On the use of radio-frequency offsets for improving double-quantum homonuclear dipolar recoupling of half-integer-spin quadrupolar nuclei

Abstract

Detecting proximities between nuclei is crucial for atomic-scale structure determination with nuclear magnetic resonance (NMR) spectroscopy. Different from spin-1/2 nuclei, the methodology for quadrupolar nuclei is limited for solids due to the complex spin dynamics under simultaneous magic-angle spinning (MAS) and radio-frequency irradiation. Herein, the performances of several homonuclear rotary recoupling (HORROR)-based homonuclear dipolar recoupling sequences are evaluated for ²⁷ Al (spin-5/2). It is shown numerically and experimentally on mesoporous alumina that $\mathrm{BR}{2}_2^1$ outperforms the supercycled S₃ sequence and its pure double-quantum (DQ) (bracketed) version, [S₃ ], both in terms of DQ transfer efficiency and bandwidth. This result is surprising since the S₃ sequence is among the best low-power recoupling schemes for spin-1/2. The superiority of $\mathrm{BR}{2}_2^1$ is thoroughly explained, and the crucial role of radio-frequency offsets during its spin dynamics is highlighted. The analytical approximation of $\mathrm{BR}{2}_2^1$ , derived in an offset-toggling frame, clarifies the interplay between offset and DQ efficiency, namely, the benefits of off-resonance irradiation and the trough in DQ efficiency for $\mathrm{BR}{2}_2^1$ when the irradiation is central between two resonances, both for spin-1/2 and half-integer-spin quadrupolar nuclei. Additionally, density matrix propagations show that the $\mathrm{BR}{2}_2^1$ sequence, applied to quadrupolar nuclei subject to quadrupolar interaction much larger than radio-frequency frequency field, can create single- and multiple-quantum coherences for near on-resonance irradiation. This significantly perturbs the creation of DQ coherences between central transitions of neighboring quadrupolar nuclei. This effect explains the DQ efficiency trough for near on-resonance irradiation, in the case of both cross-correlation and autocorrelation peaks. Overall, this work aids experimental acquisition of homonuclear dipolar correlation spectra of half-integer-spin quadrupolar nuclei and provides theoretical insights towards improving recoupling schemes at high magnetic field and fast MAS.

Keywords: double-quantum; half-integer-spin quadrupolar nuclei; homonuclear dipolar recoupling; magic-angle spinning (MAS) NMR.