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Materials Data on Ca(TiS2)2 by Materials Project

Ca(TiS2)2 crystallizes in the monoclinic P2/m space group. The structure is three-dimensional. Ca2+ is bonded to six S2- atoms to form CaS6 octahedra that share corners with six equivalent TiS6 octahedra, edges with two equivalent CaS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 7–8°. There are four shorter (2.76 Å) and two longer (2.78 Å) Ca–S bond lengths. There are two inequivalent Ti3+ sites. In the first Ti3+ site, Ti3+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with six equivalent CaS6 octahedra, edges with two equivalent CaS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 7–8°. There are two shorter (2.44 Å) and four longer (2.49 Å) Ti–S bond lengths. In the second Ti3+ site, Ti3+ is bonded to six S2- atoms to form TiS6 octahedra that share edges with four equivalent CaS6 octahedra and edges with six TiS6 octahedra. There are four shorter (2.48 Å) and two longer (2.49 Å) Ti–S bond lengths. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded to two equivalent Ca2+ and three Ti3+ atoms to form a mixture of edge and corner-sharing SCa2Ti3 square pyramids. In the second S2- site, S2- is bonded in a rectangular see-saw-like geometry to one Ca2+ and three Ti3+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on TiS2 by Materials Project

TiS2 crystallizes in the cubic Pa-3 space group. The structure is three-dimensional. Ti4+ is bonded to six equivalent S2- atoms to form corner-sharing TiS6 octahedra. The corner-sharing octahedral tilt angles are 61°. All Ti–S bond lengths are 2.47 Å. S2- is bonded in a trigonal planar geometry to three equivalent Ti4+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on TiS2 by Materials Project

TiS2 is zeta iron carbide structured and crystallizes in the orthorhombic Pnnm space group. The structure is three-dimensional. Ti4+ is bonded to six equivalent S2- atoms to form a mixture of edge and corner-sharing TiS6 octahedra. The corner-sharing octahedral tilt angles are 50°. There are four shorter (2.39 Å) and two longer (2.50 Å) Ti–S bond lengths. S2- is bonded in a 3-coordinate geometry to three equivalent Ti4+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on TiS2 by Materials Project

TiS2 crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Ti4+ is bonded in a 5-coordinate geometry to eleven S2- atoms. There are a spread of Ti–S bond distances ranging from 2.49–2.94 Å. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded in a 8-coordinate geometry to six equivalent Ti4+ and eight S2- atoms. There are two shorter (2.49 Å) and six longer (2.94 Å) S–S bond lengths. In the second S2- site, S2- is bonded to five equivalent Ti4+ and six equivalent S2- atoms to form a mixture of face and corner-sharing STi5S6 trigonal bipyramids.

36 MATERIALS SCIENCE↗

Materials Data on TiS2 by Materials Project

TiS2 crystallizes in the trigonal R3m space group. The structure is three-dimensional. there are two inequivalent Ti4+ sites. In the first Ti4+ site, Ti4+ is bonded to four S2- atoms to form corner-sharing TiS4 tetrahedra. The corner-sharing octahedral tilt angles are 60°. There are three shorter (2.26 Å) and one longer (2.45 Å) Ti–S bond lengths. In the second Ti4+ site, Ti4+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with three equivalent TiS4 tetrahedra and edges with four equivalent TiS6 octahedra. There are a spread of Ti–S bond distances ranging from 2.28–2.61 Å. There are four inequivalent S2- sites. In the first S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti4+ atoms. In the second S2- site, S2- is bonded in an L-shaped geometry to two equivalent Ti4+ atoms. In the third S2- site, S2- is bonded in a distorted tetrahedral geometry to four Ti4+ atoms. In the fourth S2- site, S2- is bonded in a distorted trigonal planar geometry to three Ti4+ atoms.

36 MATERIALS SCIENCE↗

Intrinsic Defect-Induced Local Semiconducting-to-Metallic Regions Within Monolayer 1T-TiS2 Displayed by First-Principles Calculations and Scanning Tunneling Microscopy

Using density functional theory (DFT) and scanning tunneling microscopy (STM), the intrinsic point defects, formation energy, and electronic structure of 1T-TiS2 were investigated. Defect systems include single-atom vacancies, interstitial and adatom additions, and direct atomic substitution. Using a collective approach for analyzing realistic systems for point defect investigation, we provide a more straightforward comparison to the experimental measurements, reproducing more realistic environmental conditions related to thin film growth. STM images are compared to computationally simulated electron density images to identify specific geometries that result from favorable point defects. DFT suggests that titanium interstitials are the most energetically favorable intrinsic defect, and sulfur vacancies are more likely to form than titanium vacancies within this realistic analysis, which is in agreement with STM data. A pristine, stoichiometric monolayer system is calculated to have a direct band gap of 0.422 eV, which varies based on local point defects. Local semiconducting-to-metallic electronic transitions are predicted to occur based on the presence of Ti interstitials.

