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The design of accurate helium-solute interaction potentials for thesimulation of chemically complex molecules solvated in superfluid helium haslong been a cumbersome task due to the rather weak but strongly anisotropicnature of the interactions. We show that this challenge can be met by using acombination of an effective pair potential for the He-He interactions and aflexible high-dimensional neural network potential (NNP) for describing thecomplex interaction between helium and the solute in a pairwise additivemanner. This approach yields an excellent agreement with a mean absolutedeviation as small as 0.04 kJ/mol for the interaction energy between helium andboth, hydronium and Zundel cations compared to CCSD(T) reference calculationswith an energetically converged basis set. The construction and improvement ofthe potential can be performed in a highly automated way, which opens the doorfor applications to a variety of reactive molecules to study the effect ofsolvation on the solute as well as the solute-induced structuring of thesolvent. Furthermore, we show that this NNP approach yields very convincingagreement with the CCSD(T) reference for properties like many-body spatial andradial distribution functions. This holds for the microsolvation of theprotonated water monomer and dimer by a few helium atoms up to their solvationin bulk helium as obtained from path integral simulations at about 1 K.

High-dimensional neural network potentials for solvation: The case of protonated water clusters in helium