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now I am calculateing the polarization of PbTiO3 with Berry-phase theory in VASP.
I tried to reproduce the theoretical value of 88uC/cm**2 .
The calculated result by vasp was below


For distorted case:
Expectation value term: <R>ev
<R> = ( 0.00000, 0.00000, 0.00391 ) electrons Angst
Berry-Phase term: <R>bp
<R> = ( 0.00000, 0.00000, -3.63766 ) electrons Angst
+( 0.00000, 0.00000, 4.16404 ) *2 n
ionic term: <R>ion
<R> = ( 19.49126, 19.49126, 11.23513 ) electrons Angst


For non-distorted 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, 4.16404 ) *2 n
ionic term: <R>ion
<R> = ( 19.47909, 19.47909, 20.82021 ) electrons Angst

The volume of cell : 63.28

I donot know how to use the results to get the polarization,
My method is :
(0.00391-3.63766+11.23513-20.82021)*1.6E(-19)/63.28=3.34E(-20) C/A**2=334uC/cm**2
the theoretical value is 88uC/cm**2.


Is the expressions I used right ?
and how to use the second line in Rev,such as( 0.00000, 0.00000, 4.16404 ) *2 n.

Thanks for your attenton

1) have you taken the averages over all 3 lattice directions to obtain the values?
2) the ( 0.00000, 0.00000, 4.16404 ) *2 n denotes the indeterminacy of the Berry Phase term, (please have a look at the references given in the online handbook)

I did not take the averages over 3 lattice directions.
As PbTiO3 is only polarize along c axis, I only calculate the polarization along the G3. Am I right?