The thermodynamic, structural and kinetic properties estimated from molecular simulations can deviate considerably from the true values in the thermodynamic limit due to the finite dimensions of the simulation box. Such discrepancies are typically referred to as finite size effects
. Computational studies of crystal nucleation, in particular, are known to be influenced by system size, as unphysical interactions can arise between crystalline nuclei and their periodic images . However, no rigorous guidelines exist for quantifying such artifacts and ad hoc
heuristics (such as the 10% rule) have emerged over years in the nucleation community to rule out the existence of finite-size effects. In this work, we systematically investigate the sensitivity of nucleation kinetics and mechanism to system size. We use  molecular dynamics simulations and a path sampling technique called jumpy forward flux sampling  to compute heterogeneous ice nucleation rates for the coarse-grained monoatomic water (mW)  model in the vicinity of square-shaped model structureless  ice nucleating particles (INPs) of different sizes. We identify three distinct regimes for the dependence of the computed rate on the INP dimension, L
. For small L
âs, the rate is a strong function of L
, due to the artificial spanning of the critical nuclei across the periodic boundary. For intermediate L
âs, the rate is smaller overall, and the critical nuclei are non-spanning but are âproximalâ in the sense that the supercooled liquid within the inter-image region (i.e., the region along the vector connecting a crystalline nucleus to its closest periodic image) becomes fairly structured. Finally, for sufficiently large L
âs, critical nuclei are neither spanning nor proximal, yet the rate is a weak function of L
. We propose a heuristic suggesting that finite size effects will be minimal if critical nuclei are neither spanning nor proximal and if the intermediary liquid has a region that is structurally indistinguishable from the supercooled liquid under the same conditions. Preliminary analysis of the strength of finite-size effects in homogeneous nucleation in the LJ system will also be discussed.
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