Critical comparison of classical and quantum mechanical treatments of the phase equilibria of water

The Gibbs ensemble Monte Carlo simulation technique was used to compare the phase equilibria of the rigid TIP4P water model Jorgensen et al., J. Chem. Phys. 79, 926 (1983)] utilizing classical and quantum statistical mechanics. The quantum statistical mechanical treatment generally resulted in lower liquid densities and higher vapor densities, narrowing the phase envelope. As a result, the calculated critical temperatures and normal boiling points were lower from the quantum simulations than the classical by 22 and 17 K, respectively, but the critical densities were equal within the estimated uncertainties. When the phase diagram from the quantum statistical mechanical treatment was increased by 22 K, it agreed with the classical results quite well throughout the entire simulated temperature range. A semiclassical treatment, involving a low order expansion in Planck's constant, resulted in good agreement with the path integral results for second virial coefficients, but gave densities and vapor pressures that fluctuated between the values for the classical and quantum statistical mechanics values, with no definite agreement with either.