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{\it Ab initio} $^{27}Al$ NMR chemical shifts and quadrupolar parameters for $Al_2O_3$ phases and their precursors

The Gauge-Including Projector Augmented Wave (GIPAW) method, within the Density Functional Theory (DFT) Generalized Gradient Approximation (GGA) framework, is applied to compute solid state NMR parameters for $^{27}Al$ in the $α$, $θ$, and $κ$ aluminium oxide phases and their gibbsite and boehmite precursors. The results for well-established crystalline phases compare very well with available experimental data and provide confidence in the accuracy of the method. For $γ$-alumina, four structural models proposed in the literature are discussed in terms of their ability to reproduce the experimental spectra also reported in the literature. Among the considered models, the $Fd\bar{3}m$ structure proposed by Paglia {\it et al.} [Phys. Rev. B {\bf 71}, 224115 (2005)] shows the best agreement. We attempt to link the theoretical NMR parameters to the local geometry. Chemical shifts depend on coordination number but no further correlation is found with geometrical parameters. Instead our calculations reveal that, within a given coordination number, a linear correlation exists between chemical shifts and Born effective charges.