# Dielectric tensor εij (total)

How may I calculate the Dielectric Tensor εij (total) like here? In the OUTCAR, I see both HEAD OF MICROSCOPIC STATIC DIELECTRIC TENSOR (independent particle, excluding Hartree and local field effects) and MACROSCOPIC STATIC DIELECTRIC TENSOR (including local field effects in DFT).

Flags used:

ISMEAR =  0
SIGMA  =  0.03
EDIFF  = 1.E-8
#IBRION = 8

LEPSILON = .TRUE.
LASPH = .TRUE.


PS: independent-particle (IP) approximation

The dielectric tensor can be split in the ionic $$(ϵ_{ij}^{0})$$ and electronic $$(ϵ_{ij}^{∞})$$ contributions:$$ϵ_{ij}=ϵ_{ij}^{0}+ϵ_{ij}^{∞}$$ According to VASP documentation. To obtain the ionic contributions to the static dielectric properties one needs to compute the force-constant matrices (Hessian of the total energy w.r.t. the ionic positions) and internal strain tensors (second derivative of the total energy w.r.t. strain fields and ionic postions). These properties may be obtained from finite differences (IBRION=5 or 6) or from perturbation theory (IBRION=7 or 8).

You may need to add IBRION = 8 in your INCAR file:

ISMEAR =  0
SIGMA  =  0.01
EDIFF  = 1.E-8

## to get the Born effective charges
## and the macroscopic dielectric tensor
LEPSILON = .TRUE.

## to get the ionic contribution
## to the macroscopic dielectric tensor
IBRION = 8


Then you can search for the following in your OUTCAR file:

MACROSCOPIC STATIC DIELECTRIC TENSOR IONIC CONTRIBUTION

ELASTIC MODULI IONIC CONTR (kBar)

PIEZOELECTRIC TENSOR IONIC CONTR  for field in x, y, z        (C/m^2)