Born effective charges

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.58.6224

Equation:

Z_{\kappa ,\beta \alpha }=\Omega _{0}\epsilon _{ij}^{\infty }=\delta _{ij}+{\frac {4\pi }{\epsilon _{0}}}{\frac {\partial P_{i}}{\partial {\mathcal {E}}_{j}}}\qquad {i,j=x,y,z}.

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.55.10355

Introduction

Insert something from paper/ thesis then edit

MIND THAT VASP outputs it oddly?

Calculating

Taken from Dielctric properties: There are two approaches to compute Born effective charges implemented in VASP: one is done by applying finite electric fields along the three cartesian directions and computing the forces on the atoms which are activated using LCALCEPS or by computing the derivating of the wavefunction with respect to an electric field using density functional perturbation theory (DFPT) using LEPSILON.

Note: This is different in py4vasp.

Introduction

Calculating

References