Can the density maximum of water be found by computer simulation?

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Abstract
Path integral molecular dynamics (PIMD) simulations of the extended simple point charge (SPC/E) model of liquid water (both H2O and D2O) have been performed in order to find the temperature at which the maximum liquid density is obtained. For comparison, purely classical SPC and SPC/E water have also been simulated over long periods (more than 200 ps). Structural properties and various temperature dependent quantities are reported. Special attention has been given to the fluctuations of pressure and volume in simulations run in the canonical (constant NVT) and isothermal–isobaric (constant NPT) ensembles, respectively. Although a density maximum is detected by monitoring energy–volume correlations as a function of temperature, the large statistical uncertainty in the correlations reduces the significance of this finding. The main conclusions of this work are threefold. First, the use of the energy–volume correlation moment to determine the density maximum appears to be a useful method, although a number of very long simulations of between 0.5–1.0 ns over a fairly wide temperature range are necessary to obtain accurate results. Second, neither the SPC nor the SPC/E water models are able to reproduce the density of cold water accurately. Finally, a quantum mechanical treatment of the water model is necessary to correctly represent the structure, energy, and fluctuations of the condensed phase.