Dielectric and dynamical properties of supercooled water

Water's anomalies have long intrigued scientists across various disciplines due to their profound implications for understanding fundamental properties of matter. Despite significant efforts from experimental, theoretical, and computational fronts, a consensus on the microscopic origins of water's anomalies remains elusive, fostering an open and active area of research. In the first part of this work we propose a simulation protocol, based on the Green-Kubo theory of linear response, that, by applying recently proposed data-analysis methods{,} and a combination of ab initio molecular dynamics (AIMD) and machine-learning techniques, allows us to overcome the time-scale barrier that has so far hindered a systematic exploration of the viscous properties of water. We demonstrate the reliability of this protocol by comparing its predictions with those of AIMD simulations of unprecedented length, performed using the {Perdew-Burke-Ernzerhof} (PBE) functional {in density functional theory (DFT)}. A particular attention is paid to the statistical robustness of the results thus obtained, which is often overlooked in the literature, and guidance is provided on how to appraise and improve it. Leveraging the newly proposed protocol, we finally perform the first extended simulation of the viscous properties of water with ab initio quality, using the {Strongly Constrained and Appropriately Normed} (SCAN) exchange-correlation functional, which has already demonstrated a solid predictive power for the properties of water in various thermodynamic conditions. In the second part of this work we investigate the dielectric properties of supercooled water near its putative liquid-liquid critical point (LLCP). Analyzing long molecular dynamics simulations performed using deep neural-network potentials, {trained to extensive SCAN-DFT data}, we demonstrate that the low-density liquid (LDL) phase displays a strong propensity toward spontaneous polarization. Our findings suggest that the dynamical stability of the low-density phase, and hence the transition from high-density (HDL) to low-density liquid, is strongly correlated to a collective process involving an accumulation of rotational angular jumps. This dynamical transition involves subtle changes in the electronic polarizability of water molecules which affects their rotational mobility within the two phases. Moreover, we discuss other important dielectric properties of these two liquid phases, such as dielectric constant, infrared spectra and dielectric loss, highlighting the differences and unique characteristics that distinguish LDL from HDL, thereby providing deeper insights into the dielectric behavior of supercooled water. {Our contribution offers new perspectives on the role of electronic polarization in the dynamics of the LDL phase, which will also catalyze new activity in methods development aimed at further elucidating the intricate behaviors of supercooled water.