@@ -125,8 +125,6 @@ Volume of the cell is: 75.48314005099871 AA^3

Z* for Mg is 1.9785090242786756

Z* for O is -1.9792159848836068

```

Note that because of the cubic symmetry the BEC and dielectric tensors are diagonal. Thus, in the calculations of BECs we have only displaced atom along one direction. This script extracted the necessary information from the `aims.out` files. The polarization output in the `aims.out` file looks similar to the following:

```

...

...

@@ -149,9 +147,9 @@ Note that because of the cubic symmetry the BEC and dielectric tensors are diago

The script `postprocessing.py` extracted the value for the full polarization and calculates the BEC according to the Eq. (1).

Note that BEC's of Mg and O in principle should sum up to zero -- slight deviation from this rule comes from the accuracy of our calculations.

*FHI-aims* contains a bunch of scripts, which can be used to simplify the work. These scripts are stored in the `utilities` folder in root directory of *FHI-aims* distribution. Among all the utilities there is a script

`BEC.py`, which can be used for the calculations of the BEC. In the `solutions` folder for this exercise you could find an example of calculations done with this script. Information about the usage of the script can be found in the

*FHI-aims* manual.

For more general cases (non-cubic symmetries, more none-equivalent atoms, etc.) the `BEC.py` script contained in the utilities folder in root directory of *FHI-aims* distribution can be used to simplify the work.

An example on how to use the `BEC.py` script for the MgO system discussed here can be found in the `solutions` folder of this exercise. More Information about the usage of the script is given the *FHI-aims* manual, see Sec. `How to calculate Born Effective Charges?`.

## Calculation of phonon band structure including NAC