(746b) Continuous Fractional Component Monte Carlo in the Gibbs Ensemble

Ali Poursaeidesfahani, Ariana Torres-Knoop, David Dubbeldam, Thijs J.H. Vlugt

 

We introduced a new formulation of the fractional component Monte Carlo approach in the Gibbs ensemble [1]. In our formulation, only a single fractional particle per component is used, which has three main advantages: (1) chemical potentials of the two boxes are calculated automatically (without having to resort to a separate Widomâ??s test particle computation), and we have shown analytically that the derived expression for the chemical potential is mathematically identical to that in the Gibbs ensemble; (2) independent biasing for each simulation box improves sampling of the configurational space; (3) the maximum allowed changes in the coupling parameter can be chosen differently for each box. Therefore, larger changes in the value of the coupling parameter can be used when the fractional particle is located in the box corresponding to the gas phase compared to the coupling used in the liquid phase. In addition to the trial-moves required to thermalize the system, the proposed method involves three additional trial-moves to satisfy the requirements of equal chemical potential and pressure of the gas and liquid phase in the Gibbs ensemble: (1) attempts to change the coupling parameter of the fractional particle within the range [0,1]; (2) trial-moves to swap the fractional particle from one simulation box to the other one; (3) attempts to change the fractional particle into an integer particle, and at the same time, change a randomly selected integer particle in the other simulation box into a fractional particle. Our method has been tested for the system of Lennard-Jones particles and the TIP3P-Ew water model at different system sizes and temperatures. Chemical potentials and densities calculated for two boxes are compared with values computed using the conventional Gibbs ensemble with Widomâ??s test particle method. Excellent agreement was found for both densities and chemical potentials. The acceptance probability for the particle exchange has improved significantly in our formulation compared to the conventional Gibbs ensemble (typically from 2% to 40% for LJ particles, and from 0.6% to 8.5% for simulations with TIP3P-Ew water model). We found that the method is superior to conventional MC, but also significantly better than state-of-the-art Configurational-bias MC methodology. It also represent a significant improvement over a previous formulation of CFCMC in the Gibbs ensemble, both in acceptance probabilities and performance as well as from a theoretical point of view. We have also addressed the question of including or ignoring the contribution of the fractional particle in calculation of ensemble averages. We have shown analytically that one should disregard the fractional particle while computing the average density of the system.

[1] Poursaeidesfahani A., Torres-Knoop A., Dubbeldam D, Vlugt T. J.H., J. Chem. Theory Comput., 2016, 12, 1481-1490