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Computational studies of crystal nucleation can be impacted by finite sizeeffects, primarily due to unphysical interactions between crystalline nucleiand their periodic images. It is, however, not always feasible tosystematically investigate the sensitivity of nucleation kinetics and mechanismto system size due to large computational costs of nucleation studies. Here, weuse jumpy forward flux sampling to accurately compute the rates ofheterogeneous ice nucleation in the vicinity of square-shaped modelstructureless ice nucleating particles (INPs) of different sizes, and identifythree distinct regimes for the dependence of rate on the INP dimension, $L$.For small INPs, the rate is a strong function of $L$ due to artificial spanningof critical nuclei across the periodic boundary. Intermediate-sized INPs,however, give rise to the emergence of non-spanning 'proximal` nuclei that areclose enough to their periodic images to fully structure the intermediaryliquid. While such proximity can facilitate nucleation, its effect is offset bythe higher density of the intermediary liquid, leading to artificially smallnucleation rates overall. The critical nuclei formed at large INPs are neitherspanning nor proximal. Yet, the rate is a weak function of $L$, with itslogarithm scaling linearly with $1/L$. The key heuristic emerging from theseobservations is that finite size effects will be minimal if critical nuclei areneither spanning nor proximal, and if the intermediary liquid has a region thatis structurally indistinguishable from the supercooled liquid under the sameconditions.

How to Quantify and Avoid Finite Size Effects in Computational Studies of Crystal Nucleation: The Case of Heterogeneous Ice Nucleation