Keeney, P. J.↗

Materials Data on Li(TiS2)2 by Materials Project

LiTi2S4 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. Li1+ is bonded to six S2- atoms to form LiS6 octahedra that share corners with twelve equivalent TiS6 octahedra, edges with two equivalent LiS6 octahedra, and faces with two equivalent TiS6 octahedra. The corner-sharing octahedra tilt angles range from 43–51°. There are a spread of Li–S bond distances ranging from 2.58–2.69 Å. Ti+3.50+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with six equivalent LiS6 octahedra, edges with six equivalent TiS6 octahedra, and a faceface with one LiS6 octahedra. The corner-sharing octahedra tilt angles range from 43–51°. There are a spread of Ti–S bond distances ranging from 2.39–2.56 Å. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three equivalent Ti+3.50+ atoms. In the second S2- site, S2- is bonded to two equivalent Li1+ and three equivalent Ti+3.50+ atoms to form a mixture of distorted edge and corner-sharing SLi2Ti3 trigonal bipyramids.

36 MATERIALS SCIENCE↗

Materials Data on Ti3(SeS2)2 by Materials Project

TiS2(TiSeS)2 is trigonal omega-derived structured and crystallizes in the trigonal P3m1 space group. The structure is two-dimensional and consists of one TiS2 sheet oriented in the (0, 0, 1) direction and two TiSeS sheets oriented in the (0, 0, 1) direction. In the TiS2 sheet, Ti4+ is bonded to six S2- atoms to form edge-sharing TiS6 octahedra. There are three shorter (2.44 Å) and three longer (2.45 Å) Ti–S bond lengths. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti4+ atoms. In the second S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti4+ atoms. In each TiSeS sheet, Ti4+ is bonded to three equivalent Se2- and three equivalent S2- atoms to form edge-sharing TiSe3S3 octahedra. All Ti–Se bond lengths are 2.59 Å. All Ti–S bond lengths are 2.41 Å. Se2- is bonded in a 3-coordinate geometry to three equivalent Ti4+ atoms. S2- is bonded in a distorted T-shaped geometry to three equivalent Ti4+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Ti4S8N by Materials Project

(TiS2)8N2 is trigonal omega-derived structured and crystallizes in the monoclinic Pm space group. The structure is two-dimensional and consists of one ammonia molecule and two TiS2 sheets oriented in the (0, 0, 1) direction. In each TiS2 sheet, Ti+3.75+ is bonded to six S2- atoms to form edge-sharing TiS6 octahedra. There are three shorter (2.42 Å) and three longer (2.44 Å) Ti–S bond lengths. There are four inequivalent S2- sites. In the first S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti+3.75+ atoms. In the second S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti+3.75+ atoms. In the third S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti+3.75+ atoms. In the fourth S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti+3.75+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on LiTiS2O by Materials Project

Li2O2(TiS2)2 crystallizes in the trigonal R3m space group. The structure is two-dimensional and consists of three Li2O2 sheets oriented in the (0, 0, 1) direction and three TiS2 sheets oriented in the (0, 0, 1) direction. In each Li2O2 sheet, Li1+ is bonded in a trigonal planar geometry to three equivalent O2- atoms. All Li–O bond lengths are 1.95 Å. O2- is bonded in a trigonal planar geometry to three equivalent Li1+ atoms. In each TiS2 sheet, Ti4+ is bonded to six S+1.50- atoms to form edge-sharing TiS6 octahedra. There are three shorter (2.41 Å) and three longer (2.43 Å) Ti–S bond lengths. There are two inequivalent S+1.50- sites. In the first S+1.50- site, S+1.50- is bonded in a 3-coordinate geometry to three equivalent Ti4+ atoms. In the second S+1.50- site, S+1.50- is bonded in a 3-coordinate geometry to three equivalent Ti4+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Ti5MnS10 by Materials Project

