Abstract
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 .
Highlights
First identified in 1873,1 van der Waals interactions are forces that today attract more interest than ever
Nowadays several kinds of approaches to approximately include van der Waals (vdW) interaction in density functional theory (DFT) calculations are available. Some of these are based on semiempirical, atom-based pair potentials, able to give approximate vdW corrections;[18−20] others are instead built by introducing a suitable nonlocal XC density functional, such as the vdW-DF family by Dion et al.[21] and the scheme proposed by Vydrov and Van Voorhis,[22] with the revised, more efficient version rVV10.15 rVV10 certainly represents one of the best vdW-corrected functionals nowadays available; it takes into account the entire range of vdW interactions at a reasonable computational cost using only the electron density (ED) n(r) as input
The experimental ED is characterized by three maxima in the direction of the three neighboring, symmetryrelated S atoms, while the theoretical one exhibits only one maximum directed toward the center of the S atom tetrahedron, suggesting that the theoretical DFT description of the interlayer interactions qualitatively differs from the experimental one
Summary
First identified in 1873,1 van der Waals (vdW) interactions are forces that today attract more interest than ever. The accuracy of experimental X-ray diffraction data has increased dramatically owing to the use of high-energy synchrotron sources, which significantly limit systematic errors in the data, and thanks to these modern techniques, nowadays it is possible to evaluate both structural and electronic properties of a wide class of layered materials in an extremely accurate way. In this respect, Medvedev et al.[13] have pointed out that modern DFT functionals are constructed on the basis of empirical fitting on energetic and geometrical benchmarks, neglecting the ED as a parametrization parameter. We show that this improvement in the theoretical DFT description is not limited to TiS2 and applies to other, similar layered systems involving S atoms, such as TaS2 HfS2, and MoS2
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