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We investigate energetic and electronic properties of TiS2 , an archetypal van der Waals (vdW) material, from first principles, in the framework of the Density Functional Theory (DFT). In this system a recent experimental study showed a puzzling discrepancy between the distribution of the electron density in the interlayer region obtained by X-ray diffraction data and that computed by DFT, even adopting DFT functionals that should properly include vdW effects. Such a discrepancy could indicate a partial failure of state-of-the-art DFT approaches in describing the weak interlayer interactions of TiS2 and, possibly, of similar systems too. In order to shed light on this issue, we have carried out simulations based on different DFT functionals, basically confirming the mentioned discrepancy with the experimental findings. Subsequently, we have tried to reproduce the experimental interlayer electronic density deformation both by changing the parameters characterizing the rVV10 DFT functional (in such a way to artificially modify the strength of the vdW interactions at short or long range), and also by adopting a modified pseudopotential for Sulfur atoms, involving d orbitals. The latter approach turns out to be particularly promising. In fact, using this novel, more flexible pseudopotential, we obtain not only an electronic density deformation closer to the experimental profile, but also a better estimate of the interlayer binding energy. Interestingly, this improvement in the theoretical DFT description is not limited to TiS2 but also applies to other similar layered systems involving S atoms, such as TaS2 , HfS2 , and MoS2 .