The construction of a reliable potential for GeO$_{2}$ from first-principles The construction of a reliable potential for GeO 2 , from first-principles, is described. The obtained potential, which includes dipole polarization effects, is able to reproduce all the studied properties (structural, dynamical and vibrational) to a high degree of precision with a single set of parameters. In particular, the infrared spectrum was obtained with the expression proposed for the dielectric function of polarizable ionic solutions by Weis et al. [J.M. Caillol, D. Levesque and J.J. Weis, J. Chem. Phys. , 91 , 5544 (1989)]. The agreement with the experimental spectrum is very good, with three main bands that are associated to tetrahedral modes of the GeO 2 network. Finally, we give a comparison with a simpler pair-additive potential. arXiv:1001.1843v1 [cond-mat.mtrl-sci] 12 Jan 2010 I. INTRODUCTION In the vitreous and liquid states, at ambient pres- sure, germania (GeO$_{2}$) (a close structural analog of silica (SiO$_{2}$)) forms a tetrahedrally coordinated three- dimensional network $^{1}$. Because of its lower abundance, its usage in practical applications is much less widespread than for the SiO$_{2}$. Still, GeO$_{2}$ is used in several fields, mainly related to optical technologies. For example, a mixture of SiO$_{2}$ and GeO$_{2}$ allows precise control of re- fractive index in optical fibres and waveguides. It is of interest to develop simulation methods to allow a detailed examination of the local structure in such mixtures and to predict the infrared spectrum, since this determines the long wavelength limit for their use as optical fibres. Several molecular dynamics (MD) simulations have been undertaken to study the structural and vibrational properties of the disordered phases of GeO$_{2}$. Classi- cal MD simulations were performed on glassy and liquid GeO$_{2}$ $^{7,8}$, using pairwise additive potentials with partial charges developed by Oeffner and Elliott (OE) for mod- eling the α -quartz and rutilelike phases of GeO$_{2}$ $^{9}$. More recently, first-principles molecular dynamics (FPMD) of glassy GeO$_{2}$ have also been reported $^{10,11}$. In principle, the amount of empirical information needed to set up a The structure of the simulated system can directly be compared with the neutron / X-ray diffraction exper- iments. Both classical and FPMD simulation provide structure factors which are in rather good agreement with experiments. For the classical molecular dynamics, the most noticeable difference is a shift to high q -values of the first sharp diffraction peak (FSDP), which was ob- served with both versions of the OE potential $^{7,8}$. As this peak is associated to medium range distances $^{5}$, this means that the Ge-O-Ge bond angle is too large and the topology of the tetrahedral network is not correctly described. The FPMD simulations provide a diffraction pattern with improved agreement $^{11}$, but the small size / timescales explored lead to large statistical uncertain- ties, mainly in the region of this FSDP. The vibrational properties can also be straightforwardly calculated. The vibrational density of states (VDOS) was estimated from FPMD and classical MD using the rescaled OE potential, with an overall reasonable agreement with the available experimental data extracted from inelastic neutron scat- first-principles calculation is minimal and it would nor- mally be the method of choice to study the physico- chemical properties of condensed phase systems. How- ever, it is computationally very expensive compared to classical molecular dynamics, which is a major drawback when dealing with glassy systems. Classical and FPMD simulations were also compared one with each other in a combined study 12 for temperatures above 2530 K. In this study apparent inconsistencies between the proper- ties predicted by the classical simulations of different au- thors are noted. In reality, two different parameter sets were proposed by OE: an original one, which was fitted from an ab initio energy surface, and a so-called rescaled one, which was developed from the previous one in order to give a better reproduction of the vibrational proper- ties. For example, the partial charge of the germanium ion was shifted from 1.5 e in the original potential to 0.94174 e in the rescaled potential. The apparent incon- sistencies arise because different classical potentials were being used. Our objective is a single potential which will give a good description of structure and dynamics and allow long simulations on systems of many atoms. D. Marrocchelli $^{1}$, M. Salanne2 , $^{3}$, P.A. Madden $^{4}$, C. Simon2 , 3 and P. Turq 2 , 3 1 School of Chemistry, University of Edinburgh, Edinburgh EH9 3JJ, UK 2 UPMC Univ Paris 06, UMR 7612, LI2C, F-75005, Paris, France 3 CNRS, UMR 7612, LI2C, F-75005, Paris, France and 4 Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK The essential similarity between the structures of glassy GeO$_{2}$, SiO$_{2}$ and BeF$_{2}$ was made clear by the study of vibrational properties by Galeener and co-workers 2 who showed that the inelastic neutron, infrared and Ra- man spectra of the different materials were closely re- lated. More recent infrared studies of GeO$_{2}$ have also been reported $^{3,4}$. Recently a full set of partial struc- ture factors were determined in this system by using the method of isotopic substitution in neutron diffraction experiments $^{5,6}$. The results show that the tetrahedral network structure is based on corner sharing Ge(O$_{1}$$_{/}$$_{2}$)$_{4}$ tetrahedra with a Ge-O average distance of 1.73 ˚ A and with a mean inter-tetrahedral Ge-O-Ge angle of 132 $^{◦}$. They also show that the topological and chemical order- ing in the network display two characteristic length scales at distances greater than the nearest neighbour.