J ournal J. Am. Ceram. Soc., 89 [7] 2323–2326 (2006) DOI: 10.1111/j.1551-2916.2006.01003.x r 2006 The American Ceramic Society Multiscale Modeling of GeSe 2 Glass Structure John C. Mauro w,z and Arun K. Varshneya NYS College of Ceramics at Alfred University, Alfred, New York 14802 We present a multiscale model of GeSe 2 glass structure, where interatomic potentials are calculated using M^ller–Plesset per- turbation theory and a cluster expansion approach. The ab initio calculations are fit to continuous functions and used in a clas- sical Monte Carlo simulation of 1200 atoms. The resulting GeSe 2 glass structure accurately captures the defect character- istics recently observed by a neutron diffraction experiment in- corporating isotopic substitution. Our simulation results allow for further elaboration on the structure of deformed Ge-centered tetrahedra occurring in GeSe 2 glass. This level of detail has not been captured by previous modeling efforts using density func- tional theory. I. Introduction A THOROUGH and accurate understanding of network glass structure is critical for comprehending the optoelectronic and thermophysical properties of chalcogenide glasses. Such an understanding must include not only the predominant structural motifs of the glass but also other ‘‘defective’’ configurations of atoms. The basic structure of the prototypical network glass GeSe 2 , consisting of corner- and edge-sharing Ge(Se 1/2 ) 4 tetra- hedra, has been well known since the pioneering neutron dif- fraction study of Susman et al. 1 and further investigated by subsequent experiments. 2–4 The resulting model of GeSe 2 glass structure has been supported by numerous molecular dy- namics simulations, mostly based on density functional theory (DFT). 5–10 However, a recent neutron diffraction experiment by Petri et al. 11 incorporating isotopic substitution has found that  4% of bonds in GeSe 2 glass are homopolar, breaking with the tra- ditional heteropolar-bonded Ge(Se 1/2 ) 4 tetrahedral motif. Fur- thermore, in addition to the well-known peak at 2.36 A ˚ in the Ge–Se pair distribution function, Petri and coworkers found a second peak at 3.02 A ˚ . This second peak is attributed to the presence of deformed Ge-centered tetrahedra with three Se at- oms at 2.36 A ˚ and a fourth at 3.02 A ˚ . Unfortunately, previous DFT modeling has not been able to capture these details of the GeSe 2 structure. In this paper, we describe a multiscale model of a GeSe 2 glass structure that provides a more accurate description of inter- atomic interactions compared with traditional DFT modeling, while simultaneously allowing for simulation of a larger ensem- ble of atoms. First, we derive interatomic potentials for the GeSe 2 system from ab initio calculations using the second- and fourth-order M^ller–Plesset perturbation theory 12 and a cluster expansion approach. 13 Two- and three-body interaction poten- tials are developed by fitting continuous functions to the discrete set of ab initio data. These potentials are then used in a classical Monte Carlo simulation 14,15 with 1200 atoms to compute the structure of bulk GeSe 2 glass. The resulting structure displays 3.1% homopolar bonding, close to the  4% figure reported by Petri et al. 11 The computed Ge–Se pair distribution function shows a first strong peak at 2.37 A ˚ and a second weaker peak at 3.04 A ˚ , in excellent agreement with Petri’s diffraction study. 11 Furthermore, our results clearly show the presence of the de- formed Ge-centered tetrahedra predicted by Petri, and we elab- orate on the structure of these tetrahedra through calculation of Se–Ge–Se bond angles. II. Interatomic Potentials In our ab initio simulations, we use the aug-cc-pVQZ basis sets of Dunning and coworkers, 16 where the acronym stands for ‘‘augmented correlation-consistent polarized valence quadruple- z.’’ The aug-cc-pVQZ basis sets allow for explicit representation of all electrons in a system using a superposition of several hun- dred primitive Gaussians. Two- and three-body interactions are derived using the second- and fourth-order M^ller–Plesset per- turbation theory, 12 respectively, and a cluster expansion ap- proach, 13 previously used in deriving ab initio potentials for elemental and heterogeneous chalcogen systems. 17–20 These po- tentials have been used to simulate the structure of Se, S x Se 1x , and Se x Te 1x glasses and have shown to provide very good agreement with experimental data. 17–20 We use the Gaussian 03 software 21 for all ab initio simulations. In order to be used in higher-level classical simulations, viz., Metropolis Monte Carlo, 14,15 the ab initio potentials are fit to continuous functions that accurately reproduce the quantum data. The two-body interaction is fit using a Morse potential 22 of the form V 2 r ij   ¼ D 0 1  e a rij r0 ð Þ   2 1   (1) where D 0 is the potential well depth, r 0 is the equilibrium sep- aration distance, and a is the shape parameter. Parameters for the two-body Ge–Ge, Ge–Se, and Se–Se interactions are opt- imized using a least-squares fitting routine and provided in Ta- ble I. Plots of the ab initio data and Morse fits are shown in Fig. 1. Heteropolar Ge–Se bonding is clearly preferred, as it has a stronger binding energy than the average of the homopolar Ge–Ge and Se–Se bonds. Following the cluster expansion approach, we isolate three- body interactions in the GeSe 2 system by computing the total potential energies of Ge–Ge–Ge, Se–Se–Se, Ge–Se–Ge, Ge–Ge– Se, Se–Ge–Se, and Ge–Se–Se trimers and subtracting one- and 2323 Table I. Parameters for the Two-Body Interaction Potentials Ge–Ge Ge–Se Se–Se D 0 (eV/atom) 1.239626 2.751080 1.517550 r 0 (A ˚ ) 2.399151 2.155640 2.173489 a (A ˚ 1 ) 1.465028 1.405003 1.790250 J. Du—contributing editor w Author to whom correspondence should be addressed. e-mail: mauroj@corning.com z Science and Technology Division, Corning Incorporated, Corning, New York. Manuscript No. 21370. Received January 11, 2006; approved January 28, 2006.