  Liquid-liquid phase transition (LLPT) in supercooled water has been a
long-standing controversial issue. We show simulation results of real stable
first-order phase transitions between high and low density liquid (HDL and
LDL)-like structures in confined supercooled water in both positive and
negative pressures. These topological phase transitions originate from H-bond
network ordering in molecular rotational mode after molecular exchanges are
frozen. It is explained by the order parameter-dependent free energy change
upon mixing liquid-like and ice-like moieties of H-bond orientations which is
governed by their two- to many-body interactions. This unexplored purely H-bond
orientation-driven topological phase gives mid-density and stable intermediate
mixed-phase with high and low density structures. The phase diagram of
supercooled water demonstrate the second and third critical points of water.
