`IBRION`=5, is only supported starting from VASP.4.5.
`IBRION`=6, is only supported starting from VASP.5.1.
Both flags allow to determine
the Hessian matrix (matrix of the second derivatives of the energy with respect
to the atomic positions) and the vibrational frequencies of
a system. Only zone centered (-point) frequencies are calculated automatically
and printed after

Eigenvectors and eigenvalues of the dynamical matrix

To calculate the Hessian matrix, finite differences are used, *i.e.*
each ion is displaced in the direction of each Cartesian coordinate,
and from the forces the Hessian matrix is determined.
The two modes differ in the way symmetry is considered. For `IBRION`=5,
all atoms are displaced in all three Cartesian directions, resulting
in a significant computational effort even for moderately sized high
symmetry systems. For `IBRION`=6, however only symmetry
inequivalent displacements are considered, and the remainder of
the Hessian matrix is filled using symmetry considerations.

Selective dynamics are presently only supported for `IBRION`=5; in this
case, only those components of the Hessian
matrix are calculated for which the selective dynamics tags are set to
`.TRUE.` in POSCAR .
Contrary to the conventional behavior, the selective dynamics
tags always refer to the Cartesian components of the Hessian matrix.
For the following POSCAR file, for instance,

Cubic BN 3.57 0.0 0.5 0.5 0.5 0.0 0.5 0.5 0.5 0.0 1 1 selective Direct 0.00 0.00 0.00 F F F 0.25 0.25 0.25 T F Fatom 2 is displaced in the -direction only, and only the component of the second atom of the Hessian matrix is calculated.

Three parameters influence the determination of the Hessian matrix:
The parameter `NFREE` determines how many
displacements are used for each direction
and ion, and `POTIM` determines the step size. The step size is
defaulted to 0.015 Å(up from VASP.5.1), if too large values are supplied
in the input file.
Expertise shows that this is a very reasonable compromise.
`NFREE`=2 uses central difference, *i.e.* each ion is displaced
in each direction by a small positive and negative displacement

...

Finally, `IBRION`=6 and `ISIF`3
allows to calculate the elastic constants.
The elastic tensor is determined by performing six finite distortions of the lattice
and deriving the elastic constants from the strain-stress relationship [4].
The elastic tensor is calculated both, for rigid ions, as well, as allowing for
relaxation of the ions. The elastic moduli for rigid ions are written after the line

SYMMETRIZED ELASTIC MODULI (kBar)The ionic contributions are determined by inverting the ionic Hessian matrix and multiplying with the internal strain tensor [5], and the corresponding contributions are written after the lines:

ELASTIC MODULI CONTR FROM IONIC RELAXATION (kBar)The final elastic moduli including both, the contributions for distortions with rigid ions and the contributions from the ionic relaxations, are summarized at the very end.

TOTAL ELASTIC MODULI (kBar)There are a few caveats to this approach: most notably the plane wave cutoff needs to be sufficiently large to converge the stress tensor. This is usually only achieved if the default cutoff is increased by roughly 30 %, but it is strongly recommended to increase the cutoff systematically (e.g. in steps of 15 %), until full convergence is achieved.

Born effective charges, piezoelectric constants, and
the ionic contribution to the dielectric tensor can be
calculated additionally by specifying `LEPSILON=.TRUE.`
(linear response theory, see also Sec.6.72.6) or `LCALCEPS=.TRUE.`
(finite external field, see also Sec.6.67.4).

*Comments with respect to older releases:*
In some old releases, `NSW` (number of ionic steps) must be set to 1
in the INCAR file, since `NSW=0` resets the `IBRION` tag to `-1` regardless of
the value supplied in the INCAR file. Furthermore, although VASP.4.6 supports `IBRION=5-6`,
VASP.4.6 does not change the set of k-points automatically (often the displaced configurations
require a different point grid). Hence, the finite differences
routine might yield incorrect results in VASP.4.6.