Representability problems for coarse-grained water potentials

TL;DR

This paper systematically derives coarse-grained water potentials that accurately reproduce structural properties but reveal fundamental limitations in simultaneously capturing thermodynamic properties, highlighting representability challenges.

Contribution

It demonstrates the fundamental impossibility of simultaneously representing water's structure and thermodynamics with state-dependent isotropic pair potentials.

Findings

Effective potentials reproduce pair structure accurately.

Thermodynamic properties like pressure and energy are not simultaneously captured.

Structural and dynamical anomalies are still generated despite thermodynamic inconsistencies.

Abstract

The use of an effective intermolecular potential often involves a compromise between more accurate, complex functional forms and more tractable simple representations. To study this choice in detail, we systematically derive coarse-grained isotropic pair potentials that accurately reproduce the oxygen-oxygen radial distribution function of the TIP4P-Ew water model at state points over density ranges from 0.88-1.30g/cc and temperature ranges from 235K-310K. Although by construction these effective potentials correctly represent the isothermal compressibility of TIP4P-Ew water, they do not accurately resolve other thermodynamic properties such as the virial pressure, the internal energy or thermodynamic anomalies. Because at a given state point the pair potential that reproduces the pair structure is unique, we have therefore explicitly demonstrated that it is impossible to simultaneously represent the pair-structure and several key equilibrium thermodynamic properties of water with state-point dependent radially symmetric pair potentials. We argue that such representability problems are related to, but different from, more widely acknowledged transferability problems, and discuss in detail the implications this has for the modeling of water and other liquids by coarse-grained potentials. Nevertheless, regardless of thermodynamic inconsistencies, the state-point dependent effective potentials for water do generate structural and dynamical anomalies.