Accurate quantum-chemical fragmentation calculations for ion-water clusters with the density-based many-body expansion

The many-body expansion (MBE) provides an attractive fragmentation method for the efficient quantum-chemical treatment of molecular clusters. However, its convergence with the many-body order is generally slow for molecular clusters that exhibit large intermolecular polarization effects. Ion--water clusters are thus a particularly challenging test case for quantum-chemical fragmentation methods based on the MBE. Here, we assess the accuracy of both the conventional, energy-based MBE and the recently developed density-based MBE [Schmitt-Monreal and Jacob, Int. J. Quantum Chem, 120, e26228 (2020)] for ion--water clusters. As test cases, we consider hydrated Ca^2+, F^-, OH^-, and H3O^+, and compare both total interaction energies and the relative interaction energies of different structural isomers. We show that an embedded density-based two-body expansion yields highly accurate results compared to supermolecular calculations. Already at the two-body level, the density-based MBE clearly outperforms a conventional, energy-based embedded three-body expansion. We compare different embedding schemes and find that a relaxed frozen-density embedding potential yields the most accurate results. This opens the door to accurate and efficient quantum-chemical calculations for large ion--water clusters as well as condensed-phase systems.