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

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