Dielectric Properties of Disordered Crystalline Materials: A Computational Case Study on Hexagonal Ice

The dielectric properties of disordered crystalline materials are governed by long-range orientational correlations arising from local structural disorder. We present a statistical and topological framework that connects hydrogen-bond network features to macroscopic dielectric anisotropy. Using hexagonal ice as a model system, we represent the network as a directed graph and employ the polarization index, originally introduced in the GenIce software, to measure the net traversal of percolating hydrogen-bond chains through the periodic lattice. Effective bond dipole moments, determined from moderately sized simulation cells, are combined with the variance of the polarization index to predict dielectric constants for much larger cells without additional computations on three-dimensional structures. We validate this Polarization Index–Based Effective Dipole (PIBED) model using the AMOEBA14 and neural network potentials, with and without nuclear quantum effects. The results agree with the estimates of the traditional Total Dipole Fluctuation (TBF) model and exhibit improved statistical convergence, enabling a robust estimation of the small dielectric anisotropy of ice Ih. Our findings establish a generalizable method for quantifying dielectric response in disordered crystals and may offer insights into the dielectric behavior of partially ordered systems such as hybrid perovskites and solid-state proton conductors.