As mentioned in the last weekly tip #9, a vacuum needs to be added to a supercell to make a slab structure, simulating a surface under the periodic boundary condition of a plane-wave basis.
A slab structure has two surfaces, the top and the bottom. Many materials are an asymmetric slab structures in which the atomic arrangement of the two surfaces is not identical. In this case, a dipole moment is created in a slab because of the structure’s asymmetry, and their electrostatic potentials of the slab’s top and bottom parts are different.
Even in an asymmetric slab, an electrostatic potential is also continuously repeated periodically because of the periodic boundary condition. Thus, an effect that resembles an artificial electric field is applied to the entire supercell to remove the discontinuity, caused by the difference in potentials of the boundary.
As a solution, a kind of “potential jump” area needs to be added, which offsets the effect of an electric field artificially added, by using a dipole correction.
At the time, the electric field is added represented by the sawtooth potential because of the periodic boundary condition.
Recently, an option that can apply an electric field is updated in Materials Square. With this option, there are two methods to apply a dipole correction. This weekly tip covers the method of applying the dipole correction by using the two methods with MatSQ and checking and comparing the correction result through the charge density and planar-average potential.
1. Apply Dipole Correction Using Dipole Correction Option
Applying a dipole correction indicates putting an electric field in the opposite direction to the induced electric field. For this reason, properly setting the “electric field” option can use a dipole correction. Add the Quantum Espresso module and set “Precision = High” in Scripting option. Create a template to display a correction question. Click the “Electric field” checkbox to display a keyword that can apply the electric field to the structure.
While “Model type = Slab” is set, put the Electric field option of &CONTROL to True. Then, the Dipole correction option is added. In addition, an option, necessary to set the Electric field, is displayed in &SYSTEM. Set the two options to True. Then, the dipole correction can be applied.
How to set a keyword is described as follows:
- The “Electric field direction” tag sets the electric field’s direction. For a dipole correction, the direction should be set to one of the axes where a vacuum exists (vertical to the slab surface).
- The “Electric field max position” tag sets the position wherein a sawtooth potential is added. This should be located at the center of the vacuum to minimize the effect on the structure. Furthermore, the position is indicated because of the ratio of the axis’ length, where an electric field is applied. Materials Square automatically calculates and enters the proper position.
- The “Potential decrease region” tag sets the sawtooth potential’s width to be added. It is good to adjust the ratio to make the width to 1-2 Å. The potential’s width is also the ratio for the axis’ length, where an electric field is applied. Materials Square calculates the ratio of which the width is approximately 1 Å for the cell parameter and automatically enters the value.
- The “Electric field amplitude” is a keyword that decides the electric field’s size. Once the Dipole correction option is activated, the size is automatically set. Thus, it is good to set to 0 with “Dipole correction = TRUE.”
Once the setting is completed, you are ready to get a calculation result with the application of the dipole correction. Click Start Job! to start.Start Job!
2. Apply Dipole Correction by Using Electric Field Option
The second method for a dipole correction is to add an electric field to a proper position to have the same effect when the dipole correction is applied. In this stage, set FALSE to the Dipole correction keyword. For the Electric field option, set it in the same way as the value set for the dipole correction. The difference between this case and the case of setting the dipole correction option is the Electric field amplitude keyword that decides the size of an electric field needs to be set. The unit of the Electric field amplitude keyword is an atomic unit. (1 a.u. = 51.4220632*1010V/m) The default is 0.001 a.u. It is good to set a value that is smaller than the default in consideration of the potential’s difference between the asymmetry slab surfaces. One step is added to set the electric field’s strength to apply a dipole correction by using an electric field option. In addition, if an electric field is applied too strong, the potential with an opposite slope beyond the dipole correction will be applied. Furthermore, as the energy generated from an external electric field is twice the dipole correction energy, the total energy may have an error.
Thus, if you focus on a dipole correction, it is good to use a dipole correction keyword.
3. Check the Correction Result by Using Charge Density and Planar-Average Potential
When calculating a charge density, if you plot the total potential that considers the bare potential (local part of the ionic potential) and Hartree potential, you can visually check the potential, changed by the correction. In addition, the Average function is updated to obtain a graph with the average charge density on a specific surface. Finding the charge density’s average can obtain the planar-average potential and display the potential as an intuitive 2D graph. When calculating a charge density, set the Data to plot item to “11 Total potential” in the Charge density tab to acquire the total potential.
The planar-average potential is calculated with the charge density, and the setting can be adjusted in the Charge Density solver tab. Adjusting the number of points can adjust the number of points of the planar-average potential graph. Increase the window’s size to change the shape of the macroscopic average potential, calculated with the planar-average potential.
The following shows the dipole correction result of the asymmetric slab of PbTiO3 in the perovskite structure, displayed as the charge density (total potential) and the planar-average potential.
The distribution of a charge density (total potential) shows that TiO2 and PbO, which are the two different surfaces of the PbTiO3 slab, have different potentials. In terms of the planar-average potential, if a dipole correction is not added, the potential has a slope in the vacuum because of an added artificial electric field.
In the charge density module, click the icon to display the planar-average potential graph. Right-click the graph for the screen to pop up, and set the range. Enlarge the potential graph where the correction is added. Then, the following is displayed:
When you see the enlarged planar-average potential graph, you can observe that both cases of applying the dipole correction using an electric field and that of performing the correction setting the Dipole correction option can remove the slope of the potential generated by the artificial electric field through the addition of sawtooth potential.
However, the total energy is different.
|Energy (eV)||ΔE (eV)|
In case of the energy difference from Normal, the total energy is slightly changed because of the potential changed by the electric field, and the error when the electric field is applied is larger than when the dipole correction is applied.
A calculation with the application of dipole correction may have a bad convergence, compared to a calculation without the correction. Thus, in case of a structure didn’t converge easily, decrease the mixing beta for the calculation, or perform a calculation without the dipole correction first, and then perform the restart calculation by applying the dipole correction. Then, you can efficiently carry out the calculation.
This weekly tip covers the method of applying an electric field to a structure and using a dipole correction by utilizing an “Electric Field” correction keyword, recently updated in MatSQ, and checking the electric field’s effect by using a charge density and a planar-average potential. With these methods, you can perform a calculation of a slab structure with a dipole moment without an effect of a periodic electrostatic potential and minimize errors. In addition, you can make calculations with the application of an external electric field by adjusting the electric field setting.
Explore new options of Materials Square and create calculations with an electric field or dipole correction!
 Bengtsson, L. (1999). Dipole correction for surface supercell calculations. Physical Review B, 59(19), 12301.