Monte Carlo, thermodynamic scaling

The scaled particle theory of fluids is a theory that offers an excellent conceptual framework with which to understand solvent effects. The theory was originally designed to give the thermodynamic properties of a fluid of hard spheres, but experimentally determined parameters can be introduced to treat real liquids. The treatment of simple liquids is better than the treatment of structured liquids such as water. The theory has been applied extensively to certain aspects of hydrophobic solvation and interactions. In some studies of hydrophobic solvation based on molecular dynamics or Monte Carlo simulations, scaled particle theory has provided useful guidelines for analysis of the results. ... 

Valleau, J. P. Temperature-and-density-scaling Monte-Carlo methodology and the canonical thermodynamics of Lennard-Jonesium. Mol. Sim. 2005, 31, 223-253... 

Valleau, J. P., Thermodynamic scaling methods in Monte Carlo and their application to phase equilibria, Monte Carlo Methods Chem. Phys. 1999,105, 369-404... 

Kiyohara, K. Spyriouni, T. Gubbins, K. E. Panagiotopoulos, A. Z., Thermodynamic scaling Gibbs ensemble Monte Carlo a new method for determination of phase coexistence properties of fluid, Mol. Phys. 19%, 89, 965-974. 

Figure 8.13 The function G (A) for water at 300 K at the liquid saturation conditions (Ashbaugh and Pratt, 2004). The points are obtained by direct Monte Carlo calculation, and the solid line by matching an empirical thermodynamic model for the large solute case. The dashed lines are the classic scaled-particle model (Pierotti, 1976) predictions for several solvent hard-sphere diameter parameters between cr = 2.6 A and 3.0 A in 0.1 A increments. Notice that the parameter value that provides the best fit of the classic scaled-particle model for small radii is not the same as that for the large radii results.

THERMODYNAMIC-SCALING METHODS IN MONTE CARLO AND THEIR APPLICATION TO PHASE EQUILIBRIA... 

In thermodynamic-scaling Monte Carlo (ThScMC) one estimates relative free energies like Eq. (2.7), not, however, simply between two states but among arbitrarily many states over a substantial region of the thermodynamic state space, within a single MC sampling run. 

---