Theoretical Third-Order Hyperpolarizability of Paratellurite from the Finite Field Perturbation Method Mouna Ben Yahia, † Emmanuelle Orhan,* ,† Armando Beltrán, ‡ Olivier Masson, † The´re`se Merle-Me´jean, † Andreï Mirgorodski, † and Philippe Thomas † Laboratoire Science des Proce´de´s Ce´ramiques et Traitements de Surface, UMR CNRS 6638, UniVersite´ de Limoges, 123 aV. Albert Thomas, 87060 Limoges Cedex, France, and Departament de Química Fisica i Analı´tica, UniVersitat Jaume I, P.O. Box 6029 AP, 12080 Castello´, Spain ReceiVed: June 9, 2008; ReVised Manuscript ReceiVed: July 18, 2008 Density functional theory was used to estimate the third-order hypersusceptibility  (3) of the R-TeO 2 paratellurite (as a model structure for TeO 2 glass) and the same value for R-SiO 2 cristobalite (as a model structure for glassy silica). The attempt was made to gain a physical insight into the nature of the extraordinarily high hypersusceptibility of TeO 2 glass. A finite field perturbation method implemented in the CRYSTAL code with the “sawtooth” approach was employed. The  (3) values calculated for R-TeO 2 were found to be of the same order as that measured for TeO 2 glass and much higher than the values computed for R-SiO 2 which, in turn, were close to that of glassy silica. Although oxide glasses are known to have interesting nonlinear optical properties since the work by Hall et al. in the late 1980s, 1 the origin of this phenomenon is still under debate. As a matter of fact, the wide variety of available techniques for measuring nonlinear third-order susceptibilities can lead to great discrepancies between the measured values for the very same material, mostly related to underestimated error bars. It is thus difficult to compare experiments and to interpret them univo- cally. 2 Moreover, theoretical calculations on compounds as disor- dered as glasses remain tricky and do not allow one to compute physical properties unless the glass is considered not as a whole but as an amount of small molecules. It may not be a problem, since the interesting physical and/or chemical properties of oxide glasses are frequently associated with short-range structural effects. Indeed, oxides are often characterized by typical structural units. For example, vitreous silica and SiO 2 -based glasses are built up from a well defined and rigid structural unit, the SiO 4 tetrahedron. However, this is not the case in TeO 2 -based glasses where the “building blocks” are neither so rigid nor so well defined. The tellurite glasses are built up from asymmetrical network formers which are TeO 4 disphenoids (two short and two long bonds), TeO 3+1 (three short bonds and one long bond), and/or TeO 3 (three short bonds). They are among the most interesting glasses for optoelectronic devices thanks to their high nonlinear susceptibilities, 50 times higher than that of pure SiO 2 glass. Comparative experimental studies completed by ab initio calculations on clusters have shown that the TeO 4 structural unit may be responsible for the high third-order susceptibilities. 3,4 In spite of the theoretical studies carried out in the last five years, the microscopic origin of this property is however still far from final clarity. Localized atomic orbitals have proven the importance of the tellurium lone pair for the high values of microscopic third-order susceptibilities in Te(OH) 4 molecules. 5,6 In 2006, a theoretical study carried out on (TeO 2 ) n and (SiO 2 ) n (n ) 2-12) clusters in chains, rings, or cage geometries 7 proved that linear chains were the most favorable configuration to achieve high hypersusceptibility values. The polymerization of TeO 2 molecules in chains brought to indices much higher than the addition of each TeO 2 index up to a ceiling of 12 molecules, thus highlighting the influence of collective electronic effects. The results of those studies evidenced the importance of (i) the tellurium lone pair and (ii) a cooperative effect between the TeO 4 entities if they are in a favorable arrangement. Those methodologies led to interesting elements of thought, but they do not really account for the whole glass structure; they are based on hypothetical fragments that could possibly exist in the glass. Therefore, relevant information about a stable crystalline structure into which TeO 2 glass finally transforms at heating can be of fundamental interest for a better understanding of these electronic properties at the microscopic level. In this Letter, we propose to obtain the third-order hyperpolarizability coefficients of the stable TeO 2 phase from quantum mechanical ab initio calculations. The paratellurite crystallizes in the P 41212 space group (#92) with tetragonal symmetry and four formula units per unit cell. 8 There are two independent atomic positions, one tellurium at (x, x, 0) and one oxygen at the general (x, y, z) position. The tellurium first coordination sphere consists in four oxygen atoms in a disphenoidal configuration: a trigonal bipyramid where the third equatorial position is occupied by the tellurium lone pair. The two axial Te-O distances are 2.12 Å, and the two equatorial distances are 1.88 Å. All of the results obtained on R-TeO 2 will be compared to results on SiO 2 for ensuring their validity. The R-SiO 2 cristobalite phase has been chosen rather than R-quartz * Corresponding author. E-mail: emmanuelle.orhan@unilim.fr. † Universite´ de Limoges. ‡ Universitat Jaume I. 10777 10.1021/jp805050s CCC: $40.75  2008 American Chemical Society Published on Web 08/12/2008 2008, 112, 10777–10781