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 R_ab 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 R_ab, 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 N³ with the number of molecules, compared to the N² 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 R_ab of trimers included. It is demonstrated that these long-range effects are important for accurately describing the density of liquid water, ρ(T), as a function of temperature, but are essentially negligible for several other properties of water. The effects of three-body damping onset on ρ(T) 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 R_ab, while for large R_ab, the nonpolarization three-body effects decay as 1/R_abⁿ. These findings are rationalized by calculations with the symmetry-adapted perturbation theory. Another reason for the importance of three-body effects is their N³ 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(T) is their extreme anisotropy affecting the structure of liquid water. Our work also sheds light on discrepancies between the theory and experiment for ρ(T).