Quadrupole Couplings in Nuclear Magnetic Resonance, General

Abstract

Nuclear magnetic resonance (NMR) spectroscopy is continually finding new applications. It enables the local symmetry to be probed at the atomic scale using the nuclear spins I of the compound under investigation. The nuclear spin is either a half‐integer (or odd) number or an integer (or even) number. The nuclei in the periodic table can be divided into two parts – spin‐ $\def\tovr#1#2{{\scriptstyle{#1\over #2}}} \tovr{1}{2}$ nuclei and spin larger than $\def\tovr#1#2{{\scriptstyle{#1\over #2}}} \tovr{1}{2}$ nuclei. The spin larger than $\def\tovr#1#2{{\scriptstyle{#1\over #2}}} \tovr{1}{2}$ nuclei are called quadrupole nuclei because they possess an electric quadrupole moment which interacts with the electric‐field gradient (EFG) generated by its surroundings. By extension, their spins are called quadrupole spins. Spin‐ $\def\tovr#1#2{{\scriptstyle{#1\over #2}}} \tovr{1}{2}$ nuclei are not sensitive to the EFG. Of the nuclei that possess a spin, 6% have integer quadrupole spins and 66% have half‐integer quadrupole spins. This article focuses on the half‐integer quadrupole spins ( $\def\tovr#1#2{{\scriptstyle{#1\over #2}}} {\hbox{I}} = \tovr{3}{2},\ \tovr{5}{2},\ \tovr{7}{2}$ , and $\def\tovr#1#2{{\scriptstyle{#1\over #2}}} \tovr{9}{2}$ ) in single crystals and in powder compounds. Most of these spins are observable. As they are multi‐energy‐level systems (the number of energy levels is 2I + 1), multiple quantum (MQ) transitions occur during excitation of the spin system by a radiofrequency (RF) pulse sequence. As a result, quantum mechanical concepts are needed for an understanding of the spin dynamics and for interpretation of the results. In particular, the choice of pulse sequence and the experimental conditions, such as pulse duration, pulse strength, and phase cycling in the pulse sequence, depend on the strength of the EFG surrounding the nuclear spin.

Pulse FT NMR of non-equilibrium states of half-integer spin quadrupolar nuclei in single crystals

“…For a nuclear spin system with I > 1/2, each component of the magnetization may be partitioned into individual contributions which may be represented in terms of ''fictitious spin-1/2 operators" [46][47][48][49][50]. For example, the x-magnetization, M x , for a spin-3/2 system may be decomposed into contributions from the three single-quantum transitions associated with the two STs (i.e., m I = 3/2 ?…”

“…The matrix representation for the fictitious spin-1/2 operators, I i;j x , for a spin-3/2 system are given by [46,[48][49][50]:…”

Sensitivity enhancement of NMR spectra of half-integer quadrupolar nuclei in the solid state via population transfer

“…The nuclear quadrupolar interaction (15)(16)(17)(18)(19) results from the interaction between the nuclear quadrupole moment (eQ) and the electric field gradient (EFG) at the nucleus. In the principal axis system of the EFG tensor, the quadrupolar interaction can be described by two parameters, the nuclear quadrupolar coupling constant, C Q , which in frequency units is defined by…”

“…[16] clearly introduces difficulties in achieving ideal adiabatic singleand sudden multiple-quantum transitions with MAS as opposed to NMR experiments involving stationary samples (Eq. [15]). …”

Communication: Heterogeneous water dynamics on a clathrate hydrate lattice detected by multidimensional oxygen nuclear magnetic resonance

“…In H 2 O second-order quadrupolar interactions govern 25 the central-transition frequencies ω i . These frequencies depend on the orientation of the electrical field gradient (EFG) tensor in the laboratory frame, specified via the polar angle θ and the azimuthal angle φ, and are given by 26,27 …”