# Methods

## Contents

- 1 Methods
- 1.1 VASP Wiki and Support Forum
- 1.2 Convergence and Efficiency
- 1.3 General calculations and relaxation
- 1.4 Systems
- 1.5 Defect calculations
- 1.6 Vibrational frequencies
- 1.7 Phonon calculations
- 1.8 Nudged Elastic Band (NEB)
- 1.9 Polaron localization
- 1.10 Bader charge analysis
- 1.11 Error messages
- 1.12 References

# Methods

## VASP Wiki and Support Forum

The VASP manual contains information on all INCAR tags and tutorials and guides to several types of calculations (www.vasp.at/wiki/).

The VASP Support Forum (www.vasp.at/forum/) allows users to troubleshoot and discuss technical and scientific topics. The VASP developers are also active in answering questions.

## Convergence and Efficiency

### Convergence tests

How to and relevant examples.

### Benchmark

VASP efficiency on Saga (number of nodes/cores)

Computational cost: atoms vs kpoints vs functional etc.

## General calculations and relaxation

NELM, NSW

## Systems

### Supercells

A supercell can be made in VESTA by going into Edit -> Edit data -> Unit Cell...

When the window for the unit cell has opened press Transform, change the numbers in the Transformation matrix to make a supercell of your choice.

### Surfaces and slabs

Slabs can be constructed using ASE.

A specific surface can be exposed using VESTA, here is a youtube tutorial for exposing the (110) surface of a TiO2 rutile structure, tutorials for other structures can be found on the same youtube channel.

To make a supercell or a slab from the new unit cell you have just created VESTA you have to export the unit cell in a .vasp format. Open the vasp file in VESTA and then follow the same procedure for the creation of a supercell as has been explained above.

Finite-size correction for slab supercell calculations of materials with spontaneous polarization ^{[1]}

### Grain boundaries and interfaces

Typically modeled as Coincident Site Lattice (CSL) structures that are optimized by rigid body translation.

Materials project provides a list of matching structures and terminations under the **Substrates** section for a selected structure.

Special grain boundaries in perovskites ^{[2]}

Machine learning sampling to determine rigid body translation ^{[3]}

### Disordered structures

Site occupancy disorder program: https://github.com/gcmt-group/sod

TDEP code for generating special quasirandom structures

## Defect calculations

### Charge correction

Self-Consistent Potential Correction for Charged Periodic Systems ^{[4]}

CoFFEE: Corrections For Formation Energy and Eigenvalues for charged defect simulations ^{[5]}

Limitations of empirical supercell extrapolation for calculations of point defects in bulk, at surfaces, and in two-dimensional materials ^{[6]}

### Defect configurations

Evolutionary computing and machine learning for discovering of low-energy defect configurations ^{[7]}

## Vibrational frequencies

Finite displacement method (IBRION=5) can be used to find vibrational frequencies within the harmonic approximation.

- See Phonons from finite differences
- Relax the species that will be displaced to higher force convergance (e.g., EDIFFG=0.0001 or 0.005 eV Å^1)
- Use IBRION=5, NFREE=4, POTIM=0.015. The NCORE-tag may need to be removed from INCAR
- Check the energy profile (energy of each ionic step vs displacement) to make sure that the harmonic fit is satisfactory (2nd order polynomial)

## Phonon calculations

## Nudged Elastic Band (NEB)

NEB calculations require relaxed CONTCAR files for the initial and final states, and POSCAR files for one or more states along the migration path, which are termed images. The POSCAR files can be generated by linear interpolation between neighboring states using **nebmake.pl** script which is part of VTST Tools and is available in the folder /cluster/projects/nn4604k/bin/vtstscripts-922).

The following INCAR tags can be used to initiate a NEB calculations with one image and the climbing image method

IMAGES = 1 SPRING = -5 LCLIMB = .TRUE.

POSCAR files for the initial, interpolated and final position must be placed in subfolders named 00, 01 and 02, and the job script must be modified accordingly. VTST Tools offers some improvements to the standard NEB implementation in VASP, and these can be loaded as a separate module with suffix ` -vtst `

module load VASP/5.4.4-intel-2019a-std-vtst cp -r 00 01 02 $SCRATCH savefile 01/CONTCAR 01/OUTCAR 01/DOSCAR 01/CHGCAR 01/WAVECAR

## Polaron localization

Normally polarons which are localized at d or p orbitals normally require DFT+U hybrid functionals.

The U value will determine the localization energy.

To determine the proper U value for this calculations, the a piecewise linear method is strongly recommended.

More detail can be found *Physical Review B*, *90*(3), 035204.

To visualize the polaron localization, you can generate the partial charge density, by set:

LPARD = T

IBAND = XX, the band where you localized polaron is.

The PARCHG will be generated after calculation, and it can be visualized in the VESTA.

## Bader charge analysis

INCAR

PREC = A

LAECHG = T

The core charge is written to AECCAR0 and the valance charge to AECCAR2. These two charge density files can be summed using the chgsum.pl script;

chgsum.pl AECCAR0 AECCAR2

The bader analysis can then be done on this total charge density file:

bader CHGCAR -ref CHGCAR_sum

## Error messages

## References

- ↑ Yoo, SH., Todorova, M., Wickramaratne, D. et al. Finite-size correction for slab supercell calculations of materials with spontaneous polarization. npj Comput Mater 7, 58 (2021) http://dx.doi.org/10.1038/s41524-021-00529-1
- ↑ B. M. Darinskiy, N. D. Efanova & D. S. Saiko (2020) Special grain boundaries in perovskite crystals, Ferroelectrics, 567:1, 13-19, https://doi.org/10.1080/00150193.2020.1791582
- ↑ Application of machine learning-based selective sampling to determine BaZrO3 grain boundary structures, Computational Materials Science, 164 (2019) 57-65. https://doi.org/10.1016/j.commatsci.2019.03.054
- ↑ Mauricio Chagas da Silva, Michael Lorke, Bálint Aradi, Meisam Farzalipour Tabriz, Thomas Frauenheim, Angel Rubio, Dario Rocca, and Peter Deák Phys. Rev. Lett. 126, 076401. https://doi.org/10.1103/PhysRevLett.126.076401
- ↑ Naik, Mit H., and Manish Jain. CoFFEE: corrections for formation energy and eigenvalues for charged defect simulations. Computer Physics Communications 226 (2018) 114-126. https://doi-org/10.1016/j.cpc.2018.01.011
- ↑ Christoph Freysoldt, Jörg Neugebauer, Anne Marie Z. Tan, and Richard G. Hennig, Limitations of empirical supercell extrapolation for calculations of point defects in bulk, at surfaces, and in two-dimensional materials, Phys. Rev. B 105, 01410 http://dx.doi.org/10.1103/PhysRevB.105.014103
- ↑ Arrigoni, M., Madsen, G.K.H. Evolutionary computing and machine learning for discovering of low-energy defect configurations. npj Comput Mater 7, 71 (2021). https://doi.org/10.1038/s41524-021-00537-1