A new analytic equation of state for liquid water

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Abstract
We develop a new analytical equation of state for water based on the Song, Mason, and Ihm equation of state and Poole et al.’s simple model of the free energy of strong tetrahedral hydrogen bonds. Repulsive and attractive forces are modeled using a modification of the Weeks–Chandler–Anderson decomposition of the pair potential, with closed tetrahedral hydrogen bonds contributing both internal energy and entropy to the free energy of water. Strong tetrahedral hydrogen bonds are modeled explicitly using a simplified partition function. The resulting equation of state is 20–30 times more accurate than equivalent simple cubic equations of state over a wide range of pressures (0.1→3000 bar) and temperatures (−34→1200 °C) including the supercooled region. The new equation of state predicts a second liquid–liquid critical point at p C ′ =0.954 kbar, ρ C ′ =1.045 g cm −3 and T C ′ =228.3 K. The temperature of this second critical point is above the homogeneous freezing temperature at 1 kbar, thus this region of the phase diagram may be experimentally accessible. The phase diagram also suggests that the homogeneous nucleation temperature above 1.2 kbar may be determined by a phase transition from high-density water to low-density water.