Transferability of machine learning potentials: Protonated water neural network potential applied to the protonated...

A previously published neural network potential for the description of protonated water clusters up to the protonated water tetramer, H⁺(H₂O)₄, at an essentially converged coupled cluster accuracy [C. Schran, J. Behler, and D. Marx, J. Chem. Theory Comput. 16, 88 (2020)] is applied to the protonated water hexamer, H⁺(H₂O)₆-a system that the neural network has never seen before. Although being in the extrapolation regime, it is shown that the potential not only allows for quantum simulations from ultra-low temperatures ∼1 K up to 300 K but is also able to describe the new system very accurately compared to explicit coupled cluster calculations. This transferability of the model is rationalized by the similarity of the atomic environments encountered for the larger cluster compared to the environments in the training set of the model. Compared to the interpolation regime, the quality of the model is reduced by roughly one order of magnitude, but most of the difference to the coupled cluster reference comes from global shifts of the potential energy surface, while local energy fluctuations are well recovered. These results suggest that the application of neural network potentials in extrapolation regimes can provide useful results and might be more general than usually thought.