Grand-canonical-like molecular-dynamics simulations by using an adaptive-resolution technique

TL;DR

This paper demonstrates that the adaptive resolution simulation (AdResS) technique can reliably sample the Grand Canonical ensemble, allowing molecules to exchange between regions with accuracy up to second order, supported by theoretical analysis and numerical tests.

Contribution

The paper provides a theoretical foundation and numerical validation showing AdResS can perform Grand Canonical molecular dynamics with second-order accuracy.

Findings

AdResS accurately reproduces density and radial distribution functions in the hybrid region.

The work done by the thermostat and thermodynamic force balances chemical potential differences.

AdResS is computationally more convenient than the Insertion Particle Method for large systems.

Abstract

In this work, we provide a detailed theoretical analysis, supported by numerical tests, of the reliability of the adaptive resolution simulation (AdResS) technique in sampling the Grand Canonical ensemble. We demonstrate that the correct density and radial distribution functions in the hybrid region, where molecules change resolution, are two necessary conditions for considering the atomistic and coarse-grained regions in AdResS equivalent to subsystems of a full atomistic system with an accuracy up to the second order with respect to the probability distribution of the system. Moreover, we show that the work done by the thermostat and a thermodynamic force in the transition region is formally equivalent to balance the chemical potential difference between the different resolutions. From these results follows the main conclusion that the atomistic region exchanges molecules with the coarse-grained region in a Grand Canonical fashion with an accuracy up to (at least) second order. Numerical tests, for the relevant case of liquid water at ambient conditions, are carried out to strengthen the conclusions of the theoretical analysis. Finally, in order to show the computational convenience of AdResS as a Grand Canonical set up, we compare our method to the Insertion Particle Method (IMP) in its most efficient computational implementation. This fruitful combination of theoretical principles and numerical evidence candidates the adaptive resolution technique as a natural, general and efficient protocol for Grand Canonical Molecular Dynamics for the case of large systems.