Towards homonuclear Jsolid-state NMR correlation experiments for half-integer quadrupolar nuclei: experimental and simulated 11B MAS spin-echo dephasing and calculated 2JBB coupling constants for lithium diborate

Abstract

Magic-angle spinning (MAS) NMR spin-echo dephasing is systematically investigated for the spin I = 3/2 ¹¹B nucleus in lithium diborate, Li₂O·2B₂O₃. A clear dependence on the quadrupolar frequency (ω^PAS_Q/2π = 3C_Q/[4I(2I − 1)]) is observed: the B3 (larger C_Q) site dephases more slowly than the B4 site at all investigated MAS frequencies (5 to 20 kHz) at 14.1 T. Increasing the MAS frequency leads to markedly slower dephasing for the B3 site, while there is a much less evident effect for the B4 site. Considering samples at 5, 25, 80 (natural abundance) and 100% ¹¹B isotopic abundance, dephasing becomes faster for both sites as the ¹¹B isotopic abundance increases. The experimental behaviour is rationalised using density matrix simulations for two and three dipolar-coupled ¹¹B nuclei. The experimentally observed slower dephasing for the larger C_Q (B3) site is reproduced in all simulations and is explained by the reintroduction of the dipolar coupling by the so-called “spontaneous quadrupolar-driven recoupling mechanism” having a different dependence on the MAS frequency for different quadrupolar frequencies. Specifically, isolated spin-pair simulations show that the spontaneous quadrupolar-driven recoupling mechanism is most efficient when the quadrupolar frequency is equal to twice the MAS frequency. While for isolated spin-pair simulations, increasing the MAS frequency leads to faster dephasing, agreement with experiment is observed for three-spin simulations which additionally include the homogeneous nature of the homonuclear dipolar coupling network. First-principles calculations, using the GIPAW approach, of the ²J_11B−11B couplings in lithium diborate, metaborate and triborate are presented: a clear trend is revealed whereby the ²J_11B−11B couplings increase with increasing B–O–B bond angle and B–B distance. However, the calculated ²J_11B−11B couplings are small (0.95, 1.20 and 2.65 Hz in lithium diborate), thus explaining why no zero crossing due to J modulation is observed experimentally, even for the sample at 25% ¹¹B where significant spin-echo intensity remains out to durations of ∼200 ms.