Equipartition and the temperature of maximum density of TIP4/2005 water

TL;DR

This work evaluates the TIP4P/2005 water model's ability to reproduce the temperature of maximum density (TMD) and the liquid–vapor coexistence curve, focusing on how integration time-step and ensemble sampling affect equipartition and results. Using classical molecular dynamics with time-steps of $0.25$, $0.50$, $2.00$, and $4.00$ fs across multiple thermostat/barostat setups, the study demonstrates that $0.25$–$0.50$ fs preserve equipartition and yield TMD around $277.15$ K, in excellent agreement with experiment. Increasing the time-step shifts the TMD to lower temperatures ($273.15$ K at $2.00$ fs and $269.15$ K at $4.00$ fs) and can degrade reproducibility across codes, highlighting the need for proper ensemble sampling. Enhancing water–water dispersion as in TIP4P-D worsens the liquid–vapor envelope, suggesting caution when modifying dispersion to aid protein hydration models. The key message is that maintaining equipartition with sufficiently small time-steps is essential for reliable liquid water properties and for producing transferable data for biomolecular simulations and force-field development.

Abstract

We simulate TIP4P/2005 water in the temperature range of 257 K to 318 K with time-steps $δ=$ 0.25, 0.50, 2.00, and 4.00 fs. The density-temperature behavior obtained using 0.25 or 0.50 fs are in excellent agreement with each other but differ from those obtained using time-steps that have been shown earlier to lead to a breakdown of equipartition. The temperature of maximum density (TMD) is 277.15 K with $δt = 0.25\;\mathrm{or}\; 0.50$ fs, but is shifted to progressively lower values for longer time-steps, a trend that holds for different thermostat/barostat combinations. Enhancing the water-water dispersion interaction, as has been recommended for simulating disordered proteins in TIP4P/2005, degrades the description of the liquid-vapor phase envelope. A key takeaway from this study is that using sufficiently short time-steps ($\leq 0.5$ fs) to preserve equipartition is essential for obtaining meaningful liquid water properties and for producing reliable data to parametrize biomolecular simulation models, as correct-ensemble sampling is fundamental to ensure reproducibility across codes and simulation alogrithms.

Figures (5)

• Figure 1: Density versus average simulation temperature of TIP4P/2005 water for conditions of most interest in biomolecular simulation. The average simulation temperature equals the setpoint temperature to within 0.02 K. The dashed vertical line is the experimental TMD at 277.15 K. The horizontal dashed line is a guide to the eye to highlight that within the temperature resolution of this study, the simulated TMD is at 277.15 K. The (black) solid line is the experimental density of the stable liquid under saturation conditionsnist. The black filled circles are data obtained from Table 1 Ref. vega:tip4p; the data is expected to have an uncertainty of $\pm 1$ kg/m$^3$. The size of the symbol for $\delta t = 0.25$ fs is $\approx 2$ standard error of the mean.
• Figure 2: Impact of enhancing the water-water dispersion interaction in TIP4P/2005. The time-step for integrating the equations of motion is $\delta t = 0.25$ fs. Rest as in Figure \ref{['fg:figure1']}.
• Figure 3: Time-step dependence of the predicted saturation curve for two different time-steps. The vertical lines indicate the location of the TMD for $\delta t = 0.25$ (dashed blue), 2.00 fs (dotted red), and 4.0 fs (dotted black). Rest as in Figure \ref{['fg:figure1']}.
• Figure 4: Sensitivity of density temperature behavior to thermostat/barostat combination. Data from the stochastic velocity rescaling thermostat/MC barostat (CSVR) at the smallest time-step is shown together with the results from Langevin thermostat/barostat (Langevin). The $2\sigma$ standard error of the mean is approximately the size of the filled symbol (CSVR). Left panel: $\rho$ versus the average simulation temperature. Right panel: $\rho$ versus the setpoint temperature defined in the simulation configuration file.
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