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We have prosed a new methodology to account for the long-range corrections of dispersive forces in inhomogeneous systems. This method deals separately with the two interfaces that are usually present in a simulation setup. In the figure (Fig. 1 of the manuscript published in Journal of Chemical Physics) we show an illustration of the semi-infinite boundary conditions. Full lines indi- cate the actual density profile in the simulation box, with molecules in the fi- nite interval [-D/2,D/2] and a liquid slab about z = 0. Horizontal dashed lines indicate a continuous extrapolation of the bulk densities. Top figure shows semi-infinite boundary conditions for a molecule in the interval [-D/2,0] (left interface). A molecule less than Rc away from z = 0 feels explicit Lennard– Jones interactions within the cutoff sphere (including those of molecules with z > 0 contained in the shadowed red region), plus the effective slab poten- tial with all molecules in the interval [zv(i), zl(i)] and semi-infinite slabs of vapor and liquid density at zv(i) and zl(i), respectively. Bottom figure shows semi-infinite boundary conditions appropriate for molecules in the interval [0, D/2] (right interface). A molecule less than Rc away from z = D/2 feels explicit Lennard–Jones interactions within the cutoff sphere, thus interacting with molecules at z = −D/2 across the boundary conditions (as depicted in the shaded red region). The effective slab potential is felt with all molecules in the interval [zl(i), zv(i)], while semi-infinite slabs of liquid and vapor den- sity are felt at zl(i) and zv(i), respectively.