How to calculate the dielectric constant in VASP
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To calculate the dielectric constant in VASP, add the following to your INCAR after relaxing the structure to phonon accuracy.
LEPSILON=.TRUE.
LPEAD=.TRUE.
IBRION=8
LRPA=.FALSE.
LRPA is by default set to false. The following is the description on the VASP WIKI:
For LRPA=.TRUE. local field effects are included on the Hartree level only. This means that cell periodic microscopic changes of the local potential related to the change of the Hartree potential are included.
For LRPA=.FALSE. changes of the Hartree and the exchange correlation potential are included. This usually increases the dielectric constants. The final values for the dielectric tensor can be found in the OUTCAR file after the lines.