  We have investigated the effects of either distorting hydrogen bonds or
removing proton degeneracy on the thermodynamic properties of a minimal model
for associating liquids. The presence of two liquid phases and a density
anomaly is unaffected in both cases. Increasing the degeneracy of bonded
structures leads to lower temperature critical points and a steeper
liquid-liquid coexistence line, implying a low density liquid of larger
entropy.
  Analysis of the hydrogen bond net accross the phase diagram indicates that
the density anomaly is accompanied by a steep reduction of hydrogen bond
density, which introduces a restriction on a correlation which has been
preconized long ago. This feature is present independent of bond distortion or
of the presence of proton entropy.
