The present paper is the second part of a series of papers aimed at assessing the accuracy of alchemical computational approaches based on nonequilibrium techniques for solvation free energy of organic molecules in the context of molecular dynamics simulations. In Paper I [Procacci, J. Chem. Phys. 151, 144113 (2019)], we dealt with bidirectional estimates of solvation free energies using nonequilibrium approaches. Here, we assess accuracy and precision of unidirectional estimates with the focus on the Gaussian and Jarzynski estimators. We present a very simple methodology to increase the statistics in the work distribution, hence boosting the accuracy and precision of the Jarzynski unidirectional estimates at no extra cost, exploiting the observed decorrelation between the random variables represented by the Lennard-Jones solute-solvent recoupling or decoupling work and by the electrostatic work due to the charging/discharging of the solute in the solvent.
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