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The proton disorder in ice has a key role in several properties such as the growth mode, thermodynamical properties, and ferroelectricity. While structural phase transitions from proton disordered to proton ordered ices have been extensively studied, much less is known about their electronic and optical properties. Here, we present ab initio many body perturbation theory-based calculations of the electronic and optical properties of cubic ice at different levels of proton disorder. We compare our results with those from liquid water, that acts as an example of a fully (proton- and oxygen-)disordered system. We find that by increasing the proton disorder, a shrinking of the electronic gap occurs in ice, and it is smallest in the liquid water. Simultaneously, the excitonic binding energy decreases, so that the final optical gaps result to be almost independent on the degree of proton disorder. We explain these findings as an interplay between the local dipolar disorder and the electronic correlation

Proton disorder in cubic ice: Effect on the electronic and optical properties