Computational methods Excess free energy

Mezei, M., Excess free energy of different water models computed by Monte Carlo methods, Mol. Phys. 1982, 47, 1307-1315... 

M, Mezei, Mol. Phys., 47, 1307 (1982). Excess Free Energy of Different Water Models Computed by Monte Carlo Methods. 

For calculation of the equilibrium compositions of the liquid phase either the equilibrium constants of the dissociation and polycondensation reactions have to be known or they can be computed by methods which use the approach of minimizing Gibbs free energy [200-202]. In addition, ab initio modeling techniques such as density functional theory (DFT) in combination with reactive molecular dynamic (MD) simulations could be used. Once the liquid phase system is modeled, there are in principle two options to describe the vapor-liquid equilibrium. Either equations of state (EOS) or excess Gibbs free energy models (g -models) may be used to describe the thermodynamics of the liquid... 

Some of the MD codes mentioned above (such as DL POLY, AMBER, and NAMD) can perform thermodynamic integration and various free energy perturbation calculations. These techniques can be used to compute excess chemical potentials of solutes in ionic liquids and thereby obtain information on solvation. We believe MC methods are better suited for these types of calculations, however. 

Figure 15. The potential energy surfaces for the excess electron bubble states in C He) clusters portraying the total energy EtiRi, R, N) versus the bubble radius Rf, for fixed values of N marked on the curves. The open and full points represent the results of the computations for the clusters using the density functional method for Ej Ri, R, N) and the quantum mechanical treatment for Ee(Ri, R, N), while for the bulk we took Ed Rb, R — oo, iV oo) = AttyR. The black point ( ) on each configurational diagram represents the equilibrium bubble radius. The Rj-dependence of the energy of the quasi-free electron state Vo(Rt, R, N) in the cluster of the smallest size of N = 6.5 X 10 (dashed line) and the bulk value of To (solid line) are also presented. The To values for each Rj, for iV = 8.1 x 10 to 1.88 x 10 fall between these two nearly straight fines.

---