Polarisation -reg

[GJK]

Hi,

It is very well understood from tutorial http://quantumwise.com/documents/tutorials/latest/Polarization/index.html/ that ATK calculates electronic Pe and ionic Pi polarisation.

My questions are???
1. Why you use the interval [-0.5,0.5] and can we use some other interval values by changing in the code.If then how and what values should we use???

2. How to calculate Total cartesian polarization(formula)
(In the tutorial we have the formula for Pq=e* R/omega but no formula for Total cartesian polarization)

3.Is Total cartesian polarization same as total fractional polarisation???

4.What polarisation value should we consider for the result is it Total cartesian polarization (or) Polarisation quantum??? which is correct

[Anders Blom]

The answer to all questions, essentially, is that the fractional polarization is just the Cartesian one divided by Pq (and modulus 2pi).

[GJK]

When I tried the calculation for
+------------------------------------------------------------------------------+
      | Polarization                                                                 |
      +------------------------------------------------------------------------------+
      | Electronic fractional polarization.                                          |
      | Values wrapped to the interval [-0.5,0.5]                                    |
      |       [ -1.25164671e-15 ]                                                    |
      |  Pe=  [ -6.42868666e-16 ]                                                    |
      |       [ -4.71901310e-01 ]                                                    |
      +------------------------------------------------------------------------------+
      | Ionic fractional polarization.                                               |
      | Values wrapped to the interval [-0.5,0.5]                                    |
      |       [  0.00000000e+00 ]                                                    |
      |  Pi=  [  0.00000000e+00 ]                                                    |
      |       [ -2.44642000e-01 ]                                                    |
      +------------------------------------------------------------------------------+
      | Total fractional polarization. Pt = Pe + Pi.                                 |
      | Values wrapped to the interval [-0.5,0.5]                                    |
      |       [ -1.25164671e-15 ]                                                    |
      |  Pt=  [ -6.42868666e-16 ]                                                    |
      |       [  2.83456690e-01 ]                                                    |
      +------------------------------------------------------------------------------+
      | Total cartesian polarization.                                                |
      |       [ -1.24465114e-15 ]                                                    |
      |  Pt=  [ -6.39275613e-16 ] C/Meter**2                                         |
      |       [  2.84624464e-01 ]                                                    |
      +------------------------------------------------------------------------------+
      | Polarization quantum.                                                        |
      |       [  9.94410906e-01 ]                                                    |
      |  Pq=  [  9.94410906e-01 ] C/Meter**2                                         |
      |       [  1.00411976e+00 ]                                                    |
      +------------------------------------------------------------------------------+
    I found that the term modulus 2pi is not required.I got the results with Pf=Pt/Pq.Why did u mentioned modulus 2pi.Kindly clarify?

My first question is not answered why the values are wrapped up in the interval [-0.5,0.5]

[Anders Blom]

The tutorial states this clearly: what you are computing is a phase (the Berry phase), and this only makes sense in the interval which has width 2pi. You can choose this interval as you want, from -3pi to -pi, or 125pi to 127pi, the choice is arbitrary. And this is also why the tutorial emphasizes that only differences in the Berry phase between two calculations (wrapped to the same 2pi interval, of course) are meaningful.