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

Journal Article · Tue Jul 28 00:00:00 EDT 2015 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4926827· OSTI ID:22493454

Belorizky, Elie ^[1]

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1. Université Grenoble Alpes, LIPHY, F-38000 Grenoble (France)

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.

• OSTI ID: 22493454
• Journal Information: Journal of Chemical Physics, Vol. 143, Issue 4; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

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