Simple expressions of the nuclear relaxation rate enhancement due to quadrupole nuclei in slowly tumbling molecules
Abstract
For slowly tumbling entities or quasirigid 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 SI interspin 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 fastrelaxing quadrupole {sup 14}N nuclei and mediating the QREmore »
 Authors:
 Université Grenoble Alpes, INACSCIB, RICC, F38000 Grenoble (France)
 (France)
 Université Grenoble Alpes, LIPHY, F38000 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., Email: pascalh.fries@cea.fr, CEA, INACSCIB, RICC, F38000 Grenoble, Belorizky, Elie, and CEA, LetiClinatec, F38000 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., Email: pascalh.fries@cea.fr, CEA, INACSCIB, RICC, F38000 Grenoble, Belorizky, Elie, & CEA, LetiClinatec, F38000 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., Email: pascalh.fries@cea.fr, CEA, INACSCIB, RICC, F38000 Grenoble, Belorizky, Elie, and CEA, LetiClinatec, F38000 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., Email: pascalh.fries@cea.fr and CEA, INACSCIB, RICC, F38000 Grenoble and Belorizky, Elie and CEA, LetiClinatec, F38000 Grenoble},
abstractNote = {For slowly tumbling entities or quasirigid 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 SI interspin 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 fastrelaxing 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 nanotubes 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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