to protein amide protons undergoing dipolar coupling with fast-relaxing quadrupole {sup 14}N nuclei and mediating the QREmore » to the observed bulk water protons. The theoretical QRE agrees well with its experimental counterpart for various systems such as bovine pancreatic trypsin inhibitor and cartilages. The anomalous behaviour of the relaxation rate of protons in synthetic aluminium silicate imogolite nano-tubes due to the QRE of {sup 27}Al (S = 5/2) nuclei is also explained.« less

Authors:
 [1];  [2];  [3];  [2]
  1. Université Grenoble Alpes, INAC-SCIB, RICC, F-38000 Grenoble (France)
  2. (France)
  3. Université Grenoble Alpes, LIPHY, F-38000 Grenoble (France)
Publication Date:
OSTI Identifier:
22493454
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 143; Journal Issue: 4; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ADIABATIC APPROXIMATION; ALUMINIUM 27; ALUMINIUM SILICATES; AMIDES; CARTILAGE; CORRELATIONS; COUPLING; ELECTRIC FIELDS; GYROMAGNETIC RATIO; HAMILTONIANS; MAGNETIC FIELDS; MOLECULES; NITROGEN 14; PANCREAS; QUANTUM STATES; RELAXATION TIME; SPIN; SPIN ORIENTATION; TRYPSIN; WATER

Citation Formats

Fries, Pascal H., E-mail: pascal-h.fries@cea.fr, CEA, INAC-SCIB, RICC, F-38000 Grenoble, Belorizky, Elie, and CEA, Leti-Clinatec, F-38000 Grenoble. Simple expressions of the nuclear relaxation rate enhancement due to quadrupole nuclei in slowly tumbling molecules. United States: N. p., 2015. Web. doi:10.1063/1.4926827.
Fries, Pascal H., E-mail: pascal-h.fries@cea.fr, CEA, INAC-SCIB, RICC, F-38000 Grenoble, Belorizky, Elie, & CEA, Leti-Clinatec, F-38000 Grenoble. Simple expressions of the nuclear relaxation rate enhancement due to quadrupole nuclei in slowly tumbling molecules. United States. doi:10.1063/1.4926827.
Fries, Pascal H., E-mail: pascal-h.fries@cea.fr, CEA, INAC-SCIB, RICC, F-38000 Grenoble, Belorizky, Elie, and CEA, Leti-Clinatec, F-38000 Grenoble. 2015. "Simple expressions of the nuclear relaxation rate enhancement due to quadrupole nuclei in slowly tumbling molecules". United States. doi:10.1063/1.4926827.
@article{osti_22493454,
title = {Simple expressions of the nuclear relaxation rate enhancement due to quadrupole nuclei in slowly tumbling molecules},
author = {Fries, Pascal H., E-mail: pascal-h.fries@cea.fr and CEA, INAC-SCIB, RICC, F-38000 Grenoble and Belorizky, Elie and CEA, Leti-Clinatec, F-38000 Grenoble},
abstractNote = {For slowly tumbling entities or quasi-rigid lattices, we derive very simple analytical expressions of the quadrupole relaxation enhancement (QRE) of the longitudinal relaxation rate R{sub 1} of nuclear spins I due to their intramolecular magnetic dipolar coupling with quadrupole nuclei of arbitrary spins S ≥ 1. These expressions are obtained by using the adiabatic approximation for evaluating the time evolution operator of the quantum states of the quadrupole nuclei S. They are valid when the gyromagnetic ratio of the spin S is much smaller than that of the spin I. The theory predicts quadrupole resonant peaks in the dispersion curve of R{sub 1} vs magnetic field. The number, positions, relative intensities, Lorentzian shapes, and widths of these peaks are explained in terms of the following properties: the magnitude of the quadrupole Hamiltonian and the asymmetry parameter of the electric field gradient (EFG) acting on the spin S, the S-I inter-spin orientation with respect to the EFG principal axes, the rotational correlation time of the entity carrying the S–I pair, and/or the proper relaxation time of the spin S. The theory is first applied to protein amide protons undergoing dipolar coupling with fast-relaxing quadrupole {sup 14}N nuclei and mediating the QRE to the observed bulk water protons. The theoretical QRE agrees well with its experimental counterpart for various systems such as bovine pancreatic trypsin inhibitor and cartilages. The anomalous behaviour of the relaxation rate of protons in synthetic aluminium silicate imogolite nano-tubes due to the QRE of {sup 27}Al (S = 5/2) nuclei is also explained.},
doi = {10.1063/1.4926827},
journal = {Journal of Chemical Physics},
number = 4,
volume = 143,
place = {United States},
year = 2015,
month = 7
}
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  • {sup 1}H spin-lattice field cycling relaxation dispersion experiments in the intermediate phase II of the solid [C{sub 3}H{sub 5}N{sub 2}]{sub 6}[Bi{sub 4}Br{sub 18}] are presented. Two motional processes have been identified from the {sup 1}H spin-lattice relaxation dispersion profiles and quantitatively described. It has been concluded that these processes are associated with anisotropic reorientations of the imidazolium ring, characterized by correlation times of the order of 10{sup −8} s-10{sup −9} s and of about 10{sup −5} s. Moreover, quadrupole relaxation enhancement (QRE) effects originating from slowly fluctuating {sup 1}H-{sup 14}N dipolar interactions have been observed. From the positions of themore » relaxation maxima, the quadrupole coupling parameters for the {sup 14}N nuclei in [C{sub 3}H{sub 5}N{sub 2}]{sub 6}[Bi{sub 4}Br{sub 18}] have been determined. The {sup 1}H-{sup 14}N relaxation contribution associated with the slow dynamics has been described in terms of a theory of QRE [Kruk et al., Solid State Nucl. Magn. Reson. 40, 114 (2011)] based on the stochastic Liouville equation. The shape of the QRE maxima (often referred to as “quadrupole peaks”) has been consistently reproduced for the correlation time describing the slow dynamics and the determined quadrupole coupling parameters.« less
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