Learning Polarization Using Equivariant Neural Networks

Polarization is an essential physical quantity for understanding the properties of dielectrics and ferroelectrics [1]. The modern theory of polarization [1] and further developments on electric enthalpy functionals [2] have enabled the study of polarization in periodic electronic structure calculations. Interestingly, predicting the polarization over a molecular dynamics allows for the determination of experimentally-relevant quantities such as infrared and Raman spectra from first principles. However, this remains a challenging problem in electronic structure calculations, because of their high computational cost.<br/><br/>Here, we introduce an equivariant neural network approach to efficiently learn and predict polarization for each atomic configuration, building on and extending state-of-the-art machine learning force field architectures. This allows one to determine the autocorrelation function of polarization over long-lasting molecular dynamics, thereby giving access to infrared spectrum, frequency-dependent dielectric constant, and Raman cross section from first principles. We implemented our scheme in the E(3)-equivariant NequIP/Allegro framework [3,4], and interfaced it with the LAMMPS code for performing molecular dynamics calculations.<br/><br/>[1] R. Resta, Macroscopic polarization in crystalline dielectrics: the geometric phase approach, Rev. Mod. Phys. 66, 899 (1994).<br/>[2] P. Umari and A. Pasquarello, Ab initio molecular dynamics in a finite homogeneous electric field, Phys. Rev. Lett. 89, 157602 (2002).<br/>[3] S. Batzner, A. Musaelian, L. Sun, M. Geiger, J. P. Mailoa, M. Kornbluth, N. Molinari, T. E. Smidt, and B. Kozinsky, E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. Nat. Commun., 13, 2453 (2022)<br/>[4] A. Musaelian, S. Batzner, A. Johansson, L. Sun, C. Owen, M. Kornbluth, and B. Kozinsky, Learning local equivariant representations for large-scale atomistic dynamics Nat. Commun., 14, 579 (2023)