reference position bug during dipole moment calculation?

Phil G. phil... at aol.com
Thu Jul 12 14:33:05 UTC 2018

```Dear all,

in order to get a bulk polarization of a ferroelectric slab system (2x2x1
slab with 3D periodic boundary condition) I let CP2K start to calculate the
dipole moments of the slab system (in fact the unit cell has the hexagonal
shape, but it does not matter if I cut off a piece of the large system of
the duplicates of the unit cell in xyz coordinate system and this cut piece
satisfy the 3D pbc in the xyz coordinate system?). In order to check the
influence of the choice of a reference point on the dipole moment
calculation, I let start several calculations with different reference
points, e.g. COAC, ZERO, user_defined -> reference_point x y z.

If using the reference_point ZERO, then I notice an non-explainable
difference between the quantity of the dipole moments for up-polarized slab
and down-polarized slab (the slabs are the same, but are only 180 degree
rotated to each other) and it seems to be the false choice for the dipole
moment calculation.
If I use COAC as the reference point, then the both dipole moment values
are almost of the same quantity (absolute value) in z direction, but of
opposite sign (which is correct). If using COM as the reference point, then
I am wondering why not really the center of the slab was used as expected
(consider the slab system with lengths a_x, a_y, and c_z along the three
x,y,z coordinate axes, so I expect the COM to be nearly at {a_x / 2, a_y /
2, c_z / 2}, but in the dipole moment file the reference point lies outside
of the slab system. Why?
If using the reference_point USER_DEFINED, REFERENCE_POINT X Y Z , in which
X, Y, and Z are of an arbitrary choice, for example at the center of the
top slab surface (X=a_x / 2 , Y=a_y / 2, Z=0) and the z=0 is exactly the
surface and below it there is the 2x2x1 slab system (i.e. with negative c_z
lying in the bottom slab surface), then after calculation I get the info
from dipole moment file that the y value has the opposite sign. Is there a
bug in the cp2k during the dipole moment calculation?

After obtaining the calculated dipole moment values, I am able to calculate
the bulk polarization if the z-dipole moment (which is much larger than in
x- and y- directions) is divided by the slab volume (2x2x1 unit cells in
the x,y,z coordinate system). Is that correct? If yes, why the value is
much smaller compared to the experimental value at room temperature? (e.g.
the experimental value of the polarization is 0.71 C/m^2  [APL 12 (2009),
209]  and the calculated value is 0.042 C/m^2 , i.e. it is at least one
order of magnitude smaller).
Is there any mistake I have calculated or should I take account anything
for correct polarization calculation?

The input file, output and dipole moment file after 200 geometry
optimization steps are attached here below.

Kind regards,

Phil

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