Coarse-grained potentials from Widom's particle insertion method

Abstract

Widom's particle insertion method is used to calculate effective pair potentials for binary A/B mixtures, where B molecules represent a solvent whose degrees of freedom are integrated out. Comparison of Widom's method with an alternative route via the potential of mean force shows good agreement; however, Widom's particle insertion method experiences sampling difficulties at high densities. An isotherm for a binary mixture of argon (‘solvent’, B) and krypton (‘solute’, A) is calculated. While the structure at the pair level is well represented by the effective system using only effective pair potentials and ignoring all higher multi-body contributions, increasing deviations in the pressure are observed as the density of the effective system is increased. These latter deviations are attributed to the neglect of three- and higher multi-body interactions.

Acknowledgements

We wish to thank Francisco Hung for helpful discussions. We are also grateful to the National Science Foundation for funding this research (grants CTS-0403633 and INT-0329695) and for providing computer time at the San Diego Supercomputer Center (grant CHE-050047S).

Notes

This ensemble proves more computationally convenient than the one without interactions between 1 and 2 since it allows better sampling of R ₁₂. If 1 and 2 do not interact proper sampling will be difficult because 1 and 2 will overlap most of the time.