[QE-users] Ionic Polarization calculation in Quantum Espresso

[Paul, Tanmoy Kumar]

Hello, QE Users,

I am using Quantum Espresso v6.7 and having some issues with berry phase calculation to find ferroelectric polarization. I cannot find the significance of using mod 2 for ionic polarization calculation. Let's take BaTiO3 as an example.

For non-centrosymmetric BaTiO3, the ionic polarization reported is as follows:

[cid:eca35530-51f2-41d6-9f98-c362c7cb49d3]

Case-I: If I look at the z-coordinate of Ti, it is slightly upward than the centrosymmetric position and the ionic phase is calculated as charge*position*G-vector=12*0.5199*0.98912=6.17=0.17(mod 2)
Case-II: If Ti shifts more upward, for example z co-ordinate is 0.61, then the ionic phase = 12*0.61*0.98912= 7.24= -0.76 (mod 2)
Case-III: If Ti is in centrosymmetric position, then ionic phase contribution=12*0.5*.98912=5.93= -0.07 (mod 2)
Although in both case-I and case-II, Ti shifts upward, first one gives positive ionic phase contribution while second one gives negative ionic phase contribution with reference to case-III. Both should have given same sign of ionic phase. So, why should we take mod 2 wrapping?
May be 0.5 to 0.61 ionic displacement is not possible for BaTiO3, but it is the case for some other ferroelectrics i.e. HfO2. I know that polarization calculation in quantum espresso is not thoroughly tested. But what should be the general procedure for finding ionic polarization of all ferroelectrics? Your response will highly oblige me.

I am attaching input files for scf and non-scf calculation herewith.

-Regards
Tanmoy Kumar Paul
1st year Graduate Student
Purdue University, USA


.scf input:

&control
    calculation = 'scf'
    restart_mode='from_scratch',
    prefix='asymm',
    tstress = .true.
    tprnfor = .true.
    pseudo_dir = 'Quantum_espresso/pseudos',
    outdir='Quantum_espresso/outdirb',
 /
 &system
    ibrav= 6,
    nat= 5,
    ntyp= 3,
    celldm(1)=7.5438,
    celldm(3)=1.011
    ecutwfc =60.0,
    ecutrho=600.0,
    occupations='fixed',
 /
 &electrons
    mixing_mode = 'plain'
    mixing_beta = 0.4
    conv_thr =  1.0d-8
 /
 &ions
 /
 &cell
 /

ATOMIC_SPECIES
Ba    137.34 Ba.pbe-nsp-van.UPF
Ti    47.90     Ti.pbe-sp-van_ak.UPF
O     16.0      O.pbe-rrkjus.UPF

ATOMIC_POSITIONS {crystal}
Ba            0.0000000000        0.0000000000        0
Ti            0.5000000000        0.5000000000        0.51427
O             0.5000000000        0.5000000000        0.974477
O             0.5000000000        0.0000000000        0.4876
O             0.0000000000        0.5000000000        0.4876

K_POINTS {automatic}
5 5 5   0 0 0


.nscf input:

&control
    calculation = 'nscf'
    prefix='asymm',
    pseudo_dir = 'Quantum_espresso/pseudos',
    outdir='Quantum_espresso/outdirb',
    lberry=.true. ,
    gdir          = 3,
    nppstr        = 20
 /
 &system
    ibrav= 6,
    nat= 5,
    ntyp= 3,
    celldm(1)=7.5438,
    celldm(3)=1.011
    ecutwfc =60.0,
    ecutrho=600.0,
    occupations='fixed',
 /
 &electrons
    mixing_mode = 'plain'
    mixing_beta = 0.4
    conv_thr =  1.0d-8
 /
 &ions
 /
 &cell
 /

ATOMIC_SPECIES
Ba    137.34 Ba.pbe-nsp-van.UPF
Ti    47.90     Ti.pbe-sp-van_ak.UPF
O     16.0      O.pbe-rrkjus.UPF

ATOMIC_POSITIONS {crystal}
Ba            0.0000000000        0.0000000000        0
Ti            0.5000000000        0.5000000000        0.51427
O             0.5000000000        0.5000000000        0.974477
O             0.5000000000        0.0000000000        0.4876
O             0.0000000000        0.5000000000        0.4876

K_POINTS {automatic}
5 5 20   0 0 0

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