  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 .
