Spontanious Polarization Value of PbTiO3

[okuno]

Dear Vasp Users.

I'm now calculating the spontanious polarization of PbTiO3.
I had optimize the atomic position, and then re-calculate the
ground state wavefunction with the optimized atomic position,
finally, I calculated polarization by Berry phase method.

The experimental spontanious polarization is about 0.75C/m2 (at 295K),
and FLAPW calculation is 0.88C/m2,
but I got rather deviated value from these.

I know the calculated spontanious Polarization has ambiguity by
module 2*c*e/V (V vomule of the system, c length of c-axis of lattice, the spontanious polarization direction, e ie elementary electron charge.).

So I had changed the atomic position from the centro-symmetric position
to optimized ferro electric state like

z(\lambda) = z_{0} + lambda * (z - z_{0})

where , z_{0} is the centro-symmetric position of each atom in perovskite
structure, and z is optimized atomic position. lambda we vary 0 ( centro-
symmetric case) to 1 (optimized position). and difference the
lambda=1 and lambda=0 value to get the spontanious polarization.

I had get the result of the polarizition of sysmte with various lambda.
like below.

lambda <Rev> <Rbp> <Rion> (e/Angst)
0.0 0.00 0.00 20.84263
0.1 -0.00097 1.27466 19.93480
0.2 -0.00188 2.54734 19.02697
0.3 -0.00249 3.81699 18.11915
0.4 -0.00288 -3.25519 17.21132
0.5 -0.00291 -1.99583 16.30349
0.6 -0.00256 -0.74234 15.39566
0.7 -0.00177 0.50541 14.48784
0.8 -0.00053 1.74711 13.58001
0.9 0.00118 2.98271 12.67218
0.925 0.00169 3.29062 12.44522
0.95 0.00223 3.59818 12.21827
1.0 0.00341 -1.34586 11.76435

We can see the <R>bp, berry-phase term, has
discontinuity between 0.3 and 0.4, and also between
0.95 and just 1.0. The discontinuity between 0.3 and 0.4
is ~ 2*c*e/V, so if we plus 2*c*e/V to <R>bp from lambda=0.4 to lambda=0.95
we can get liner line from 0 to 0.95 with lambda.
But the discontinuity between lambda=0.95 and 1.0 is not
~ integer * 2*c*e/V.

Why such a discontinuity happens ??

If we linealy interpolate the spontanious polarization at lambda=1.0 value
by the line which we got between lambda=0.0 to 0.95, we can get the reasonable value of spontanious polarization (0.88C\m2!)!

I want to know the reason of the discontinuity between lambda=0.95
and lambda=1.0 whichi is not integer * 2*c*e/V.

My input file is KPOINT is (6,6,6)

and for scf calculation below,

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
ALGO = NORMAL # default for IALGO=38
IALGO = 38 # default Davodason block iteration scheme
EDIFF = 1E-06 # stopping -criterion for ELM
PREC = High
NELM =50 # maximum electronic SC steps (default=60)
NELMIN = 6 # minimum number of SC steps default=2
NELMDM = -3 # number of non-SC steps at the beginning

GGA = 91 # GGA PB PW LM 91 PE RP
ISMEAR = 0
SIGMA = 0.1

# for berry phase calculation is
SYSTEM = PbTiO3
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
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)

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

My Atomic position is
PbTiO3-tetra
1.00000000000000
3.8958188134500000 0.0000000000000000 0.0000000000000000
0.0000000000000000 3.8958188134500000 0.0000000000000000
0.0000000000000000 0.0000000000000000 4.1685261303900001
1 1 3
Direct
0.0000000000000000 0.0000000000000000 0.0000000000000000
0.5000000000000000 0.5000000000000000 0.5380810847389981
0.5000000000000000 0.5000000000000000 0.1044018384179992
0.0000000000000000 0.5000000000000000 0.6165899713899989
0.5000000000000000 0.0000000000000000 0.6165899713899989

[okuno]

Sorry Self reply.

It is indistinct　 to see my calculated value.

lambda <Rev> <Rbp> <Rion> (e/Angst)
0.0 0.00 0.00 20.84263
0.1 -0.00097 1.27466 19.93480
0.2 -0.00188 2.54734 19.02697
0.3 -0.00249 3.81699 18.11915
0.4 -0.00288 -3.25519 17.21132
0.5 -0.00291 -1.99583 16.30349
0.6 -0.00256 -0.74234 15.39566
0.7 -0.00177 0.50541 14.48784
0.8 -0.00053 1.74711 13.58001
0.9 0.00118 2.98271 12.67218
0.925 0.00169 3.29062 12.44522
0.95 0.00223 3.59818 12.21827
1.0 0.00341 -1.34586 11.76435

We can see the <R>bp, berry-phase term, has
discontinuity between 0.95 and 1.0 (lambda).
This discontinuity is problem.

[lufly89]

How did you get "optimized atomic position"? Through ISIF?