pydefect_2d

First-principles calculations are increasingly used to study dominant point defects in 2D materials. However, the number of studies on these defects is still limited compared to those in 3D materials. A major reason for this limitation is the difficulty in finite size corrections, which are crucial for calculating charged defects under periodic boundary conditions (PBC). Several groups have reported methods to correct defect formation energies, yet routinely applying these techniques in practical applications remains challenging. This is because each defect-charge combination requires a unique correction process. Considering typical native defects in 2D materials, such as vacancies, antisites, interstitials, and adsorbed atoms, requires calculations of dozens of defect-charge combinations. Therefore, automating the correction process and minimizing computational costs is vital for advancing defect calculations in 2D materials. To this end, we have developed a code to automate these corrections. We have also introduced an interpolation technique to lessen computational costs and simplify the processes.

• In this code, we employ the correction method proposed by Noh et al. Phys. Rev. B, 89, 205417 (2014) and Komsa Phys. Rev. X 4, 031044 (2014) (NK method).

• In the current implementation, we can treat tetragonal systems only For convention, the directions perpendicular to the surfaces are aligned with the $z$-direction.

• In the current implementation, only VASP is supported.

• This code creates the correction.json and eigenvalue_shift.yaml files, which can be used in the pydefect code.

Requirements

• Python 3.10 or higher
• vise
• pydefect
• see requirements.txt for others

License

Python code is licensed under the MIT License.

Workflow for 2D Point Defect Calculations

Our goal is to evaluate the corrections of defect formation energies (E_f). The workflow is depicted above.

1. (Step 5) Generate unitcell.yaml that is generated from the pristine slab model calculations using pydefect. Only dielectric constants are used in this code.

2. (Step 6) The NK correction method necessitates knowledge of the dielectric profiles. To create a dielectric profile, use either gauss_diele_dist (gdd) or step_diele_dist (sdd) subcommand. An example is: pydefect_2d sdd -c 0.5 -s 0.5 -w 7.15 -wz 7.15 -u unitcell.yaml -pl ../../defects/6_30A/perfect/LOCPOT --denominator 2

3. Create correction/ in the defect calculation directory.

4. (Step 7) T determine the charge center position, we need a series of one-dimensional (1D) potential profiles as a function of the Gaussian charge position (z₀). To achieve this, we firstly create 1d_gauss/ in correction/ and create gauss1_d_potential_xxxx.json using the 1d_gauss_models (1gm) subcommand: An example is: pydefect_2d 1gm -s ../../supercell_info.json -r 0.3 0.5 -dd ../dielectric_const_dist.json

5. (Step 8) Compute the one-dimensional potential from first-principles calculations and determine the Gaussian charge center. An example is: pydefect_2d 1fp -d . -pl ../../perfect/LOCPOT -od ../1d_gauss

6. (Steps 9 and 10) We next prepare the Gaussian charge energies under both three-dimensional (3D) periodic boundary conditions and open boundary conditions as a function of z₀. An example is: pydefect_2d gmz -z 0.3{0,2,4,6,8} 0.4{0,2,4,6,8} 0.5 -s ../../supercell_info.json -cd . -dd ../dielectric_const_dist.json

7. (Step 11) Then, we interpolate long-range correction term as a function of z₀, and
   generate gauss_energies.json inside defects/correction/. An example is: pydefect_2d ge

8. (Step 12) Generate slab_model.json and correction.json (at this point, it converges with pydefect). If slab_center is given, eigenvalue_shift.yaml is also generated, which can be used for shifting the eigenvalues in the pydefect processes. An example is: pydefect_2d 1sm -d Va_MoS6_-2 -dd dielectric_const_dist.json -od 1d_gauss -g correction/gauss_energies.json -s 0.5

Development notes

Bugs, requests and questions

Please use the Issue Tracker to report bugs, request features.

Code contributions

Although pydefect_2d is free to use, we sincerely appreciate if you help us to improve this code. The simplest but most valuable contribution is to send the feature requests and bug reports.

Please report any bugs and issues at PyDefect's GitHub Issues page. Please use the "Fork and Pull" workflow to make contributions and stick as closely as possible to the following:

• Code style follows PEP8 and Google's writing style.
• Add unittests wherever possible including scripts for command line interfaces.

Tests

Run the tests using pytest pydefect_2d.

Citing pydefect_2d

If pydefect_2d has been used in your research, please cite the following paper.

[Corrections on Formation Energies and Eigenvalues of Point Defect Calculations in Two-Dimensional Materials]
Yu Kumagai

Contact info

Yu Kumagai
[email protected]

Tohoku University (Japan)