Ab initio study of stability and quadrupole coupling constants in borophosphates

The DFT method was used to predict the formation energies and quadrupole coupling constants C_Q in a series of borophosphates: Li₃BP₂O₈, Li₂NaBP₂O₈, Na₃BP₂O₈, Li₂B₃PO₈, Na₅B₂P₃O₁₃, LiNa₂B₅P₂O₁₄ and Na₃B₆PO₁₃ composed of different networks and different amounts of borate and phosphate units. The change in formation energies with increasing number of B atoms in this series is attributed to the multiplicity of boron sites and is explained by density of states calculations. The calculated C_Q values of ⁷Li, ²³Na and ¹¹B are correlated with the coordination and distortion of polyhedra to elucidate the influence of local and more distant environments. As for the C_Q of ¹¹B, it should be in the ranges of 0.26-0.36, 0.48-0.84 and ∼1 MHz for boron tetrahedral distortion indices of 0.004-0.013, 0.015-0.019 and 0.033, respectively, whereas C_Q ∼3.0 MHz corresponds to boron in a triangular site. The obtained numerical relationships make it possible to predict the quadrupole frequencies for these nuclei based only on their local environment, and vice versa, to propose structural models from NMR data. These results provide guidance for studying similar characteristics of other borophosphates, the structure of which varies depending on the initial reaction, composition and temperature.