Large-scale simulations (up to 32 000 molecules) are used to analyze local structures and fluctuations for the TIP4P/2005 and TIP5P water models, under deeply supercooled conditions, near previously proposed liquid-liquid critical points. Bulk freezing does not occur in our simulations, but correlations between molecules with local ice-like structure (ice-like molecules) are strong and long ranged (∼4 nm), exceeding the shortest dimension of smaller simulation cells at the lowest temperatures considered. Correlations between ice-like molecules decay slowly at low temperature, on the order of a hundred nanoseconds. Local ice-like structure is strongly correlated with highly tetrahedral liquid structure at all times, both structures contribute to density fluctuations, and to the associated anomalous scattering. For the TIP4P/2005 and TIP5P models, we show that the apparent spontaneous liquid-liquid phase separations, recently reported [T. Yagasaki, M. Matsumoto, and H. Tanaka, Phys. Rev. E 89, 020301 (2014)] for small rectangular simulation cells below the proposed critical points, exhibit strong system size dependence and do not occur at all in the largest systems we consider. Furthermore, in the smaller rectangular systems where layers of different densities do occur, we find that the appearance of a region of low density is always accompanied simultaneously by an excess of local ice density, with no separation in time. Our results suggest that the density differences observed in direct simulations for the two models considered here are likely due to long-range correlations between ice-like molecules and do not provide strong evidence of liquid-liquid phase separation.

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