  Low accuracy of the Solvation Free Energy (SFE) calculation is a known
problem of the numerical methods of the Integral Equation Theory of Liquids and
the Classical Density Functional Theory (Classical DFT). Although functionals
with empirical corrections can essentially improve the predictability of the
methods, their universality is still a question. In our recent paper we
connected the SFE calculation errors with the incorrect pressure in the
Classical DFT and proposed the a posteriory correction to improve the results
(J. Phys. Chem. Lett., 5, 1925-1942 ). This paper raised a discussion in the
community. In particular, recently appeared a critical reply where pointed some
thermodynamical inconsistencies of the derivations in our paper (J. Chem.
Theory Comput., 11, 378-380). In the present work we re-derive the pressure
correction in a more simple way and show that despite the inaccuracies during
the derivation, the final form of the previously derived correction is correct.
We also test the applicability of the proposed correction to the functionals
which include a three- and many- body terms from the fundamental measure theory
(FMT) for hard sphere fluid. We test all the functionals on a set of model
systems and discuss the obtained results.
