Machine learning inference of molecular dipole moment in liquid water

Molecular dipole moment in liquid water is an intriguing property, partly due to the fact that there no unique way partition total electron density into individual molecular contributions. The prevailing method circumvent this problem use maximally localized Wannier functions, which perform a unitary transformation of occupied orbitals by minimizing spread function Boys. Here we revisit using data-driven approach satisfying two physical constraints, namely: i) displacement atomic charges proportional Berry phase polarization; ii) Each molecule has formal charge zero. It turns out distribution moments inferred from latent variables surprisingly similar obtained functions. Apart putting maximum-likelihood footnote established method, work highlights capability graph convolution based models and importance constraints on improving interpretability.