Deep neural network for Wannier function centers

We introduce a deep neural network (DNN) model that assigns the position of the centers of the electronic charge in each atomic configuration on a molecular dynamics trajectory. The electronic centers are uniquely specified by the unitary transformation that maps the occupied eigenstates onto maximally localized Wannier functions. In combination with deep potential molecular dynamics, a DNN approach to represent the potential energy surface of a multi-atom system at the ab-initio density functional level of theory, the scheme makes possible to predict the dielectric properties of insulators using samples and trajectories inaccessible to direct ab-initio molecular dynamics simulation, while retaining the accuracy of that approach. As an example, we report calculations of the infrared absorption spectra of light and heavy water at a dispersion inclusive hybrid functional level of theory, finding good agreement with experiment. Extensions to other spectroscopies, like Raman and sum frequency generation, are discussed.