How Long-Range Are Three-Body “Exchange” Interactions in Liquid Water?

Three-body interactions in water play a crucial role in accurately modeling its structural and thermodynamic properties. These interactions consist of a polarization term that decays as an inverse power of the intermolecular separations <i>R</i>_<i>ab</i> and a term that is usually assumed to describe exchange interactions and decay exponentially. Due to the complexity of fitting the latter term at large <i>R</i>_<i>ab</i>, it is often damped or truncated beyond a certain distance, also because the computational cost of including three-body effects in molecular simulations scales as <i>N</i>³ with the number of molecules, compared to the <i>N</i>² scaling of two-body interactions. Here, investigations of the impact of long-range three-body exchange interactions on the results of such simulations have been performed by systematically extending the average <i>R</i>_<i>ab</i> of trimers included. It is demonstrated that these long-range effects are important for accurately describing the density of liquid water, ρ(<i>T</i>), as a function of temperature, but are essentially negligible for several other properties of water. The effects of three-body damping onset on ρ(<i>T</i>) are larger than they would have been with an exponential decay; however, it is shown here that the decay is dominated by exponential components only at fairly small <i>R</i>_<i>ab</i>, while for large <i>R</i>_<i>ab</i>, the nonpolarization three-body effects decay as 1/<i>R</i>_<i>ab</i>^<i>n</i>. These findings are rationalized by calculations with the symmetry-adapted perturbation theory. Another reason for the importance of three-body effects is their <i>N</i>³ scaling. Clearly, long-range three-body exchange interactions should be included in high-accuracy water models. It is shown that the reason these interactions have such large effects on ρ(<i>T</i>) is their extreme anisotropy affecting the structure of liquid water. Our work also sheds light on discrepancies between the theory and experiment for ρ(<i>T</i>).