Automated Fitting of Neural Network Potentials at Coupled Cluster Accuracy: Protonated Water Clusters as Testing Ground

Highly accurate potential energy surfaces are of key
interest for
the detailed understanding and predictive modeling of chemical systems.
In recent years, several new types of force fields, which are based
on machine learning algorithms and fitted to ab initio reference calculations,
have been introduced to meet this requirement. Here, we show how high-dimensional
neural network potentials can be employed to automatically generate
the potential energy surface of finite sized clusters at coupled cluster
accuracy, namely CCSD­(T*)-F12a/aug-cc-pVTZ. The developed automated
procedure utilizes the established intrinsic properties of the model
such that the configurations for the training set are selected in
an unbiased and efficient way to minimize the computational effort
of expensive reference calculations. These ideas are applied to protonated
water clusters from the hydronium cation, H3O+, up to the tetramer, H9O4+, and lead to a single potential energy
surface that describes all these systems at essentially converged
coupled cluster accuracy with a fitting error of 0.06 kJ/mol per atom.
The fit is validated in detail for all clusters up to the tetramer
and yields reliable results not only for stationary points but also
for reaction pathways and intermediate configurations as well as different
sampling techniques. Per design, the neural network potentials (NNPs)
constructed in this fashion can handle very different conditions including
the quantum nature of the nuclei and enhanced sampling techniques
covering very low as well as high temperatures. This enables fast
and exhaustive exploration of the targeted protonated water clusters
with essentially converged interactions. In addition, the automated
process will allow one to tackle finite systems much beyond the present
case.