The effective potential through the internal energy (stars) and pair correlation function (circles) coarse-graining procedures for (a) and and (b) and , illustrating the difference between the unique potential generated through the pair correlation function route and generated through the internal energy route. Clearly the former potential will not reproduce the internal energy through standard formula (3).
(Color) Isotropic potentials derived through the pair correlation route. (a) The family of isotropic potentials derived from the TIP4P-Ew at and for temperatures of 235.5, 248, 260.5, 273, 285.5, 298, and . (b) The family of isotropic potentials derived from TIP4P-Ew at and for densities of .
(a) The dimensionless compressibility factor vs along the isobar for TIP4P-Ew and the family of isotropic potentials. The pressure for the isotropic potentials is measured through both the compressibility route, which correctly reproduces the TIP4P-Ew result by construction, and through the virial route, which does not. represents the ideal gas. Inset demonstrates that agreement is not perfect due to errors introduced by numerical integration of compressibility equation and extrapolation of to large . (b) The internal energy for the TIP4P-Ew and the family of isotropic potentials. The simulated values are shown with the LJ tail correction removed from the TIP4P-Ew values.
Pressure-volume phase diagram for TIP4P-Ew and the family of isotropic potentials along four isotherms 310.5 (stars), 285.5 (triangles), 260.5 (squares), and 235.5 (circles). (a) TIP4P-Ew: The density anomaly occurs in regions where lower isotherms cross above a higher isotherm. (b) Isotropic potentials: The pressure is the average virial pressure from each simulated point, and the lines act only as a guide.
Bond angle distributions at as a function of density for (a) TIP4P-Ew and (b) isotropic potentials. was chosen as .
Translational diffusion constants vs density along four isotherms 310.5 (stars), 285.5 (triangles), 260.5 (squares), and 235.5 (circles). Lines are fifth order polynomial fits to data points (a) TIP4P-Ew and (b) isotropic potentials.
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