Toward Efficient Chemical Potential Calculations by Expanded Ensemble Simulations; to Make the Free Energy Pathway Fairly Level

Abstract

A scheme is suggested of how to construct good bias potentials ("balancing factors") to be used in expanded ensemble (EE) calculations of chemical potentials of solutions. A combination of two strategies are used: (i) to use a pathway for particle insertions that avoids large variations in free energy and (ii) to use calculated free energy derivatives to construct a bias potential that makes the pathway fairly level. Only a few very short simulations are needed to accomplish the latter, and then, a full EE simulation is done to obtain the chemical potential. By practical calculations of the chemical potential of benzene, cyclohexane, and benzylamine in water, it is shown that this method is at least equally efficient to the recent adaptive EE (AEE) method by Aberg et al. (J. Chem. Phys. 2004, 120, 3370). Furthermore, the new method provides an alternative strategy that complements existing EE methods.

Structural Evidence for the Ordered Crystallites of Ionic Liquid in Confined Carbon Nanotubes

“…44,[46][47][48] It was argued that this may be not efficient for large molecules because effective LJ size of the particle changes very slowly with R, and some other couplings of the solute-solvent interaction were considered. 49 In the present work, we used the following procedure of scaling the solute-solvent interaction with R: the electrostatic energy is scaled as R 2 , the ε parameter scales linearly with R, while σ parameter scales as R 1/3 (the last condition corresponds to a linear scaling of the effective particle volume with R). Such scheme has allowed us to make repeated insertion/deletions for rather large molecules during several nanoseconds time with reliable determination of the probabilities in eq 3.…”

“…In previous works on the expanded ensembles, a linear dependence of h on α was typically used. ,− It was argued that this may be not efficient for large molecules because effective LJ size of the particle changes very slowly with α, and some other couplings of the solute−solvent interaction were considered . In the present work, we used the following procedure of scaling the solute−solvent interaction with α: the electrostatic energy is scaled as α 2 , the ε parameter scales linearly with α, while σ parameter scales as α 1/3 (the last condition corresponds to a linear scaling of the effective particle volume with α).…”

Temperature-Dependent Physicochemical Properties and Solvation Thermodynamics of Nitrotoluenes from Solvation Free Energies

“…The partial atomic charges were scaled as the square of the λ m , and the Lennard-Jones well-depth parameters were scaled with the fourth power of λ m ; the rationale for choosing this power law scaling scheme is described elsewhere . Compatibility of this scaling method with the so-called “soft-core”potential − has been verified by implementing the soft-core potential in the framework of the EE algorithm and found to reproduce results within the standard deviations of each (see Supporting Information of ref 32). Also, the applicability of the power law scaling scheme used here has been verified previously by comparing the results with other methods (e.g., thermodynamic integration and Bennett acceptance ratio methods) that use the soft-core potential scheme. − The balancing factors were determined and optimized in an automated way using the Wang–Landu (WL) algorithm .…”