Frequencies and IR intensities of the OH stretching vibrations in proton-ordered ices VIII, II, IX and XI are computed using B3LYP/6-311G** with periodic boundary conditions. In accord with the experiment, the average downshift of the OH or OD frequencies has a trend in changing from small to large shift in the order: VIII < II < IX < XI. The H-bond enthalpy values, evaluated from the IR intensities of the OH stretching vibrations, are consistent with this trend. PBE/6-311G** and BLYP/6-311G** overestimate the OD frequency downshift. The bond paths in the periodical electron density, which are associated with the O center dot center dot center dot O interactions in ices VIII, II and IX, have been found. (C) 2010 Elsevier B.V. All rights reserved.