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Supporting Information Akola et al. 10.1073/pnas.1300908110 SI Text Detail of DFT Simulation Central in the CP2K method are two representations of the electron density: localized Gaussian and plane wave (GPW) basis sets. This representation allows for an efficient treatment of the electrostatic interactions and leads to a scheme that is formally linearly scaling as a function of the system size. The valence electron–ion interaction is based on the norm-conserving and separable pseudopotentials of the analytical form derived by Goedecker, Teter, and Hutter (1). We considered the following valence configurations: O (2s 2 2p 4 ), Ca (2s 2 2p 6 3s 2 3p 6 4s 2 ), and Al (3s 2 3p 1 ). For the Gaussian-based (localized) expansion of the Kohn–Sham orbitals, we use a library of contracted molecularly optimized valence double-zeta plus polarization (m-DZVP) basis sets (2), and the complementary plane wave basis set has a cutoff of 600 Rydberg for electron density (this equals to 150 Ry for wave functions in standard plane wave schemes). The molecularly optimized m-DZVP functions result in highly accurate results with less computational cost as expe- rienced with the traditional basis sets that are fitted to atomic properties. Together with the GPW basis set, this enables density functional theory (DFT) simulations of systems up to 1,000 atoms or more. Effective charges of individual atoms have been evaluated from electron density (3), and chemical bond orders between atomic pairs (and Mulliken charges) have been computed from the over- laps of the atomic orbital components (with a projected com- pleteness of 97.5%). Description of the DFT–RMC Approach i ) Initial hard-sphere Monte Carlo (HSMC) simulations (re- verse Monte Carlo, RMC, simulation without experimental data) with a constrained fourfold coordination for Al were used for generating starting structures. ii ) These HSMC structures were subjected to standard Monte Carlo simulations, which were fitted to the experimental X-ray, neutron diffraction, and extended X-ray absorption fine structure (EXAFS) data. Several RMC models were tested in parallel with preliminary DFT simulation, and the ones that gave acceptable agreement with the EXAFS data after DFT optimization were selected. The total energy of the RMC models (before DFT optimization) reduced by 0.48 electron volt (eV)/atom and 0.42 eV/atom for the 50CaO and 64 CaO glass, respectively, in comparison with the HSMC models (step i ). iii ) The RMC structures were optimized by DFT, and the result- ing structures were simulated at 300 K for 10 ps. During molecular dynamics (MD), the DFT-optimized structures undergo minor structural changes during the first 5 ps, which corresponds to an energy decrease of 0.04 eV/atom for the final optimized structures of both compositions. The energy decrease with respect to the previous RMC model (step ii ) is 0.58 eV/atom and 0.64 eV/atom for 50 mol % CaO (50CaO) and 64CaO, respectively. iv) The final RMC-refinement is performed with respect to the DFT structures. The final energy differences between the DFT minima (base structures) and RMC are 0.09 and 0.06 eV/atom for 50CaO and 64CaO, respectively. It is obvious from the energetics alone that the effect of DFT simulations is considerable. The total energy reduces by ∼0.6 eV/ atom from the initial RMC models in materials where the cohesive energies are of the order of 5.8 eV/atom (one should compare this also with the energy difference between the initial HSMC and RMC models, steps i and ii ). In terms of atomic structure, the DFT treatment affects the distributions of bond lengths and angles and coordination numbers, and there are differences in the longer length scale also (e.g., rings). Importantly, there are several atoms with unfavorable bonds in the initial RMC struc- ture, which dissociate upon DFT simulations and form new bonds with other atoms. Cavity Analysis A cavity analysis has been performed as described in ref. 4. The system is divided into a cubic mesh with a grid spacing of 0.20 Å, and the points farther from any atom at a given cutoff (here 2.3 and 2.5 Å) are selected and defined as “cavity domains.” Each domain is characterized by the point where the distance to all atoms is a maximum. If there are no maxima closer than the di- vacancy cutoff (here 2.0 Å), we locate the center of the largest sphere that can be placed inside the cavity. This point can be used for calculating partial pair distribution functions, including vacancy–vacancy correlations. Around the cavity domains we con- struct cells analogous to the Voronoi polyhedra in amorphous phases (compare the Wigner–Seitz cell) and analyze their vol- ume distribution. 1. Goedecker S, Teter M, Hutter J (1996) Separable dual-space Gaussian pseudopotentials. Phys Rev B Condens Matter 54(3):1703–1710. 2. VandeVondele J, Hutter J (2007) Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases. J Chem Phys 127(11):114105–114109. 3. Tang W, Sanville E, Henkelman G (2009) A grid-based Bader analysis algorithm without lattice bias. J Phys Condens Matter 21(8):084204–084207. 4. Akola J, Jones RO (2007) Structural phase transitions on the nanoscale: The crucial pattern in the phase-change materials Ge2Sb2Te5 and GeTe. Phys Rev B 76(23): 235201-1–235201-10. Akola et al. www.pnas.org/cgi/content/short/1300908110 1 of 6
