Symmetry-adapted models for the hyperpolarizability of water

Accurately modeling nonlinear optical experiments such as second-harmonic scattering and hyper-Raman spectroscopy requires the hyperpolarizability, a nonlinear 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 predictfor 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 predictedmoleculartensors vary wildly between models. This means that while experiments whose outputs depend on total hyperpolarizability can be accurately modeled, those that require molecular quantities will require improved models.