Vapor Phase Properties
Uncertainties were obtained from 5 independent simulations and represent 67% confidence limits (one standard deviation). Liquid-vapor coexistence was determined by adjusting the activity such that the pressures of the liquid and vapor phases were equal. Following, identification of state points below the coexistence pressure was accomplished by adjusting the activity until the pressure of the vapor phase was equal to the desired fraction of psat. Here, the pressure is not the conventional virial pressure [2, 3] but is the actual thermodynamic pressure, based on the fact that the absolute free energies can be obtained from the distributions determined from simulation . Alternative methods, for example Gibbs-ensemble Monte Carlo and combination grand-canonical Monte Carlo and histogram re-weighting, can be used to determine liquid-vapor coexistence. A review of standard methods of phase equilibria simulations can be found in Ref. 5.
As introduced in Refs. 2 and 3, the activity, z, is defined as
z = Λ-3 exp(βμ)
where Λ is the de Broglie wavelength, β = 1/(kBT)
(where kB is Boltzmann's constant),
and μ is the chemical potential. It is sometimes more convenient to
work with ln z in the simulations and in post-processing.
Phase-coexistence energies were obtained by determining the
mean potential energy at a given value of N for an additional 8 billion
MC trials. Combining this information with the particle number
probability distribution, the mean potential energy of the coexisting
phases can be calculated .
For the Lennard-Jones fluid, linear force shifted at 2.5σ, the critical properties are Tc*=0.937, ρc*=0.320, and pc*=0.0820 .
 J. R. Errington, J. Chem. Phys. 118,