Refinement of borate structures from 11B MAS NMR spectroscopy and density functional theory calculations of 11B electric field gradients

The refinement of borate structures using DFT calculations combined with experimental (11)B quadrupole coupling parameters from solid-state NMR spectroscopy is presented. The (11)B electric field gradient (EFG) tensors, calculated using the WIEN2k software for trigonal and tetrahedral boron sites in a series of model compounds, exhibit a convincing linear correlation with the quadrupole coupling tensor elements, determined from (11)B MAS NMR spectra of the central or satellite transitions. The model compounds include Li(2)B(4)O(7), Mg(2)B(2)O(5), Mg(3)B(2)O(6), NH(4)B(C(6)H(5))(4), and colemanite (CaB(3)O(4)(OH)(3).H(2)O). The (11)B quadrupole moment, Q = 0.0409 +/- 0.0002 barn, derived from the linear correlation, is in excellent agreement with the accepted value for Q((11)B). This demonstrates that DFT (WIEN2k) calculations can provide precise (11)B quadrupole coupling parameters on an absolute scale. On the other hand, DFT calculations based on the reported crystal structures for datolite (CaBSiO(4)(OH)) and danburite (CaB(2)Si(2)O(8)) cannot reproduce the experimental (11)B quadrupole coupling parameters to the same high precision. However, optimization of these structures by minimization of the forces between the atoms (obtained by DFT) results in a significant improvement between the calculated and experimental (11)B quadrupole coupling parameters, which indicates that reliable refinements of the borate structures are obtained by this method. Finally, the DFT calculations also provide important structural information about the sign and orientation of the EFG tensor elements in the crystal frame, a kind of information that cannot be achieved from (11)B NMR experiments on powdered samples.