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Communication: Hole localization in Al-doped quartz SiO2
within ab initio
28.R. Dovesi, V. R. Saunders, C. Roetti, R. Orlando, C. M. Zicovich-Wilson, F. Pascale, B. Civalleri, K. Doll, I. J. Harrison, N. M. Bush, P. DArco, and M. Llunell, CRYSTAL09 User’s Manual (University of Torino, Torino, 2009).
36. The defined thresholds for the maximum and the root-mean-square of the energy gradients (atomic displacements) are 0.000 45 a.u. (0.001 80 a.u.) and 0.000 30 a.u. (0.001 20 a.u.), respectively.28
47. The obtained ground state is almost isoenergetic with the one yielded by starting the optimization from the ideal SiO2 structure: the latter is favored by only 6 meV.
48.V. Barone, in Recent Advances in Density Functional Methods, Part I, edited by D. P. Chong (World Scientific Publishing Company, Singapore, 1996), Chap. 8, pp. 287–334.
49. The 17O(2) EPR parameters, computed at the sc-PBE0αϵ∞ (B3LYP) level are (in G) Aiso = − 3.6(−15.3), B1 = − 2.9(−31.7), B2 = 1.4(15.7), B3 = 1.5(16.0).
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We investigate the long-standing problem of hole localization at the Al impurity in quartz SiO2, using a relatively recent DFT hybrid-functional method in which the exchange fraction is obtained ab initio, based on an analogy with the static many-body COHSEX approximation to the electron self-energy. As the amount of the admixed exact exchange in hybrid functionals has been shown to be determinant for properly capturing the hole localization, this problem constitutes a prototypical benchmark for the accuracy of the method, allowing one to assess to what extent self-interaction effects are avoided. We obtain good results in terms of description of the charge localization and structural distortion around the Al center, improving with respect to the more popular B3LYP hybrid-functional approach. We also discuss the accuracy of computed hyperfine parameters, by comparison with previous calculations based on other self-interaction-free methods, as well as experimental values. We discuss and rationalize the limitations of our approach in computing defect-related excitation energies in low-dielectric-constant insulators.
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