Ti2MnS4(TiS2)3 is trigonal omega-derived structured and crystallizes in the trigonal P-3m1 space group. The structure is two-dimensional and consists of one Ti2MnS4 sheet oriented in the (0, 0, 1) direction and three TiS2 sheets oriented in the (0, 0, 1) direction. In the Ti2MnS4 sheet, Ti+3.60+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with six equivalent MnS6 octahedra, edges with six equivalent TiS6 octahedra, and a faceface with one MnS6 octahedra. The corner-sharing octahedral tilt angles are 47°. There are three shorter (2.41 Å) and three longer (2.52 Å) Ti–S bond lengths. Mn2+ is bonded to six equivalent S2- atoms to form MnS6 octahedra that share corners with twelve equivalent TiS6 octahedra, edges with six equivalent MnS6 octahedra, and faces with two equivalent TiS6 octahedra. The corner-sharing octahedral tilt angles are 47°. All Mn–S bond lengths are 2.48 Å. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded to three equivalent Ti+3.60+ and three equivalent Mn2+ atoms to form a mixture of distorted corner and edge-sharing STi3Mn3 pentagonal pyramids. In the second S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti+3.60+ atoms. In each TiS2 sheet, Ti+3.60+ is bonded to six S2- atoms to form edge-sharing TiS6 octahedra. There are three shorter (2.43 Å) and three longer (2.44 Å) Ti–S bond lengths. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti+3.60+ atoms. In the second S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti+3.60+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Ti4MnS8 by Materials Project

Ti2MnS4(TiS2)2 crystallizes in the trigonal P-3m1 space group. The structure is two-dimensional and consists of one Ti2MnS4 sheet oriented in the (0, 0, 1) direction and two TiS2 sheets oriented in the (0, 0, 1) direction. In the Ti2MnS4 sheet, Ti+3.50+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with six equivalent MnS6 octahedra, edges with six equivalent TiS6 octahedra, and a faceface with one MnS6 octahedra. The corner-sharing octahedral tilt angles are 47°. There are three shorter (2.42 Å) and three longer (2.52 Å) Ti–S bond lengths. Mn2+ is bonded to six equivalent S2- atoms to form MnS6 octahedra that share corners with twelve equivalent TiS6 octahedra, edges with six equivalent MnS6 octahedra, and faces with two equivalent TiS6 octahedra. The corner-sharing octahedral tilt angles are 47°. All Mn–S bond lengths are 2.46 Å. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded to three equivalent Ti+3.50+ and three equivalent Mn2+ atoms to form a mixture of distorted edge and corner-sharing STi3Mn3 pentagonal pyramids. In the second S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti+3.50+ atoms. In each TiS2 sheet, Ti+3.50+ is bonded to six S2- atoms to form edge-sharing TiS6 octahedra. All Ti–S bond lengths are 2.44 Å. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti+3.50+ atoms. In the second S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti+3.50+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on LiTi(SO)2 by Materials Project

LiO2TiS2 crystallizes in the monoclinic C2/m space group. The structure is two-dimensional and consists of one LiO2 sheet oriented in the (0, 0, 1) direction and one TiS2 sheet oriented in the (0, 0, 1) direction. In the LiO2 sheet, Li1+ is bonded to six equivalent O2- atoms to form edge-sharing LiO6 octahedra. There are four shorter (1.91 Å) and two longer (2.51 Å) Li–O bond lengths. O2- is bonded in a 4-coordinate geometry to three equivalent Li1+ and one O2- atom. The O–O bond length is 1.37 Å. In the TiS2 sheet, Ti3+ is bonded to six equivalent S atoms to form edge-sharing TiS6 octahedra. There are two shorter (2.42 Å) and four longer (2.46 Å) Ti–S bond lengths. S is bonded in a distorted T-shaped geometry to three equivalent Ti3+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on TiS2N by Materials Project

STiNS is trigonal omega-derived structured and crystallizes in the trigonal R3m space group. The structure is two-dimensional and consists of three ammonia molecules and three TiS2 sheets oriented in the (0, 0, 1) direction. In each TiS2 sheet, Ti3+ is bonded to six equivalent S2- atoms to form edge-sharing TiS6 octahedra. All Ti–S bond lengths are 2.43 Å. S2- is bonded in a distorted T-shaped geometry to three equivalent Ti3+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on LiTi(SO)2 by Materials Project

LiO2TiS2 crystallizes in the monoclinic C2/m space group. The structure is two-dimensional and consists of one LiO2 sheet oriented in the (0, 0, 1) direction and one TiS2 sheet oriented in the (0, 0, 1) direction. In the LiO2 sheet, Li1+ is bonded to six equivalent O2- atoms to form edge-sharing LiO6 octahedra. There are four shorter (1.91 Å) and two longer (2.56 Å) Li–O bond lengths. O2- is bonded in a 4-coordinate geometry to three equivalent Li1+ and one O2- atom. The O–O bond length is 1.38 Å. In the TiS2 sheet, Ti3+ is bonded to six equivalent S atoms to form edge-sharing TiS6 octahedra. There are two shorter (2.42 Å) and four longer (2.46 Å) Ti–S bond lengths. S is bonded in a distorted T-shaped geometry to three equivalent Ti3+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Ti5S8 by Materials Project

