reference position bug during dipole moment calculation?

[Phil G.]

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

[Matt W]

Hello,

not a complete answer to all your points (and I've not looked at the files), but a couple of ideas.

(i) to get a good result for the non-periodic direction I'd suggest using a non-periodic setup in that direction - life is much easier then. Personally using the WAVELET poisson solver and XZ periodic boundary conditions has been reliable (i.e.make the slab normal in Y direction). The slab need to be centred at Y/2 in that case.

(ii) to get a dipole moment in a periodic direction you need to use the berry phase dipole moment.

Matt

[hut...@chem.uzh.ch]

Hi

all choices of reference position should give (for a non charged
system) the same polarization in a Berry phase calculation.
Different reference positions are useful to minimize the number
of hops between branches of the complex logarithm.
Different branches are apart by L/2pi in cubic boxes. For non-cubic
boxes you have to use the more complicated formula with the box matrix.

If your results should not be different by other values than that.

Polarizations are given by dipole moment per volume.

regards

Juerg Hutter
--------------------------------------------------------------
Juerg Hutter Phone : ++41 44 635 4491
Institut für Chemie C FAX : ++41 44 635 6838
Universität Zürich E-mail: hut...@chem.uzh.ch
Winterthurerstrasse 190
CH-8057 Zürich, Switzerland
---------------------------------------------------------------

-----"'Phil G.' via cp2k" <cp...@googlegroups.com> wrote: -----
To: "cp2k" <cp...@googlegroups.com>
From: "'Phil G.' via cp2k" <cp...@googlegroups.com>
Date: 07/12/2018 04:33PM
Subject: [CP2K:10512] reference position bug during dipole moment calculation?

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[attachment "input.inp" removed by Jürg Hutter/at/UZH]
[attachment "out" removed by Jürg Hutter/at/UZH]
[attachment "mom-moments-1_200.dat" removed by Jürg Hutter/at/UZH]

[Phil G.]

Dear Matt and Juergen,

thank you for your replies and hints.

@Matt: because I want to calculate the bulk polarization, I have to use the periodic system. So the Berry phase method was used  (in the DFT/PRINT section under MOMENTS I used PERIODIC .TRUE.). Do you think that the result would be different if I use non-periodic setup as you suggested?

@Juerg: yes, exactly I get the same results (with very small distinctions of the dipole moments after using different reference points). But why is the value of the polarization (as calculated by the dipole moment per slab volume) much smaller than the experimentally obtained value?

I would like to add a remark (as in my first mail above) that the sign of Y-value of the reference point is opposite than I gave it (e.g. if I write Y=a_y /2 (user defined value), then in the dipole moment output file it looks so: Y= - a_y / 2 , with an opposite sign). Is there a bug?

Kind regards,

Phil

[hut...@chem.uzh.ch]

Hi

have you checked that the reference point in the output is just
a periodic image of your input value?
Internally we do:
r_val = PBC(r_val)

regards

Juerg

--------------------------------------------------------------
Juerg Hutter Phone : ++41 44 635 4491
Institut für Chemie C FAX : ++41 44 635 6838
Universität Zürich E-mail: hut...@chem.uzh.ch
Winterthurerstrasse 190
CH-8057 Zürich, Switzerland
---------------------------------------------------------------

-----"'Phil G.' via cp2k" <cp...@googlegroups.com> wrote: -----
To: "cp2k" <cp...@googlegroups.com>
From: "'Phil G.' via cp2k" <cp...@googlegroups.com>

Date: 07/13/2018 11:51AM
Subject: [CP2K:10523] Re: reference position bug during dipole moment calculation?

[Sergiu C]

Dear CP2K developers,

does the printed electric dipole moment sign correspond to normal convention for electric dipole (from negative pole to positive pole)?

Thank you.

Sergiu

EDIT:

I checked on a H2O molecule AIMD under applied electric field - CP2K follows the standart physics convention: P from - to +, E from + to -

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