Theory of Solutions in Energy Representation in NPT-ensemble: Derivation Details

Abstract

Theory of solutions in energy representation (ER method) developed by Matubayasi and Nakahara provides with an approximate way of calculating solvation free energies (or, identically, the excess chemical potentials) from atomistic simulations. In this document we provide some derivation details of this, to our opinion, theoretically involved method, which will help a non-specialist to follow. There are three points which differ this document from a regular textbook on statistical mechanics or research articles:1. Derivation is detailed and all approximations are explicitly stated; 2. Statistical mechanics derivations are performed in NPT-ensemble;

Accurate Calculation of Solvation Free Energies in Supercritical Fluids by Fully Atomistic Simulations: Probing the Theory of Solutions in Energy Representation

“…Since the ideal gas contributions of the solute molecule cancel out (see ref 29), this free energy is equal to the free energy of an imaginary process of transferring one solute molecule from a fixed position of center of mass in the gas phase to a fixed position of center of mass in the solution. Moreover, by accident the free energy difference in this process is equal to the excess chemical potential of solute molecules in the system ΔG solv ≡ μ ex (please, see the proof in ref 29).…”

“…This identity preserves also for finite solute concentrations and when the solute's internal molecule degrees of freedom are affected by solvation, in contrast to what is sometimes wrongly believed 1 (see ref. 29 for more details).…”