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A lot of materials electronic structure research focuses on periodic structures like polymers, nanotubes/sheets, Metal Organic Frameworks (MOFs) and crystals, which makes them amenable to PBC calculations and delocalized basis sets. If the periodicity is broken, say by some kind of defect site, a composite approach might be required where one still does a PBC calculation of the idealized bulk, but does a cluster calculation of the defect.

But how is the problem of modeling an explicitly aperiodic bulk structure like amorphous silica addressed? It does not seem to be as easy to form a composite model, as it is not just a small perturbation on an otherwise periodic structure.

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Creating amorphous structures is non-trivial and always rather expensive. Generally you are using large supercells such that you can achieve mid-range disorder. That means, since the cell is still periodic, you cannot truly achieve the long range disorder of amorphous materials, but in a medium range (> the unit cell volume) you can. As such, we some times speak of pseudo-amorphicity.

After you created the starting structure the general procedure is to quenching an ab-initio MD simulation. The principle is very similar to creating amorphous aterails in the lab: heat up a crystaline sample and then rapidly cool it down. This procedure is discussed at length in

Molecular Dynamics Simulations of Disordered Materials: From Network Glasses to Phase-Change Memory Alloys by C. Massobrio et. al.

Recently people have started experimenting with evolutionary structure generation programs like USPEX to create amorphous structures, but as far as I am aware the jury is still out on the prospects of that.

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A common approach for generating the starting model is the method of Wooten, Winer, and Weaire [1]. The WWW algorithm is a bond switching Monte Carlo approach: a Monte Carlo move is the exchange of two bonds, followed by a structural relaxation (either MD or MC of the newly connected structure). In the case of silicon, you would start from a large cell of diamond cubic Si, and go through a simulated annealing procedure. To generate a starting model of amorphous silica (SiO$_2$), the completed model of amorphous Si can be decorated with oxygen atoms at the midpoints of the Si--Si bonds, then run through a structural relaxation.

The quench-from-the-melt molecular dynamics approach has been rather successful; however, struggles more with a limited box size for the structural solution [2]. Regardless of approach, these starting structural solutions are compared against the pair distribution function (attained from a total scattering experiment) for verification.

From the resulting models, ab initio electronic structure methods can be used to calculate properties of interest. A modern use of these methods with amorphous metal-organic frameworks has been accomplished with zinc imidazolate [3].

  1. F. Wooten, K. Winer, D. Weaire, Phys. Rev. Lett. 54, 1392 (1985).
  2. A. Tilocca, J. Chem. Phys. 139, 114501 (2013).
  3. P. Adhikari, J. Phys. Chem. C 120, 15362 (2016).
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