# [Pw_forum] finite electric field calculation (Paolo Umari)

umari at democritos.it umari at democritos.it
Mon Aug 4 10:43:16 CEST 2008

```Dear Alan,

>    I have two questions about finite electric field calculation based on
> Berry phase.
>     First, I have found in the source code that the formula to calcuate the
> polarization in the presence of finite electric field is different in
> Version 4.0 from in Version 3.2. A couple of factors like sqrt(2) and alat
> are added in the new version. I just want to make sure that if I use
> ultrasoft psedupotential and turn on finite electric field, does the latest
> version (4.0) of PWSCF calculate the polarization and atomic force
> correctly? No offense intended.

In the version 3.2 the electric field intensity was erroneously divided
by a factor of sqrt(2.), at the same time the reported polarization
was multiplied by the same factor. Note that sqrt(2) is the value
of the electronic charge in Rydberg atomic units (in Hartree atomic
units this value is 1.) Note also that in the linear limit this error
doesn't cause any change in the calculated polarizabilitis.

Moreover, the version 4.0 has other improvents with respect to the 3.2:
-better treatment of the quantum of polarization
-it works also for non-orthorombic cells
-parallel also for gdir=1, and gdir=2
-faster
-atomic forces are correctly calculated also for US pseudopotentials

permits to treat electric fields on  arbitrary Cartesian directions
and reports the polarization also on Cartesian coordinates.
You can find some documentation in the exemple 31.

>    Second, is there a range of electric field in which the Berry phase
> method works? In the example31 the electric field is 0.001 a.u. I want to
> calculate some properties under the electric field as large as 0.01 a.u. In
> principle I think the method works for any value of electric field but in
> practice any restriction on the maximum of electric field?

Above a certain maximum value of the electric field, which depends
on the system and on the number of k-points in the string,
the electric enthalpy functional can no longer be minimized. Based on
my experience, usually elctric fields of 0.01 a.u. can be reached.
Note that , depending on the studied system, non-linear effects
can become important.

Best regards,

Paolo Umari

DEMOCRITOS

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