N.B.: As of VASP.5.2, calculating the macroscopic polarization and
Born effective charges along the lines of the following example
(using `LBERRY`=.TRUE. etc) is unnecessary.
The use of `LCALCPOL` (Sec. 6.67.2) or `LCALCEPS`
(Sec. 6.67.4) is much more convenient.

Setting `LBERRY`= .TRUE. in the INCAR file switches on the evaluation
of the Berry phase expression for the electronic polarization of an insulating
system, as modified for the application of USPP's and PAW datasets
(see Refs. [85], [86] and [89]).
In addition, the following keywords must be specified in order to generate the mesh
of -points:

IGPAR = 1|2|3

This tag specifies the socalled*parallel*or direction in the integration over the reciprocal space unit cell.NPPSTR = number of points on the strings in the IGPAR direction

This tag specifies the number of -points on the strings (with ).-
DIPOL = center of cell (fractional coordinates)

This tag specifies the origin with respect to which the ionic contribution to the dipole moment in the cell is calculated. When comparing changes in this contribution due to the displacement of an ion, this center should be chosen in such a way that the ions in the distorted and the undistorted structure remain on the same side of`DIPOL`(in terms of a minimum image convention).

**An example: The fluorine displacement dipole (Born effective charge) in NaF**

First one needs to determine the electronic polarization of the undistorted NaF.

__Calculation 1__

It is usually convenient to calculate the self-consistent Kohn-Sham potential of the
undistorted structure, using a symmetry reduced (666)
Monkhorst-Pack sampling of the Brillouin zone.
Using for instance the following INCAR file:

PREC = Med ISMEAR = 0 EDIFF = 1E-6

KPOINTS file:

6x6x6 0 Gamma 6 6 6 0 0 0

POSCAR file:

NaF 4.5102 0.0 0.5 0.5 0.5 0.0 0.5 0.5 0.5 0.0 1 1 Direct 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.5000000000000000 0.5000000000000000 0.5000000000000000

and LDA Na_sv and F PAW datasets.

__Calculation 2__

To calculate the electronic contribution to the polarization, along the
reciprocal lattice vector (i.e.
),
add the following lines to the INCAR file:

LBERRY = .TRUE. IGPAR = 1 NPPSTR = 8 DIPOL = 0.25 0.25 0.25

Setting `LBERRY`=.TRUE. automatically sets `ICHARG`=11,
i.e., the charge density of the previous calculation is read and kept fixed,
and only the orbitals and one-electron eigenenergies are recalculated for the
new -point set.
This is advantageous, since the number of -points used to evaluate
the Berry phase expression can be quite large, and precalculating the
charge density (`ICHARG`=11) saves significant CPU time.

The OUTCAR will now contain the following lines:

e<r>_ev=( 0.00000 0.00000 0.00000 ) e*Angst e<r>_bp=( 0.00000 0.00000 0.00000 ) e*Angst Total electronic dipole moment: p[elc]=( 0.00000 0.00000 0.00000 ) e*Angst ionic dipole moment: p[ion]=( 2.25510 2.25510 2.25510 ) e*Angst

__Calculations 3 and 4__

The procedure mentioned under Calculation 2 now has to be repeated with
`IGPAR`=2 and `IGPAR`=3 (again using the charge density obtained
from Calculation 1), to obtain the contributions to the electronic
polarization along and , respectively.

__Calculations 5-8__

To calculate the change in the electronic polarization of NaF due to the
displacement of the fluorine sublattice, one should repeat Calculations 1-4,
using the following POSCAR file:

NaF 4.5102 0.0 0.5 0.5 0.5 0.0 0.5 0.5 0.5 0.0 1 1 Direct 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.5100000000000000 0.5100000000000000 0.4900000000000000

This corresponds to a displacement of the F ion by
Åalong the direction.
The output of the Berry phase calculation using `IGPAR`=1 should
now similar to:

e<r>_ev=( 0.00000 0.00000 0.00004 ) e*Angst e<r>_bp=( 0.00000 0.18028 0.18028 ) e*Angst Total electronic dipole moment: p[elc]=( 0.00000 0.18028 0.18031 ) e*Angst ionic dipole moment: p[ion]=( 2.25510 2.25510 1.93939 ) e*Angst

__Collecting the results__

The change in the electronic contribution to the polarization due to the
F-sublattice displacement should be calculated as follows:

- Take the average of the terms obtained in Calculations 2-4. Lets call this
- Add the terms obtained in Calculations 2-4. Lets call this
- The electronic polarization of the undistorted structure is then given by:
- Repeat the above three steps for the results obtained using the distorted structure (Calculations 6-8), to evaluate , , and
- The change in the electronic contribution to the polarization due to the F-sublattice displacement, is then given by

To calculate the total change in polarization, , one should account for the ionic contribution to this change. This contribution can be calculated from p[ion] as given above from Calculations 2 and 5: .

is then given by
.
In this example we find
electrons Å.
Considering that moved the F-sublattice was displaced by 0.045102 Å,
this calculation yields a Born effective charge for fluorine in NaF of
.

N.B.(I) In the case of spinpolarized calculations (`ISPIN`=2),
the Berry phase of the orbitals is evaluated separately for each spin direction.
This means a grep on "" will yield two sets of
and
terms, which have to be added to oneanother to
obtain the total electronic polarization of the system.

N.B.(II) One should take care of the fact that the calculated "Berry phase" term along is, in principle, obtained modulo a certain period, determined by the lattice vector ( ), the spin multiplicity of the orbitals, the volume of the unit cell, the number of -point in the "perpendicular" grid, and some aspects of the symmetry of the system. More information on this particular aspect of the Berry phase calculations can be found in Refs. [85] and [89].