Despite the successful implementation of the original ABC method in a series of

Despite the successful implementation of the original

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Despite the successful implementation of the original ABC method in a series of studies on different unit processes [ 14 , 25 27 , 45 47 ], the 1D nature of the ABC method can lead to an overestimation of the system evolution time [ 30 32 ] if there are multiple competitive processes governing the system evolution. To give an illustration we consider a synthetic J. Phys.: Condens. Matter 26 ( 2014 ) 365402
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Y Fan et al 5 comparison between ABC and full catalogue kMC using a pre-constructed hypothetical 2D PES (figure 3 ( a )). To simu- late a scenario with multiple processes, we randomly intro- duced 100 intermediate minima with varying depths and widths (figure 3 ( a )) to form a rough energy landscape con- necting the initial and final states. In the kMC simulations, the transition catalog is defined by a cut-off radius r c . In other words, if the distance between two minima is smaller than r c , then the two states are defined as connected and a direct transition between them is allowed. In the kMC simulations, for a state with residence time τ , a random number between 0 and 1 is generated during each step, and the time is pre- ceded by the amount − τ /ln( μ ), following the kMC convention [ 42 44 ]. Note that r c is an empirically chosen parameter in kMC simulations, and below we demonstrate the effect of the choice of r c in the quantitative results. A 1D trajectory of events describing the evolution from the same prescribed ini- tial state to the final state was found using ABC calculations; this was used to estimate the temperature-dependent system evolution time and the effective activation energy in the kMC method, statistically averaged over hundreds of simulations. As shown by the Arrhenius plot in figure  3 ( b ), the slope of the ABC results is identical to the full-catalog kMC results, which indicates that both results give the same effective bar- rier. This demonstrates that ABC is providing the dominant transition pathway. On the other hand, the evolution time in ABC results is overestimated by about two orders of magni- tude, in this case compared to kMC with r c = 0.2. This results from the 1D nature of the original ABC algorithm, because the residence time at each state, as introduced above, is governed by + k k 1/( ) forward backward , whereas in kMC simulations using a full catalog of transition pathways, it is governed by uni2211 k 1 / i . Therefore, the evolution time calculated by the ABC method for a scenario with multiple competing processes can be over- estimated here because uni2211 + > k k k 1 / ( ) 1 / i forward backward . On the other hand, the magnitude of the overestimation by ABC compared to kMC simulations also depends on the accuracy of the full-catalog kMC results with a selected value of r c . We show two kMC results in figure  3 ( b ) with different cut-off radii of 0.2 and 0.15. For the larger cut-off radius, the tran- sition catalog is more extensive than for the smaller cut-off radius, and thus, yields a faster evolution time. However, this does not mean that all the events sampled with the larger r c
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  • Summer '19
  • Transition state, KMC

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