Optical Anisotropy as a Probe of Proton Ordering at Ice Surfaces

Ice surfaces play a central role in climate processes, astrochemistry, and materials science, yet their microscopic structure remains elusive. In particular, the degree of proton ordering at ice Ih surfaces critically influences surface reactivity, stability, and phase transitions. In this work, we employ advanced computational techniques─density functional theory to optimize equilibrium geometries, and many-body perturbation theory (GW and Bethe-Salpeter equation) to describe electronic and optical properties─to investigate ordered and partially disordered thin films of hexagonal ice (Ih). First, we analyzed six surface models featuring distinct arrangements of dangling OH bonds, quantified via an order parameter, and computed their Reflectance Anisotropy spectra, which exhibit a pronounced dependence on proton ordering. Among these, two representative models, the Ih-striped and Ih-low-ordered surfaces, emerge as the most stable. For these cases, we demonstrate that proton ordering governs the anisotropy of the optical response: the striped surface supports strongly directional excitonic states, in contrast to the nearly isotropic excitons observed in the low-ordered surface. Our results establish optical anisotropy as a robust fingerprint of proton order, providing a theoretical benchmark for polarization-resolved spectroscopic studies of ice. Furthermore, we show that excitonic effects serve as a sensitive probe of surface proton configurations, paving the way for experimental discrimination between competing models of ice surfaces under cryogenic conditions.