Because , the number of -points in the Brillouin zone sampling used to evaluate Eq. (7) tends to be quite large (typically ), and because this equation will have to be evaluated six times to establish and , it is computationally advantageous to generate and , the self-consistent Kohn-Sham potentials for respectively the undistorted and the distorted unit cell, using some adequate but less extensive Monkhorst-Pack sampling of the Brillouin zone. These potentials are kept fixed in the subsequent calculations of the wave functions and , for all -points .
The total difference in polarization between the distorted ( ) and undistorted ( ) structures is
with the electronic contribution to the difference in polarization given by Eq. (4), and the ionic or core contribution by
where in the context of a pseudopotential calculation, is the valence atomic number of pseudoatom .
Once is known, column of the Born effective charge tensor is found from