Monte Carlo simulation thermodynamic perturbation

What has been developed within the last 20 years is the computation of thermodynamic properties including free energy and entropy [12, 13, 14]. But the ground work for free energy perturbation was done by Valleau and Torrie in 1977 [15], for particle insertion by Widom in 1963 and 1982 [16, 17] and for umbrella sampling by Torrie and Valleau in 1974 and 1977 [18, 19]. These methods were primarily developed for use with Monte Carlo simulations continuous thermodynamic integration in MD was first described in 1986 [20]. 

The implementation of the thermodynamic perturbation methods is relatively straightforward. An ensemble generated by a Monte Carlo simulation or the time trajectory generated by a molecular dynamics simulation for a system described by Hamiltonian "Kq is used to evaluate the ensemble average of expi-AM/k T). The free energy difference between the reference system described by Hamiltonian o> for which the ensemble is generated, and the perturbed system with Hamiltonian + A% is found using Eq, [17],... 

The thermodynamic free energy perturbation route was used by Gao [228] in the analysis of the benzene dimer formation in supercritical water at 673K and 35MPa, via NPT Monte Carlo simulation of TIP4P water model and OPLS benzene. The resulting PMF indicated no local water density increase around benzene, as if benzene behaved as a weakly repulsive solute [187]. In fact, the calculated association constant was approximately three times smaller than that corresponding to water at ambient conditions. 

The correspondence between a concentrated dispersion and an assembly of hard spheres has been pursued by several authors. " The Kirkwood-Alder hard-sphere transition is in qualitative agreement with experiment, but the coexistence region is in general too narrow. Introduction of attractive forces, in the Monte Carlo simulations and approximate perturbation-cell theories, leads to iijiprovement at high salt concentrations and large volume fractions. But at low salt concentrations there remains the fundamental problem that the particles are not in proper thermodynamic equilibrium with bulk electrolyte as Ninham and coauthors put it the diffuse double-layers of the particles fill up the entire volume of the system, and there is no place to be regarded as bulk . 

The elaborated in [R. V. Chepulskii, Analytical method for calculation of the phase diagram of a two-component lattice gas, Solid State Commun. 115 497 (2000)] analytical method for calculation of the phase diagrams of alloys with pair atomic interactions is generalized to the case of many-body atomic interactions of arbitrary orders and effective radii of action. The method is developed within the ring approximation in the context of a modified thermodynamic perturbation theory with the use of the inverse effective number of atoms interacting with one fixed atom as a small parameter of expansion. By a comparison with the results of the Monte Carlo simulation, the high numerical accuracy of the generalized method is demonstrated in a wide concentration interval. 

EDMD and thermodynamic perturbation theory. Donev et developed a novd stochastic event-driven molecular dynamics (SEDMD) algorithm for simulating polymer chains in a solvent. This hybrid algorithm combines EDMD with the direa simulation Monte Carlo (DSMC) method. The chain beads are hard spheres tethered by square-wells and interact with the surrounding solvent with hard-core potentials. EDMD is used for the simulation of the polymer and solvent, but the solvent-solvent interaction is determined stochastically using DSMC. 

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