Ti5S8 crystallizes in the trigonal R3m space group. The structure is two-dimensional and consists of three Ti3S4 sheets oriented in the (0, 0, 1) direction and six TiS2 sheets oriented in the (0, 0, 1) direction. In each Ti3S4 sheet, there are three inequivalent Ti+3.20+ sites. In the first Ti+3.20+ site, Ti+3.20+ is bonded to six S2- atoms to form a mixture of edge, face, and corner-sharing TiS6 octahedra. The corner-sharing octahedral tilt angles are 45°. There are three shorter (2.41 Å) and three longer (2.54 Å) Ti–S bond lengths. In the second Ti+3.20+ site, Ti+3.20+ is bonded to six S2- atoms to form a mixture of edge and corner-sharing TiS6 octahedra. The corner-sharing octahedral tilt angles are 3°. There are three shorter (2.42 Å) and three longer (2.47 Å) Ti–S bond lengths. In the third Ti+3.20+ site, Ti+3.20+ is bonded to six S2- atoms to form a mixture of edge, face, and corner-sharing TiS6 octahedra. The corner-sharing octahedra tilt angles range from 3–45°. There are three shorter (2.38 Å) and three longer (2.58 Å) Ti–S bond lengths. There are four inequivalent S2- sites. In the first S2- site, S2- is bonded to six Ti+3.20+ atoms to form a mixture of distorted edge and corner-sharing STi6 pentagonal pyramids. The corner-sharing octahedral tilt angles are 6°. In the second S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti+3.20+ atoms. In the third S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti+3.20+ atoms. In the fourth S2- site, S2- is bonded to six Ti+3.20+ atoms to form a mixture of edge and corner-sharing STi6 octahedra. In each TiS2 sheet, Ti+3.20+ is bonded to six S2- atoms to form edge-sharing TiS6 octahedra. All Ti–S bond lengths are 2.43 Å. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti+3.20+ atoms. In the second S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Ti+3.20+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on ZrTiS4 by Materials Project

ZrS2TiS2 is trigonal omega-derived structured and crystallizes in the trigonal P-3m1 space group. The structure is two-dimensional and consists of one TiS2 sheet oriented in the (0, 0, 1) direction and one ZrS2 sheet oriented in the (0, 0, 1) direction. In the TiS2 sheet, Ti4+ is bonded to six equivalent S2- atoms to form edge-sharing TiS6 octahedra. All Ti–S bond lengths are 2.47 Å. S2- is bonded in a distorted T-shaped geometry to three equivalent Ti4+ atoms. In the ZrS2 sheet, Zr4+ is bonded to six equivalent S2- atoms to form edge-sharing ZrS6 octahedra. All Zr–S bond lengths are 2.56 Å. S2- is bonded in a distorted T-shaped geometry to three equivalent Zr4+ atoms.

36 MATERIALS SCIENCE↗

Perspectives on van der Waals Density Functionals: The Case of TiS 2

The van der Waals interaction is of foundational importance for a wide variety of physical systems. In particular, van der Waals forces lie at the heart of potential device technologies that may be realized from the functional organization of layered two-dimensional (2D) nanomaterials. Furthermore, for intermediate to large-scale applications modeling, van der Waals density functionals have become the de facto choice for first-principles calculations. In particular, the vdW-DF family of functionals have provided a systematic approach to this theoretically challenging problem. While much progress has been made, there remains room for improvement in the microscopic description of vdW forces from these density functionals. In this work, we compute benchmark results for the binding energy and the electronic density response to binding in TiS2 via accurate diffusion quantum Monte Carlo calculations. We compare these benchmark data to results obtained from local, semilocal, and van der Waals functionals. In particular, we gauge the quality of the original vdW-DF/vdW-DF2 functionals, as well as updated variants such as vdW-DF-C09, vdW-DF-optB88, vdW-DF-optB86b, and vdW-DF2-B86R. We find a close relationship between the accuracy of predicted interlayer separation distances and binding energies for TiS 2 , with the vdW-DF-optB88 functional performing very well in terms of both quantities. In general, the more recently developed functionals are systematic improvements over older ones. However, when considering the response of the electron density to binding, we find that local-density approximation (LDA) and PBEsol generally outperform the vdW-DF functionals in describing the interlayer charge accumulation with vdW-DF-C09 variants performing the best overall.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