An optimal double-magic flip angle for performing the distance measurement REDOR experiment on a spin S=1

Distance measurements to quadrupolar nuclei: Evolution of the rotational echo double resonance technique

Molecular structure determination is the basis for understanding chemical processes and the property of materials. The direct dependence of the magnetic dipolar interaction on the distance makes solid-state nuclear magnetic resonance (NMR) an excellent tool to study molecular structure when X-ray crystallography fails to provide atomic-resolution data. Although techniques to measure distances between pairs of isolated nuclear spin-1/2 pairs are routine and easy to implement using the rotational echo double resonance (REDOR) experiment (Gullion & Schaefer, 1989), the existence of a nucleus with a spin > 1/2, appearing in approximately 75% of the elements in the periodic table, poses a challenge due to difficulties stemming from the large nuclear quadrupolar coupling constant (QCC). This mini-review presents the existing solid-state magic-angle spinning NMR techniques aimed toward the efficient and accurate determination of internuclear distances between a spin-1/2 and a "quadrupolar" nucleus having a spin larger than one half. Analytical expressions are provided for the various recoupling curves stemming from different techniques, and a coherent nomenclature for these various techniques is suggested. Treatment of some special cases such as multiple spin effects and spins with close Larmor frequencies is also discussed. The most advanced methods can recouple spins with quadrupolar frequencies up to tens of megahertz and beyond, expanding the distance measurement capabilities of solid-state NMR to an increasingly growing number of applications and nuclear spin systems.

Pushing the limit of NMR-based distance measurements - retrieving dipolar couplings to spins with extensively large quadrupolar frequencies

Dipolar recoupling under magic-angle spinning allows to measure accurate inter-nuclear distances provided that the two interacting spins can be efficiently and uniformly excited. Alexander (Lex) Vega has shown that adiabatic transfers of populations in quadrupolar spins during the application of constant-wave (cw) radio-frequency pulses lead to efficient and quantifiable dipolar recoupling curves. Accurate distance determination within and beyond the adiabatic regime using cw pulses is limited by the size of the quadrupolar coupling constant. Here we show that using the approach of long-pulse phase modulation, dipolar recoupling and accurate distances can be obtained for nuclei having extensively large quadrupolar frequencies of 5-10 MHz. We demonstrate such results by obtaining a ³¹P-^79/81Br distance in a compound for which bromine-79 (spin-3/2) has a quadrupolar coupling constant of 11.3 MHz, and a ¹³C-²⁰⁹Bi distance where the bismuth (spin-9/2) has a quadrupolar coupling constant of 256 MHz, equaling a quadrupolar frequency of 10.7 MHz. For Bromine, we demonstrate that an analytical curve based on the assumption of complete spin saturation fits the data. In the case of bismuth acetate, a C-Bi₃ spin system must be used in order to match the correct saturation recoupling curve, and results are in agreement with the crystallographic structure.

Analysis of large-anisotropy-spin recoupling pulses for distance measurement under magic-angle spinning NMR shows the superiority and robustness of a phase modulated saturation pulse

The distance between a spin one-half and an attached spin possessing a large anisotropy can be obtained using different dipolar recoupling sequences that are based on the rotational-echo double resonance technique under magic-angle spinning solid-state NMR. The general difference between these sequences with respect to the coupled spin is the set of pulses applied in order to drive this spin out of equilibrium, thereby recoupling the dipolar interaction. Since complete inversion is practically not possible due to the coupled-spin anisotropy, using one or another pulse depends on the experimental and spin conditions: the spinning speed, the strength of the radio frequency field, the size of the anisotropic interaction (quadrupolar or chemical shiftanisotropy couplings), the offset, and the accuracy of setting the magic angle. Here we present a detailed description of the behavior of the anisotropic spin magnetization, including the macroscopic level transition probabilities, the degree of inversion, and the microscopic and macroscopic magnetizations during the applications of these pulses under different experimental conditions. As simulations show, a complete randomization of spin populations under a wide range of experimental conditions occurs under a specific phase modulation of the recoupling pulse while for all other cases dependence on experimental conditions is large and the achievable bandwidth is limited. A result of this detailed analysis is that the extension of the phase modulated pulse extends even further its robustness. The saturation capability is demonstrated experimentally for the quadrupolar spin of boron-11 in 4-methoxyphenylboronic acid.