Displacement algorithms used to initiate saddle point searches: (i) Displace all atoms, (ii) displace atoms around a central (green) atom, and (iii) displace atoms around a targeted central atom, in this case an undercoordinated surface atom. (Blue circles represent atoms in a box from a side view.)
Reaction mechanisms with barriers within of the lowest saddle point energy are considered relevant. For a choice of , the chance of a higher barrier process occurring in the dynamics is approximately .
Test of the aKMC confidence parameter for a dynamics simulation of (a) nine Al adatoms, which ripen into (b) a compact island on Al(100) at . The fraction of the total rate (red, left) and the relevant saddles found (green, right) follow the analytic confidence relations of Eq. (6) (blue, upper curve) and Eq. (14) with (green, lower curve).
For systems with local events, the mechanism and rates of distant events can be recycled to build a new rate table very quickly. New searches are concentrated in the region around the chosen process, for which there is a hole in the rate table. Then, the cost of updating the rate table does not increase with system size.
Examples of recycling saddle points from a previous state for Al diffusion on Al(100). To recycle a saddle, atoms that move significantly in the chosen process (a) are identified. Here, the one atom that moved by more than is marked with a (●). Then, in the saddle geometry of all other processes [(b), (c), and (d)], these moving atoms are set in their final-state positions of the chosen process.
The computational cost for a KMC step is significantly reduced by recycling saddles from the previous step.
For a system with local processes, recycling saddles from one state to the next results in a computational effort (measured by the number of force evaluations) that does not increase with system size. The insets show how the smallest system was expanded to make larger systems for this calculation.
A superbasin is composed of states ( and ) that are connected by much lower barriers than the barriers to leave the superbasin . To avoid a large number of oscillations between states in the superbasin, they are taken to be a single state in local equilibrium.
An aKMC script automatically submits calculations on a cluster of computers, restarts incomplete jobs, finds saddles and corresponding final states, collects kinetic processes and rate, and performs the KMC steps.
The DFT-based aKMC simulation of a Pd tetramer formation at an O vacancy site (●) on the MgO(100) surface over a time scale of at . [Circles: O (red), Mg (green), and Pd (purple)].
Reaction mechanisms from an initial state with adsorbed next to a Ca atom at a step on the MgO(100) surface, found using DFT forces with dimer searches. (Red atoms are O from MgO, pink are O from , green are Mg, gray are Ca, and the dashed line is the step edge. The pink dot is used to distinguish the atoms.)
DFT dynamics of Ca oxidation on the MgO(100) surface at .
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