One of the most controversial hypotheses for explaining the origin of the thermodynamic anomalies characterizing liquid water postulates the presence of a metastable second-order liquid-liquid critical point [] located in the “no-man’s land” []. In this scenario, two liquids with distinct local structure emerge near the critical temperature. Unfortunately, since spontaneous crystallization is rapid in this region, experimental support for this hypothesis relies on significant extrapolations, either from the metastable liquid or from amorphous solid water [, ]. Although the liquid-liquid transition is expected to feature in many tetrahedrally coordinated liquids, including silicon [], carbon [] and silica, even numerical studies of atomic and molecular models have been unable to conclusively prove the existence of this transition. Here we provide such evidence for a model in which it is possible to continuously tune the softness of the interparticle interaction and the flexibility of the bonds, the key ingredients controlling the existence of the critical point. We show that conditions exist where the full coexistence is thermodynamically stable with respect to crystallization. Our work offers a basis for designing colloidal analogues of water exhibiting liquid-liquid transitions in equilibrium, opening the way for experimental confirmation of the original hypothesis.
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