The low-temperature proton-ordered counterparts for ice-Ih, ice-III, ice-VI and ice-VII are investigated by first principle methods in conjunction with a graph enumeration technique. Two experimentally well calibrated disorder/order transitions, ice-Ih/ice-XI and ice-VII/ice-VIII, are used to validate the methodology we used herein and in both cases our approach is able to reproduce major experimental features. For ice-III and ice-VI, direct structural determination on the fully proton-ordered counterparts by neutron diffraction is not available and in the literature different ordering schemes have been proposed. Our calculation results serve as an independent reference, and we shall discuss our findings and their relevance to previous experimental works.
