Gibbs ensemble Monte Carlo simulations were carried out to investigate the properties of a frozen-electron-density (or Kim–Gordon, KG) model of water along the vapor–liquid coexistence curve. Because of its theoretical basis, such a KG model provides for seamless coupling to Kohn–Sham density functional theory in mixed quantum mechanics/molecular mechanics implementations. The Gibbs ensemble simulations indicate limited transferability of a KG model to other state points. Specifically, a KG model that was parameterized by Barker and Sprik to the properties of liquid water at 300 K, yields saturated vapor pressures and a critical temperature that are significantly under- and overestimated, respectively.