Code and Data Release: Fast electrostatic solvers for kinetic Monte Carlo simulations
| Main Authors: | Saunders, William Robert, Grant, James, Mueller, Eike Hermann, Thompson, Ian |
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| Format: | info software eJournal |
| Terbitan: |
, 2019
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| Online Access: |
https://zenodo.org/record/3584236 |
Daftar Isi:
- Kinetic Monte Carlo (KMC) is an important computational tool in theoretical physics and chemistry. In contrast to standard Monte Carlo, KMC permits the description of time dependent dynamical processes and is not restricted to systems in equilibrium. Compared to Molecular Dynamics, it allows simulations over significantly longer timescales. Recently KMC been applied successfully in modelling of novel energy materials such as Lithium-ion batteries and organic/perovskite solar cells. Motivated by this, we consider general solid state systems which contain free, interacting particles which can hop between localised sites in the material. The KMC transition rates for those hops depend on the change in total potential energy of the system. For charged particles this requires the frequent calculation of electrostatic interactions, which is usually the bottleneck of the simulation. To avoid this issue and obtain results in reasonable times, many studies replace the long-range potential by a phenomenological short range approximation. This, however, leads to systematic errors and unphysical results. On the other hand standard electrostatic solvers such as Ewald summation or fast Poisson solvers are highly inefficient in the KMC setup or introduce uncontrollable systematic errors at high resolution. In this paper we describe a new variant of the Fast Multipole Method by Greengard and Rokhlin which overcomes this issue by dramatically reducing computational costs. We exploit the fact that each update in the transition rate calculation corresponds to a single particle move and changes the configuration only by a small amount. This allows us to construct an algorithm which scales linearly in the number of charges for each KMC step, something which had not been deemed to be possible before.