A Full-Dimensional Neural Network Potential-Energy Surface for Water Clusters up to the Hexamer

Water clusters have attracted a lot of attention as prototype systems to study hydrogen bonded molecular aggregates but also to gain deeper insights into the properties of liquid water, the solvent of life. All these studies depend on an accurate description of the atomic interactions and countless potentials have been proposed in the literature in the past decades to represent the potential-energy surface (PES) of water. Many of these potentials employ drastic approximations like rigid water monomers and fixed point charges, while on the other hand also several attempts have been made to derive very accurate PESs by fitting data obtained in high-level electronic structure calculations. In recent years artificial neural networks (NNs) have been established as a powerful tool to construct high-dimensional PESs of a variety of systems, but to date no full-dimensional NN PES for water has been reported. Here, we present NN potentials for water clusters containing two to six water molecules trained to density functional theory (DFT) data employing two different exchange-correlation functionals, PBE and RPBE. In contrast to other potentials fitted to first principles data, these NN potentials are not based on a truncated many-body expansion of the energy but consider the interactions between all water molecules explicitly. For both functionals an excellent agreement with the underlying DFT calculations has been found with binding energy errors of only about 1%.