Flow diagram for the LSKMC algorithm described in the text.
Illustration of our algorithm for identifying local superbasin states/moves, as described in the text.
Illustration of one possible way for integrating superbasin exits with non-superbasin KMC events by using two separate time lines. A superbasin exit time t exit is generated at a time of t s = t 2. The superbasin exit is scheduled for a time of t s + t exit on the superbasin time line. A non-superbasin KMC event occurs at time t 3, after which the superbasin exit occurs, then two more non-superbasin KMC events occur at times t 4 and t 5.
One-dimensional, periodic potential for Example 1. For 0.4 < E min < 0.8 eV, the algorithm detects states 4–8 (and similar) as superbasin states. For a superbasin in which states 4 and 8 are absorbing states and states 5, 6, and 7 are transient states, we indicate a possible re-numbering of the states.
Trajectories for 100 MCS on the PES in Fig. 4 with k B T = 0.04, n = 3, and t min = (2.0r 34)−1 for a conventional KMC simulation (a) and for a LSKMC simulation with E min = 0.5 eV (b).
One-dimensional, periodic potential for Example 2. For 0.2 < E min < 0.45 eV, the algorithm identifies states 20–26 (and similar) as a superbasin and for 0.45 < E min < 0.70 eV, states 15–31 (and similar) constitute a superbasin.
Trajectories for 100 MCS on the PES in Fig. 7 with k B T = 0.03, n = 50, and for a conventional KMC simulation (a), for a LSKMC simulation in which states 20–26 (and similar) in Fig. 7 constitute a superbasin (E min = 0.3 eV) (b), and for a LSKMC simulation in which states 15–31 (and similar) in Fig. 7 constitute a superbasin (E min = 0.5 eV) (c).
Cross-section of the two-dimensional trap potential for Example 3. The algorithm detects a superbasin for 0.1 < E min < 0.7 eV.
Results from a conventional KMC simulation at k B T = 0.04 of two random walkers on a lattice containing a square trap. In (a), we show the evolution of real time as a function of the number of MCS. The simulated time increment decreases when one of the walkers enters the trap around 1 MCS. In (b), we show the walker trajectories (with periodic boundary conditions removed) and we see that one of the walkers has entered the trap, indicated by the heavily populated square.
Trajectories (with periodic boundary conditions removed) from a LSKMC simulation (k B T = 0.04, E min = 0.2 eV, n = 100, ) of two random walkers on a lattice containing a square trap using the method of revising superbasins to account for interactions between superbasin and non-superbasin states.
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