  The ST2 interaction potential has been used in a large number of simulation
studies to explore the possibility of a liquid-liquid phase transition (LLPT)
in supercooled water. Using umbrella sampling Monte Carlo simulations of ST2
water, we evaluate the free energy of formation of small ice nuclei in the
supercooled liquid in the vicinity of the Widom line, the region above the
critical temperature of the LLPT where a number of thermodynamic anomalies
occur. Our results show that in this region there is a substantial free energy
cost for the formation of small ice nuclei, demonstrating that the
thermodynamic anomalies associated with the Widom line in ST2 water occur in a
well-defined metastable liquid phase. On passing through the Widom line, we
identify changes in the free energy to form small ice nuclei that illustrate
how the thermodynamic anomalies associated with the LLPT may influence the ice
nucleation process.
