(482b) Improvements of the Continuous Fractional Component Monte Carlo Method

Authors: 
Hens, R., TU Delft
Rahbari, A., Delft University of Technology
Vlugt, T. J. H., Delft University of Technology
The Continuous Fractional Component Monte Carlo (CFCMC) simulation method is an expanded ensemble methodology used to solve the problem of low insertion/deletion efficiencies in open ensembles. It allows for direct calculation of the chemical potential without any post-processing. Chemical potentials can be obtained by binning of the coupling parameter λ and using the probability values p(λ=0) and p(λ=1) which require extrapolation. We show that this extrapolation leads to systematic errors when the distribution p (λ) is steep, and we propose an alternative binning scheme which significantly improves the accuracy of computed chemical potentials. Chemical potentials of coexisting gas and liquid phases for water for the temperature range 330 K to 350 K are computed using the CFCMC technique. In sharp contrast to Widom-like test particle methods, accurate chemical potentials in the liquid phase are computed using the CFCMC technique. The CFCMC simulation methodology is also applied to the reaction ensemble (serial RxMC). The key ingredient is that fractional molecules of either reactants or reaction products are present and that chemical reactions always involve fractional molecules. The advantage is that the chemical potentials of all reactants and reaction products are obtained without any post-processing. The efficiency of the algorithm can be increased significantly by applying independent biasing to the fractional molecules of reactants and reaction products. The serial Rx/CFC approach is tested for the reaction of ammonia synthesis at various temperatures and pressures. Excellent agreement was found between results obtained from serial Rx/CFC, experimental results from literature, and thermodynamic modeling using the Peng–Robinson equation of state. The efficiency of reaction trial moves is improved by a factor of 2 to 3 (depending on the system) compared to the RxMC/CFCMC formulation by Rosch and Maginn (Journal of Chemical Theory and Computation, 2011, 7, 269–279). We also combined the CFCMC simulation methodology with the original idea of Frenkel, Ciccotti, and co-workers (Chemical Physics. Letters, 1987, 136, 3) to calculate partial molar excess enthalpies and partial molar volumes of components in a single CFCMC simulation. Simulations are performed at constant mixture composition, constant temperature and pressure in the expanded version of the NPT ensemble (CFCNPT). Computation of partial molar properties in the CFCNPT ensemble does not have the drawbacks of Widom-like test particle methods, since particle insertions/removals take place in a gradual manner. Our method is applied to mixtures of NH3, N2 and H2 at chemical equilibrium. It is shown that the contribution of the partial molar enthalpies in calculating the reaction enthalpy of the Haber-Bosch process is significant at high pressures (up to 64% at a pressure of 80 MPa, relative to the reaction enthalpy at a pressure of 1 bar).