How Small is Large Enough? Determining Minimal Cluster Sizes for Molecule Adsorption on Interstellar Amorphous Ice

Binding energies of molecules on ice mantles are important to understand the evolution of molecular complexity in molecular clouds. They are often computed using density functional theory (DFT) calculations, typically on either small amorphous ice clusters or crystalline slabs. Since these calculations require an accurate description of the electronic structure, hybrid functionals with dispersion corrections, basis set superposition error corrections and zero point energy corrections are typically employed. This, however, comes at a high computational cost, so most often small ice clusters are considered, frequently containing no more than twenty water molecules or so. While several recent studies have explored binding energy distributions, the effect of finite cluster size remains insufficiently quantified. To address this gap, we perform DFT calculations using six different functionals, on ice clusters containing 10 to 100 H2O molecules, separating the direct electronic effect of cluster truncation from the geometry-relaxation effects. As probe molecules, we use CO, CO2 and NH3. These calculations demonstrate that, irrespective of the molecule and functional used, interaction energies only start to converge from thirty to forty water molecules onwards. The dispersion energy flattens out earlier, whereas induction and polarisation effects require larger clusters to stabilise, particularly at structurally confined (cavity) sites. We conclude that ice cluster sizes of at least 30-40 water molecules are needed to obtain reliable binding energies, and that cluster size is as important as the choice of the functional.