Modeling glasses from first-principles using random structure sampling

TL;DR

The paper presents a first-principles random structure sampling method that models glasses as a composite ensemble of small-cell local minima on the potential energy surface, circumventing the need for large MD simulations. By generating thousands of random, 24-atom (and other sizes) periodic structures and relaxing them with DFT, the authors predict static glass properties through ensemble averaging, applying both reciprocal- and real-space structure functions, as well as electronic and elastic metrics. For vitreous SiO2, ensemble-averaged structure factors, PDFs, density, electronic DOS, and bulk modulus show good agreement with experimental data, with convergence achievable using on the order of 100–1000 structures depending on the property. The approach reduces computational cost and enables the use of high-accuracy electronic structure methods for glasses, though a small density overestimation and dependence on the chosen subset of structures are noted and discussed as areas for refinement.

Abstract

We present an approach to approximating static properties of glasses without experimental inputs rooted in the first-principles random structure sampling. In our approach, the glassy system is represented by a collection (composite) of periodic, small-cell (few 10s of atoms) local minima on the potential energy surface. These are obtained by generating a set of periodic structures with random lattice parameters and random atomic positions, which are then relaxed to their closest local minima on the potential energy surface using the first-principles methods. Using vitreous SiO2 as an example, we illustrate and discuss how well various atomic and electronic structure properties calculated as averages over the set of such local minima reproduce experimental data. The practical benefit of our approach, which can be rigorously thought of as representing an infinitely quickly quenched liquid, is in that it transfers the computational burden to linearly scaling and easy to converge averages of properties computed on small-cell structures, rather than simulation cells with 100s if not 1000s of atoms while retaining a good overall predictive accuracy. Because of this it enables the future use of high-cost/high-accuracy electronic structure methods thereby bringing modeling of glasses and amorphous phases closer to the state of modeling of crystalline solids.

Figures (9)

• Figure 1: Dependence of the results on (a) the cell size, and (b) on the exchange-correlation functional used in calculations. Normalized Thermodynamic Density of States (TDOS), the mass density distribution over the random structures, and the average neutron structure factor are shown. Gaussian broadening of 0.015 eV and 0.035 g/cm$^{3}$ was used for the TDOS and the density distributions, respectively. Dashed vertical lines show the average density only for the PBE density distribution.
• Figure 2: Neutron and X-ray structure functions from computation (red) and experimentSusman_1991Mei_2007 (purple). Panel (a) shows reciprocal space function $q(S^{N/X}(q)-1)$ and panel (b) the reduced pair distribution function $D^{N/X}(r)$ calculated both directly in real space (orange curve) and as the sine Fourier transform (red), both averaged over 3000 random structures (see text for details).
• Figure 3: Atom-pair specific real space functions from which coordination numbers from Table \ref{['table:coord_no']} are obtained using Eq. (\ref{['eq:coord']}). Dashed vertical lines show integration bounds identifying the peaks, right bound is identified as the next local minimum.
• Figure 4: Reduced PDFs from sine Fourier transformation of both modified (blue) and unmodified (red) neutron diffraction structure factor and experimentsSusman_1991 (purple). Difference between the red and blue curves is shown with an offset in grey. Inset shows the reciprocal space structure factors from which the reduced PDFs are obtained (vertical offset for clarity). The modified structure factor is obtained by replacing first peak (shaded region in the inset) with the experimental one.
• Figure 5: (a) The ensemble-averaged mass density and (b) neutron scattering structure factors as a function of ($k_{B}\mathrm{T}$). Shaded regions in (a) show one and two standard deviation intervals. The vertical offset between curves in panel (b) is for clarity.