Spectral assignments and NMR parameter–structure relationships in borates using high-resolution 11B NMR and density functional theory

Abstract

High-resolution, solid-state ¹¹B NMR spectra have been obtained at high magnetic fields for a range of polycrystalline borates using double-rotation (DOR), multiple-quantum magic angle spinning and isotopic dilution. DOR linewidths can be less than 0.2 ppm in isotopically diluted samples, allowing highly accurate values for the isotropic chemical shift, δ_iso, and electric field gradient to be obtained. The experimental values are used as a test of density functional calculations using both projector augmented wave based CASTEP and WIEN2k. The CASTEP calculations of δ_iso are generally in very good agreement with experiment, having r.m.s. deviation 0.40 ppm. WIEN2k calculations of electric field gradient magnitude, C_Q, and asymmetry, η, are also in excellent agreement with experiment, with r.m.s. deviations 0.038 MHz and 0.042 respectively. However, whilst CASTEP gives a similar deviation for η (0.043) it overestimates C_Q by ∼15%. After scaling of the calculated electric field gradient by 0.842 the deviation in C_Q is practically identical to that of the WIEN2k calculations. The spectral assignments that follow from the experimental and computational results allow identification of correlations between δ_iso and (a) the average B–O–B bond angle, θ, for both three and four coordinated boron, giving δ_iso(B^III) = (185.1 − θ)/3.42 ppm and δ_iso(B^IV) = (130.2 − θ)/5.31 ppm; and (b) the ring-site T³ unit trigonal planar angular deviation, S_tri, giving δ_iso(T³(ring)) = (1.642 × 10⁻² − S_tri)/(8.339 × 10⁻⁴) ppm.