Symmetry-Adapted Models for the Hyperpolarizability of Water.

Accurately modelling nonlinear optical experiments such as second-harmonic scattering and hyper-Raman scattering requires the hyperpolarizability $\boldsymbol{\beta}$, a nonlinear dielectric response to an applied electric field. The hyperpolarizability tensor is a computationally expensive quantity to calculate, making it a natural target for machine-learning methods. We test a family of recently developed models for the hyperpolarizability of water, trained on small clusters containing up to 8 water molecules. These models are able to predict $\boldsymbol{\beta}$ for larger clusters, with more complex structures than those observed in the training set. For configurations of bulk water, the agreement is not so straightforward: while the total hyperpolarizability is quite well described, the predicted \textit{molecular} $\boldsymbol{\beta}$ tensors vary wildly between models. This means that while experiments whose outputs depend on total hyperpolarizability can be accurately modelled, those that require molecular quantities will require improved models.