Efficient computation of free energy of crystal phases due to external potentials by error-biased Bennett acceptance ratio method

TL;DR

This paper introduces the error-biased Bennett Acceptance Ratio (EBAR) method, a new approach for accurately computing free energies of crystal phases without hysteresis issues, applicable to various thermodynamic calculations.

Contribution

The paper presents the EBAR method, a novel, easy-to-implement technique that eliminates the need for constraints in free energy calculations of crystal phases.

Findings

EBAR effectively reduces hysteresis in free energy calculations.

The method successfully computes crystal-melt interfacial energy and free energy differences.

Applicable to silicon model potentials and potentially other materials.

Abstract

Free energy of crystal phases is commonly evaluated by thermodynamic integration (TDI) along a reversible path that involves an external potential. A persistent problem in this method is that a significant hysteresis is observed due to differences in the center of mass position of the crystal phase in the presence and absence of the external potential. To alleviate this hysteresis, a constraint on the translational degrees of freedom of the crystal phase is imposed along the path and subsequently a correction term is added to the free energy to account for such a constraint. In this work, we propose a new methodology termed as error-biased Bennett Acceptance ratio (EBAR) method that effectively solves this problem without the need to impose any constraint. This method is simple to implement as it does not require any modification to the path or to the simulation code. We show the applicability of this method in the computation of crystal-melt interfacial energy by cleaving wall method [J. Chem. Phys., 118, 7651 (2003)] and bulk crystal-melt free energy difference by constrained fluid $\lambda$-integration method [J. Chem. Phys., 120, 2122 (2004)] for a model potential of silicon.