On the electronic polarization

[okuno]

Dear Vasp users.

I'm biginner of Vasp program.

I'm now checking the method of electron polarizion by Vasp.
I want to check the spotanious polarization value of PbTiO3 which
has publised value 0.88 C/m^{2} (G. Saghi-Szabo et al PRL vol80(4321)).

The calculated result by vasp was below ( with ferromagnetic case)

Expectation value term: <R>ev
<R> = ( 0.00000, 0.00000, 0.00320 ) electrons Angst

Berry-Phase term: <R>bp
<R> = ( 0.00000, 0.00000, -2.04138 ) electrons Angst
+( 0.00000, 0.00000, 8.33705 ) *c
ionic term: <R>ion
<R> = ( 19.47909, 19.47909, 11.76435 ) electrons Angst

and with centro-symmetric case (not distorted and not ferro electronic case)

Expectation value term: <R>ev
<R> = ( 0.00000, 0.00000, 0.00000 ) electrons Angst
Berry-Phase term: <R>bp
<R> = ( 0.00000, 0.00000, 0.00000 ) electrons Angst
+( 0.00000, 0.00000, 8.33705 ) *c
ionic term: <R>ion
<R> = ( 19.47909, 19.47909, 20.84263 ) electrons Angst

I thnk <R>bp is berry phase term but what is <R>ev ?
I want to compare C/m^{2} whch is written by PRL vol(80)p4321.
What should I do for transforming the vasp unit to C/m^{2}?

I think I must divide the polarization by volume(A^{3}) for transforming
it to C/m^{2} but what is the unit of polarization by vasp (electrons Angst)?
Is it e*A ?

My INCAR fils is like below, '\

For SCF calculation

SYSTEM = PbTiO3_tetra
#Startparameter for this Run:
NWRITE = 2; LPETIM=F write-flag & timer
ISTART = 0 job : 0-new 1-cont 2-samecut
ICHARG = 2 initial charge 0-calc 1-from CHGCAR, 2-super potision


#Electronic minimization
ENCUT = 500.0 # ev
ALGO = NORMAL # default for IALGO=38
IALGO = 38 # default Davodason block iteration scheme
EDIFF = 1E-06 # stopping -criterion for ELM
PREC = Accurate

NELM =40 # maximum electronic SC steps (default=60)
NELMIN = 2 # minimum number of SC steps default=2
NELMDM = -3 # number of non-SC steps at the beginning
#( for ISTART=0 from random) negative means a delay only for start config
# positive mean apploed after each ion movement

GGA = 91 # GGA PB PW LM 91 PE RP

# DOS related TAG
ISMEAR = 1

for Berry Phase.
SYSTEM = PbTiO3 tetra
#Startparameter for this Run:
NWRITE = 2; LPETIM=F write-flag & timer
ICHARG = 11 initial charge 0-calc 1-from CHGCAR, 2-super potision


#Electronic minimization
ENCUT = 500.0 # ev
ALGO = NORMAL # default for IALGO=38
IALGO = 38 # de

EDIFF = 1E-06 # stopping -criterion for ELM
PREC = Accurate

NELM =40 # maximum electronic SC steps (default=60)

GGA = 91 # GGA PB PW LM 91 PE RP

ISMEAR = 0
SIGMA = 0.1

#Berry Phase
LBERRY = .TRUE.
IGPAR = 3
NPPSTR = 20
DIPOL = 0.50 0.50 0.50

[admin]

1) Rev is the 'expectation value' term, which comes from the augmentation charge distribution (please see refs 54 and 56 of the online handbook) which is particular to the US-PPs.
2) units : yes, VASP calculates the Berry phase terms in electrons*Angstroem
3) please let me make 2 short remarks concerning your INCAR:
NPPSTR =20 may be too large
for insulators, ISMEAR=0 (or -5) is more appropriate than 1

[okuno]

Dear administrator.
Thank you for your reply.

I wan to reduce the caluculated polarization to the observed spontanious polarization.

I think I must take the difference between the relaxed ferroelectronic state and the centrocymmetric paraelectronic state
on the ionic parts and electronic parts.

On the ionic parts, it is only the defference of calculated value.
But the electronic Berry phase case, there are 2pi part of phase,
P_{mod}, so I think I must add P_{mod} with multiply some interger to the P_{bp} parts.

Is the 2pi part , P_{mod}, in the second line of output
<R>bp ? ((8.33705)*c part sample below.), or we must devide it by
the electron number ( in this case 2 ) ?

<R> = ( 0.00000, 0.00000, -2.04611 ) electrons Angst
+( 0.00000, 0.00000, 8.33705 ) *c

[vasp]

Could you show your other input files? thank you very much.