Virtual single-particle energy distributions determined by the energy moments calculated from constant-volume heat capacity (C-v) at a constant volume v* were presented for liquid water, methanol, ethanol, carbon disulfide, mercury, and benzene. The distribution curves were obtained by directly solving the coefficients in the distribution function in terms of the first three energy moments (four, counting normalization). A bimodal distribution was found for water. Conversely, methanol, ethanol, carbon disulfide, mercury, and benzene exhibit a single-peaked distribution. The distinctive characteristic of the virtual single-particle energy distribution in water is the appearance of a lower-energy peak in the neighborhood of 1.0 kcal/mol and a higher-energy peak around 3.1 kcal/mol. The energy distribution reveals molecular characteristics through examination of its dependence not only on the temperature but also on the volume. At a fixed v*, the ratio of the higher- to the lower-energy peak increases as t increases. At a constant t, the ratio increases as v* decreases (or as pressure increases). The possibility of employing virtual single-particle energy distributions to gain insight into the structure of bulk liquids was discussed. If such energy distributions confer visibility upon the structure which is present in 1 mol of liquid, the two energy peaks in water could represent two distinguishable states in the structure of liquid water.