TLDR¶

The data contain 5933 MoS2 structures with 1-3 point defects simulated with VASP. Each structure is relaxed, and then the relevant properties are computed.

File format¶

defects.csv¶

1. (unnamed first column) structure number in the file
2. _id unique structure identifier
3. descriptor_id identifier of the defect type as specified in descriptors.csv
4. defect_id unused
5. energy total potential energy of the system, eV
6. energy_per_atom total potential energy of the system divided by the number of atoms, eV
7. fermi_level Fermi level, eV
8. homo highest occupied molecular orbital (HOMO) energy, eV
9. lumo lowest unoccupied molecular orbital (LUMO) energy, eV
10. normalized_homo is HOMO value normalised respective to the host valence band maximum (VBM) (see section "DFT computations" in the paper), eV
11. normalized_homo is LUMO value normalised respective to the host valence band maximum (VBM) (see section "DFT computations" in the paper), eV
12. band_gap is the band gap, LUMO - HOMO, eV

initial¶

The folder initial contains the unrelaxed structures in the CIF format. Names correspond to the unique identifiers _id in defects.csv. Note that the structures were relaxed prior to computing the properties.

descriptors.csv¶

1. _id unique identifier of the defect type, corresponds to the descriptor_id column in defects.csv
2. description is a short semantic abbreviation of the defect type
3. base is the chemical formula of the pristine material
4. cell is the supercell size
5. pbc is WTF, in DFT pbc were in all dimensions
6. defects is a dictionary describing each point defect

elements.csv¶

Contains chemical potentials (in eV) of the elements, to be used in formation energy computation.

initial_structures.csv¶

Contains the properties of pristine material.

1. (unnamed first column) structure number in the file
2. base is the chemical formula of the pristine material
3. cell_length is the supercell length, the supercell size is [cell_length, cell_length, 1]
4. energy total potential energy of the system, eV
5. fermi is the Fermi level, eV

Structures generation¶

As the base MoS₂ cell we use MoS₂ cell from the Materials Project, ID: mp-2815. The base cell in the database has two MoS₂ triplets, we take only one of them. We generate the supercell by repeating the triplet 8 times in $x$ and $y$ directions.

We generate the structures with several point defects by iteratively introducing point defects to the original supercell. The dataset contains configurations with 1, 2, and 3-point defects. Each defect can be either a vacancy or a substitution of the original atom (Mo $\rightarrow$ W and S $\rightarrow$ Se). The dataset contains 5933 unique structures for MoS₂ TMDC.

DFT¶

Our calculations are based on density functional theory (DFT) using the PBE functional as implemented in the Vienna Ab Initio Simulation Package (VASP). The interaction between the valence electrons and ionic cores is described within the projector augmented (PAW) approach with a plane‐wave energy cutoff of 500 eV. Spin polarization was included for all the calculations. The monolayer of MoS₂ and defects calculations were performed using an 8x8 supercell, and the Brillouin zone was sampled using a (3x3x1) Monkhorst‐Pack grid. We use periodic boundary conditions, and add a 15Å vacuum space above the material surface to avoid interaction between neighboring layers. In the structural energy minimization, the atomic coordinates are allowed to relax until the forces on all the atoms are less than 0.01 eV/Å. The energy tolerance is $10^{-6}$ eV.

We compute the formation energy, i.e., the energy required to create a defect as \begin{equation} E_{f} = E_{D}-E_{\text{MoS}_2}+\sum_{i\in\{\text{Mo}, \text{S}\}}{n_i \mu_i}-\sum_{i\in\{\text{W}, \text{Se}\}}{m_i \mu_i} \end{equation} where $E_{D}$ is the total energy of the structure with defects, $E_{\text{MoS}_2}$ is the total energy of the pristine MoS₂, $n_i$ is the number of atoms transferred from the supercell to a chemical reservoir, $m_i$ is the number of atoms transferred from a chemical reservoir to the supercell to form the substitution-type defects, and $\mu_i$ is the chemical potential of $i$-th element. Finally, to make the results better comparable across examples with different numbers of defects, we normalize the formation energy by dividing it by the number of defect sites: \begin{equation} E'_{f} = E_f/N_d, \end{equation} where $N_d$ is the number of defects in the structure.

The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies are computed respective to the host valence band maximum (VBM) and are normalized according to \begin{equation} E_\text{HOMO} = E_\text{HOMO}^D-E_1^D-(E_\text{VBM}^\text{pristine}-E_1^\text{pristine}) \end{equation} Where $E_\text{HOMO}^D$ is the eigenvalue of the highest occupied Kohn-Sham states of defects, $E_\text{VBM}^\text{pristine}$ is the eigenvalue of the valence band maximum of pristine MoS₂, $E_1^D$ and $E_1^\text{pristine}$ are the energy of the lowest Kohn-Sham orbital of the calculated defect and pristine MoS₂ structures. Bangap is computed as the difference between LUMO and HOMO.