Contribution of first-principles calculations to multinuclear NMR analysis of borosilicate glasses.

Boron-11 and silicon-29 NMR spectra of xSiO(2)-(1-x)B(2)O(3) glasses (x=0.40, 0.80 and 0.83) have been calculated using a combination of molecular dynamics (MD) simulations with density functional theory (DFT) calculations of NMR parameters. Structure models of 200 atoms have been generated using classical force fields and subsequently relaxed at the PBE-GGAlevel of DFT theory. The gauge including projector augmented wave (GIPAW) method is then employed for computing the shielding and electric field gradient tensors for each silicon and boron atom. Silicon-29 MAS and boron-11 MQMAS NMR spectra of two glasses (x=0.40 and 0.80) have been acquired and theoretical spectra are found to well agree with the experimental data. For boron-11, the NMR parameter distributions have been analysed using a Kernel density estimation (KDE) approach which is shown to highlight its main features. Accordingly, a new analytical model that incorporates the observed correlations between the NMR parameters is introduced. It significantly improves the fit of the (11)B MQMAS spectra and yields, therefore, more reliable NMR parameter distributions. A new analytical model for a quantitative description of the dependence of the silicon-29 and boron-11 isotropic chemical shift upon the bond angles is proposed, which incorporates possibly the effect of SiO(2)-B(2)O(3) intermixing. Combining all the above procedures, we show how distributions of Si-O-T and B-O-T (T=Si, B) bond angles can be estimated from the distribution of isotropic chemical shift of silicon-29 and boron-11, respectively.