We have performed ab initio quantum-chemical calculations on clusters of atoms modeling a divalent Ge defect in Ge-doped SiO 2 glasses. It has been found that the divalent Ge defect interacts with a nearby GeO 4 tetrahedron, forming complex structural units that are responsible for the observed photoabsorption band at ϳ5 eV. We have shown that these structural units can be transformed into two equivalent Ge E 0 centers by way of the positively charged defect center. PACS numbers: 61.43.Fs,

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... . + w, 61.72.Ji Photosensitivity and photoinduced holographic Bragg gratings were discovered in Ge-doped SiO 2 glasses about 20 years ago [1]. Presently photoinduced Bragg fiber and planar waveguide gratings in the glasses are widely used in telecommunication technology for wavelength-divided multiplexing, signal shaping, fiber lasers, and amplifers, etc. In contrast to these spectacular advances in practical applications, however, the fundamental understanding of the respective photoinduced processes in glass is incomplete. In Ge-doped SiO 2 glasses, there exists an intense photoabsorption band at 5 eV [2] , which is believed to be related to oxygen deficiency. Although the defect center associated with the 5-eV band most likely plays an important role in the photorefractive index change induced by ultraviolet (uv) irradiation [3], the details of the processes and mechanisms involved have remained obscure. It has been demonstrated that the 5-eV band is composed at least of two components centered at 5.06 and 5.16 eV [4] . The 5.06-eV band is bleached upon uv irradiation to generate the paramagnetic oxygen vacancy, called the Ge E 0 center [4]. The 5.06-eV band was once ascribed to the unrelaxed neutral oxygen vacancy [4], but the physical origin of this band is still under discussion [5, 6] . On the other hand, the 5.16-eV band, which is pumping the photoluminescence emissions at 3.2 and 4.3 eV, was attributed to divalent Ge defects having a lone pair of electrons, namely, -Ge - [4, 7] . This assignment was recently supported by first-principle quantum-chemical calculations on clusters of atoms modeling a divalent Ge defect in Ge-doped SiO 2 glasses [8, 9] . While the 5.16-eV band is almost stable against low-power uv exposure [4], irradiation with a dense flux of uv photons such as KrF excimer laser pulses can induce the appreciable photobleaching for this band [10-12], which accompanies the generation of Ge E 0 (and other unknown defect centers) as in the case of the bleaching of the 5.06-eV band [11] . This result suggests that the defect centers associated with the 5.16-eV band can be a precursor of Ge E 0 centers depending on the power densities of uv photons. However, it is not easy to understand why the bleaching of the 5.16-eV band results in the formation of Ge E 0 if this band is due to the divalent Ge defects [6] . Although several models have been proposed to explain this problem [6, [11] [12] [13] [14] , no satisfactory explanation has yet been given. In this paper we, therefore, investigate the formation mechanism of Ge E 0 centers from the divalent Ge defect in Ge-doped SiO 2 glasses by using ab initio cluster model calculations at the Hartree-Fock (HF) level. It has been demonstrated that ab initio quantum-chemical cluster approaches are useful to investigate the structure and vibrational properties of glassy systems [15, 16] . In particular, since the defect states in glasses are in general quite localized, their structure and energy states will be reasonably modeled by the cluster calculations [5, 8, 9, 17] . Appropriate cluster models hence allow us to investigate the geometries and electronic structures of the defect centers in glasses, and the calculated results will shed new light on the unsolved problem concerning the formation mechanism of Ge E 0 centers associated with the photobleaching of the 5.16-eV band and other photoinduced phenomena of interest in Ge-doped SiO 2 glasses. The photoabsorption (PA) and photoluminescence (PL) properties of the divalent defects have been previously studied by means of ab initio quantum-chemical calculations on the ͑H 3 T O͒ 2 T cluster (where T is Ge or Si) [8, 9] , and the calculated PA and PL energies for the clusters have been shown to agree well with the corresponding experimental values. In this work, we, therefore, used a similar cluster, ͓͑OH͒ 3 SiO͔ 2 Ge, as a model for the divalent Ge defect though the dangling bonds of the model cluster were not saturated by H atoms but by OH groups. Furthermore, we added a ͑OH͒ 3 Ge -O -Ge͑OH͒ 3 cluster to the above ͓͑OH͒ 3 SiO͔ 2 Ge cluster to consider a possible effect of the condensed environments in which the divalent Ge defect actually resides. In actual Ge-doped silica, a divalent Ge defect is most certainly surrounded by one or more T O 4 units in addition to the two T O 4 units that are originally bonded to the center -Ge -atom. It is natural to expect that these nearby T O 4 units play a key role in generating, if possible, Ge E 0 centers upon uv irradiation. The geometry of the ground-state singlet ͑S 0 ͒ structure of the cluster was fully optimized at the HF level of theory with the 0031-9007͞00͞84(7)͞1475(4)$15.00