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I read several papers regarding the use of cluster-based kinetic Monte Carlo (kMC) simulations

They mention the need to use a kinetically resolved activation barrier by averaging over the forward and reverse migration barriers because it is "difficult to treat its configuration dependence with a cluster expansion," but do not explain why.

I am wondering why the barrier must be treated as a kinetically resolved one rather than treating the forward and reverse barriers separately.

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For any reaction, the forward barrier height must be equal to the reverse barrier height plus free energy change (or minus, depending on signs). Violating this would break detailed balance.

However, separately fitting configurational energies and barrier heights in all directions as a function of the cluster polynomials is likely to violate this relationship.

The kinetically-resolved activation barrier is a way to automatically conserve this relationship, by only fitting a direction-independent barrier to the cluster polynomials and entirely attributing directional energetics to the configurational energies (hence, "kinetically-resolved", in that these are barriers preserving only the kinetic drivers of selectivity between pathways but not the energetic drivers).

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  • $\begingroup$ "However, separately fitting configurational energies and barrier heights in all directions as a function of the cluster polynomials is likely to violate this relationship." - Why would this violate detailed balance if the barriers and configurations are both included in the cluster fitting? $\endgroup$
    – rmza7
    Commented May 9, 2023 at 14:57
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    $\begingroup$ Because polynomial fitting isn't exact (hence "fitting"). Here's a "toy" example: let's say I am fitting the functions sin(x) and cos(x) as polynomials in x about x = 0. Well, sin(x) ~= x and cos(x) ~= 1-x^2/2. But now notice my polynomial fits don't obey sin^2(x) + cos^2(x) = 1 any more! If I want to keep that relationship I should impose it before fitting. $\endgroup$ Commented May 9, 2023 at 17:59

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