Free energy reconstruction/decomposition from WHAM, force integration and free energy perturbation for an umbrella sampling simulation

Comparisons between methodologies are usually made by performing separated sampling simulations in conjunction with the corresponding estimator. Here, the accuracy and convergence of three typical approaches (WHAM, force integration, and FEP) for estimating the ion-pairing free energy in water are carefully examined in order to identify which estimator is the most efficient for a particular set of trajectories. The force integration is superior among these methods, whereas the FEP introduces relatively prominent uncertainty arising from the perturbed potential energy. The direct solute-solvent interaction term and the indirect solvent contribution accounting for the reorientation of non-spherically symmetric ions could be straightforwardly extracted using force integration and FEP.