Probability distribution P(N) (solid black line) and corresponding weight function w(N) (dashed blue line) obtained for the Lennard-Jones fluid at T* = 1 and μ* = βμ = −11.1843. The biased probability distribution P bias(N) is shown as dotted gray line.
Comparison of bias potentials for an Umbrella Sampling GCMC simulation determined after sufficient sampling (solid blue lines) and the estimated potential from the DFT using PC-SAFT (dashed black lines). Results are shown for (a) methane at different temperatures and (b) ethane (T = 214 K) and methanol (T = 400 K).
(a)–(c) Coexisting vapor and liquid densities ρ as a function of temperature for the considered fluids. Symbols indicate experimental data 63,66 (□) and simulation data (♦). Reference data from molecular simulations are included 50,62,67 (△). Equation (19) , adjusted to the simulation results, is given by the connecting lines. The statistical error of the simulations is within the symbol size.
Speed up over number of work packages for ethane at a temperature of 214 K. Simulations were performed for a division of molecule number N in 1, 2, 4, 8, 16, 32, 64 windows.
Liquid phase region of the probability distribution P(N) for ethane (T = 183K) prior to reweighting. The symbols represent results of molecular simulations of a small system (open symbols). The liquid phase is stable at N = 310. The solid line is obtained from the PC-SAFT equation of state that was reweighted and scaled to simulation data N = 260 up to 280 as well as to vapor phase data, only (filled symbols).
Non-bonded force field parameters: Lennard-Jones pseudoatoms and point charges.
Errors in thermodynamic properties when molecular simulations at high densities are substituted by results of an analytic equation of state (PC-SAFT). The highest density considered from molecular simulations is about 10% lower than the value in the coexisting liquid phase.
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