First-principles calculation of 11B solid-state NMR parameters of boron-rich compounds II: the orthorhombic phases MgB7 and MgB12C2 and the boron modification γ-B28

Abstract

Based on the work on referencing ¹¹B nuclear magnetic resonance (NMR) spectra for molecular icosahedral boranes and the subsequent transfer to the rhombohedral boron-rich borides of the α-rB₁₂ type, we show that the magic angle spinning (MAS) NMR spectra of boron-rich borides with four or five symmetry-independent boron atoms can also be calculated. The calculations are performed on the level of density functional theory (DFT) using the gauge-including projector-augmented wave (GIPAW) approach. As model compounds o-MgB₁₂C₂ and MgB₇ are used, for which the experimental spectra could be calculated in excellent agreement with a deviation of 1 to 2 ppm. Based on the calculations, the different B atoms can be assigned to the respective signals, taking into account the quadrupolar coupling constants C_q from computation of the electric field gradient (EFG) with its main axis V_zz. It is shown that due to the specific geometric conditions of icosahedra, the magnitudes of V_zz for the boron atoms involved in exohedral B–B bonds to neighbouring icosahedra depend only on the valence electron density of the bond critical point and the distance. This also applies to the bonds to the interstitial B₂ unit in MgB₇, but not to bonds to the heteroatom of the C₂ dumbbell in o-MgB₁₂C₂. Both results are in line with our previous observations for the rhombohedral species (α-rB₁₂; B₁₂X₂ with X = P, As, O). Finally, the spectrum of γ-B₂₈ was calculated, whose structure also contains B₁₂ icosahedra and interstitial B₂ dumbbells. Here, a very similar bonding situation is found for the icosahedron, but the calculations show that the situation for the B₂ unit is clearly different. In general, the only parameter that needs to be varied to fit calculated and measured spectra is the linewidth, as this cannot be calculated. For the cases of o-MgB₁₂C₂ and MgB₇ signal areas are related to corresponding site multiplicities. A prerequisite for the successful application of the chosen method seems to be the presence of a semiconductor with a sufficiently large band gap, which is the case for the compounds investigated.