“Umbrella sampling” has been incorporated in the thermodynamic integration method to obtain a potential of mean force by slow growth molecular-dynamics simulations. The method was tested for liquid argon, for which good agreement was obtained with a standard potential of mean force, as derived from the radial pair-correlation function. For a sodium chloride ion-pair in aqueous solution the calculations showed resonable agreement with a literature result. The method was also applied to the decomplexation of 18-crown-6 and a potassium cation in aqueous solution.
van Eerden, J., Briels, W. J., Harkema, S., & Feil, D. (1989). Potential of mean force by thermodynamic integration: molecular-dynamics simulation of decomplexation. Chemical physics letters, 164(4), 370-376. https://doi.org/10.1016/0009-2614(89)85222-4