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

High-resolution, solid-state B-11 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, delta(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 delta(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, eta, 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 eta (0.043) it overestimates CQ by similar to 15%. After scaling of the calculated electric field gradient by 0.842 the deviation in CQ 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 delta(iso) and (a) the average B-O-B bond angle, (theta) over bar, for both three and four coordinated boron, giving delta(iso)(B-III) = (185.1- (theta) over bar)/3.42 ppm and delta(iso)(B-IV) = (130.2 - (theta) over bar)/5.31 ppm; and (b) the ring-site T-3 unit trigonal planar angular deviation, S-tri, giving delta(iso)(T-3(ring)) = (1.642 x 10(-2) - S-tri)/(8.339 x 10(-4)) ppm.