On the estimation of the free energy, from a single equilibrium statistical ensemble, via particle reinsertion

In this work, we propose the evaluation of the free energy in molecular systems, in a "single" step, by "deleting" all the molecules in the system. The approach can be considered as the statistical mechanics analogue of the evaluation of the potential energy in classical mechanics by accounting for the necessary work to transfer all particles one by one to infinite distance. As a result, the free energy of an atomistic system can now be expressed as an ensemble average over a configurational function that corresponds to the contribution of each microstate to the free energy of the ensemble. Moreover, the proposed method is capable of evaluating the free energy as a function of the density, from the simulated density down to zero. Finally, the proposed method is related to the Rosenbluth sampling of the inverse process, that of inserting (instead of deleting) and provide the analogous theorems to Bennett's and Crooks' work (Bennett, C. H. J. Comput. Phys. 1976, 22, 245; Crooks, G. E. Phys. Rev. E 1999, 60, 2721). When the proposed process is envisioned as the transformation of an interacting to a noninteracting system, the proposed scheme reduces to the Jarzynski identity linking the free energy of the system to the chemical work related to this transformation.