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LCALCPOL-tag: Macroscopic polarization (again)

LCALCPOL=.TRUE. (Available as of VASP.5.2) switches on the evaluation of the Berry phase expressions for the macroscopic electronic polarization (like LBERRY=.TRUE., see Sec. 6.67.1). For LCALCPOL=.TRUE., however, VASP calculates the electronic contribution to the polarization, along the three reciprocal lattice vectors $ {\bf G}_i,\; i=1,2,3$ (i.e.  $ \sum^3_{i=1}{\bf P} \cdot {\bf G}_i$) in a single run (unlike LBERRY=.TRUE.).

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

Rerun the example from the previous section ( 6.67.1) using LCALCPOL=.TRUE.

With INCAR file:

PREC = Med
EDIFF= 1E-6

ISMEAR = 0
DIPOL  = 0.25 0.25 0.25

LCALCPOL = .TRUE.

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.

The OUTCAR file should now contain the following lines:

            Ionic dipole moment: p[ion]=(     2.25510     2.25510     2.25510 ) electrons Angst

 Total electronic dipole moment: p[elc]=(     0.00000     0.00000     0.00000 ) electrons Angst

To calculate the change in the electronic polarization of NaF due to the displacement of the fluorine sublattice we repeat the previous calculation with 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

The OUTCAR should now contain something very similar to the following lines:

            Ionic dipole moment: p[ion]=(     2.25510     2.25510     1.93939 ) electrons Angst

 Total electronic dipole moment: p[elc]=(     0.00000     0.00000     0.36061 ) electrons Angst

From the above one easily recognizes that the change in the electronic dipole moment due to the F-sublattice displacement is:
$ \Delta {\rm p[elc]}=0.36061\hat{z}$ electrons Å

and the corresponding change in the ionic dipole moment:
$ \Delta {\rm p[ion]}=1.93939-2.25510=-0.31571\hat{z}$ electrons Å

Thus the total change is found to be:
$ \Delta {\rm p[tot]}=0.36061-0.31571=0.0449\hat{z}$ electrons Å
and considering that the F-sublattice was displaced by 0.045102$ \hat{z}$ Å, these calculations yield a Born effective charge for fluorine of $ Z^{*}=0.0449/0.045102=-0.995$, exactly the same value as in Sec. 6.67.1 (n.b.: $ Z^*_{ij}=(\Omega/\vert e\vert)\partial P_i / \partial u_j$).


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N.B. Requests for support are to be addressed to: vasp.materialphysik@univie.ac.at