Direct Free Energy Calculation in the Continuous Fractional Component Gibbs Ensemble

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Thermodynamics

Background:

• The conventional Gibbs ensemble (GE) method is widely used for simulating phase equilibria.
• Calculating chemical potentials in GE often requires computationally expensive test particle insertions.
• Previous formulations of fractional component Monte Carlo in GE utilized two fractional molecules per component.

Purpose of the Study:

• To present a new formulation of the Gibbs ensemble combined with continuous fractional component Monte Carlo.
• To simplify the calculation of chemical potentials by eliminating the need for test particles.
• To improve the efficiency and applicability of Gibbs ensemble simulations.

Main Methods:

• A modified Gibbs ensemble formulation using a single fractional molecule per component.
• Independent biasing of simulation boxes and adaptable scaling parameters for intermolecular interactions.
• Direct calculation of chemical potentials and comparison with conventional GE methods.

Main Results:

• The new formulation directly yields chemical potentials, analytically shown to be identical to conventional GE.
• Demonstrated excellent agreement for average densities and chemical potentials with Lennard-Jones particles and TIP3P-Ew water.
• Achieved significantly higher acceptance probabilities for molecule exchange (e.g., >40% for LJ) compared to conventional GE (<2%).

Conclusions:

• The proposed method offers a more efficient and direct route to obtaining chemical potentials in Gibbs ensemble simulations.
• The approach facilitates thermodynamic modeling and serves as a reliable check for chemical equilibrium.
• The algorithm is readily extendable to complex systems, including mixtures and molecules with intramolecular interactions.