Theoretical description of hole localization in a quartz Al center: The importance of exact electron exchange Gianfranco Pacchioni,* Fabiano Frigoli, and Davide Ricci Dipartimento di Scienza dei Materiali, Universita` di Milano-Bicocca, Istituto Nazionale per la Fisica della Materia, via R. Cozzi 53, 20125 Milano, Italy John A. Weil Department of Chemistry, University of Saskatchewan, 110 Science Place, Saskatoon SK, Canada S7N 5C9 ~Received 30 August 2000; published 27 December 2000! The ‘‘classical’’ model of the @AlO 4 # 0 defect center in irradiated quartz, an Al impurity having replaced a four-coordinated Si atom, is that a hole forms in a nonbonding orbital of an oxygen atom, with consequent asymmetric relaxation along that particular Al-O direction. This model has been proposed years ago, based on the analysis of the electron-paramagnetic-resonance spectra of Al-containing crystalline SiO 2 and analysis of Hartree-Fock cluster model calculations. Three recent theoretical studies based on first-principle density- functional theory ~DFT! and band-structure plane-wave calculations proposed an alternative model where the hole is completely delocalized over four oxygen neighbors to the Al impurity, at 0 K. Using cluster models containing as many as 104 Si and O atoms and various theoretical approaches, we show that the delocalized picture is an artifact of the DFT approach and that a fully localized hole is obtained when an exact treatment of the exchange term is used. The validity of this conclusion is based on the direct comparison of computed and measured quantities such as the 17 O hyperfine and 27 Al, 29 Si superhyperfine coupling parameters, the 27 Al nuclear quadrupole effect, and the derivable local distortion around the defect. This work shows that great care is needed when DFT is used to describe localized holes in insulators. DOI: 10.1103/PhysRevB.63.054102 PACS number~s!: 61.72.Bb, 61.72.Ji, 31.15.Ar, 42.70.Ce I. INTRODUCTION Al-doped SiO 2 has been studied in great detail, both theo- retically and experimentally in the past four decades. 1–14 Early experimental studies based on electron-paramagnetic- resonance ~EPR! spectroscopy have shown that the defect center corresponding to an Al atom substituting for a four- coordinated Si atom in the lattice, the neutral @AlO 4 # 0 center, contains a hole trapped in a nonbonding 2 p orbital of an O atom adjacent to Al. 1–3,6 The existence of a fully localized hole at sufficiently low temperatures has been shown by the accurate analysis of the EPR spectrum and in particular by the determination of the hyperfine coupling constants with the 27 Al, 29 Si, and 17 O nuclides. 6 Above room temperature, the hole jumps rapidly among all four adjacent O atoms. Cluster calculations performed at the Hartree-Fock level have then confirmed the model proposed based on the ex- perimental data, showing the occurrence of the hole localiza- tion at 0 K and the elongation of the corresponding Al-O bond. 9,10,12,13 This ‘‘classical’’ model has recently been challenged by three theoretical papers based on advanced first-principle approaches. 15,16,17 These studies were based on supercell cal- culations with proper inclusion of boundary conditions and density-functional theory ~DFT!. They all concluded that the hole in the @AlO 4 # 0 defect is completely delocalized over the four O neighbors 15–17 ‘‘in contrast to the phenomenological model results’’ reported previously. 16 Paramagnetic centers in pure and doped SiO 2 play a major role in determining the electrical properties of the material and are of paramount importance for the elucidation of sev- eral processes occurring in silicate glasses. 18 Their impor- tance is also connected to the proven possibility for use of the highly sensitive EPR spectroscopy in combination with other techniques ~such as optical absorption and photolumi- nescence measurements! to identify the structure of point defects. 19 The theoretical description of these centers is of great help for the correct assignment of an observed spectral feature to a given structural defect. 20 Therefore the contra- dictory results reported in the literature about the nature of holes associated to Al impurities in crystalline SiO 2 open questions which go beyond the simple scientific controversy, and make the elucidation of the reasons for the different answers given by the various theoretical methods of highest priority. In this study we have examined the electronic structure and spin distribution in the @AlO 4 # 0 center using cluster mod- els of various sizes, as well as various first-principle theoret- ical methods. These range from unrestricted Hartree-Fock ~UHF! with exact treatment of the electron exchange but neglect of electron correlation, to more sophisticated ap- proaches where the exchange and correlation terms are de- scribed in various ways. In particular, we explicitly included correlation effects using second-order Mo” ller-Plesset pertur- bation theory ~MP2!. We compared these results with those of DFT calculations or of hybrid methods where the HF exchange is mixed in with the DF exchange or where the exchange is treated at the HF level and only correlation is included through a self-consistent DF treatment. The validity of our theoretical results has been checked by comparing the hyperfine coupling parameters computed at various levels of theory with the corresponding experimental quanti- ties. Herein, we present a very complete theoretical PHYSICAL REVIEW B, VOLUME 63, 054102 0163-1829/2000/63~5!/054102~8!/$15.00 ©2000 The American Physical Society 63 054102-1