Equilibration between Translational and Rotational Modes in Molecular Dynamics Simulations of Rigid Water Requires a Smaller Integration Time-Step Than Often Used

In simulations of aqueous systems it is common to freeze the bond vibration and angle bending modes in water to allow for a longer time-step $\delta t$ for integrating the equations of motion. Thus $\delta t = 2$ fs is often used in simulating rigid models of water. We simulate the SPC/E model of water using $\delta t$ from 0.5 fs to 3.0 fs. We find that for all but $\delta = 0.5$ fs, equipartition between translational and rotational modes is violated: the rotational modes are at a lower temperature than the translation modes. The autocorrelation of the velocities corresponding to the respective modes shows that the rotational relaxation occurs at a time-scale comparable to vibrational periods, invalidating the original assumption for freezing vibrations. $\delta t$ also influences thermodynamic properties: the mean system potential energies are not converged until $\delta t = 0.5$ fs, and the excess entropy of hydration of a soft, repulsive cavity is also sensitive to $\delta t$.