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

Free energy of crystal phases is commonly evaluated by thermodynamic integration along a reversible path that involves an external potential. However, this method suffers from the hysteresis caused by the 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. The estimation of the correction term is often computationally expensive. In this work, we propose a new methodology, termed as error-biased Bennett acceptance ratio method, which effectively solves this problem without the need to impose any constraint. This method is simple to implement and it does not require any modification to the path. We show the applicability of this method in the computation of crystal-melt interfacial energy by cleaving wall method [ R. L. Davidchack and B. B. Laird , J. Chem. Phys. 118 , 7651 ( 2003 ) ] and bulk crystal-melt free energy difference by constrained fluid λ -integration method [ G. Grochola , J. Chem. Phys. 120 , 2122 ( 2004 ) ] for a model potential of silicon.