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Vibrational frequencies, relaxed-ion static dielectric tensor and relaxed-ion piezoelectric tensor

Setting IBRION=8 or IBRION=7 selects the calculation of the interatomic force constants using density functional perturbation theory (see also Sec. 6.22.7), whereas IBRION=6 or IBRION=5 uses finite displacements to determine the interatomic force constants (see also Sec. 6.22.6). For IBRION=8 and IBRION=6, symmetry is taken into account, whereas the other setting neglect symmetry considerations and are thus significantly slower.

If IBRION=5-8 is selected and LEPSILON=.TRUE. is selected, the relaxed-ion static dielectric tensor, or low frequency dielectric tensor, as well as the relaxed-ion piezoelectric tensors are determined [110]. All values are collected and printed at the end of the OUTCAR file. Specifically the ionic contribution to the piezoelectric tensor is printed after

 PIEZOELECTRIC TENSOR IONIC CONTR  for field in x, y, z        (C/m^2)
and the ionic contributions to the dielectric tensor are printed after:
Note that LRPA=.FALSE. (default) must be selected to obtain these values.

For hybrid functionals, vasp presently does not support linear response calculations. However, one can set LCALCEPS=.TRUE. and IBRION=6 in the INCAR file to calculate the Born effective charges by applying a finite field and the interatomic force constants using finite differences. The ionic contribution to the piezoelectric tensor and the dielectric tensor are then calculated as well.

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