DIPOL for Berry phase calculation

[wxiaom86]

Hi,

Do I need set DIPOL for Berry phase calculations when using LCALCPOL = TRUE? How to set the DIPOL value? From the manual, "When comparing changes in this contribution due to the displacement of an ion, this center should be chosen in such a way that the ions in the distorted and the undistorted structure remain on the same side of DIPOL (in terms of a minimum image convention)." What does it mean by 'same side' of a point?

Best,
Xiaoming

[rubel]

The dipole moment of a periodical set of charges is not well defined. It depends on the choice of origin. When Berry phase calculations are preformed, one is typically interested in a _difference_ in dipole moments. Unlike the moment itself, the difference is well defined.

Now back to your question: Let's first look at 1D problem. In this case "on the same side" means that no atoms should cross the R_center as illustrated below with two sets of atoms "a" and "b" displaced along the x-axis as a result of some structural deformation.

----a---b-------> x
Before displacement

-------a---b----> x
After displacement

  |
Good position of the R_center

     |
Bad position for the R_center

In the last case, the a-atom starts on the left side of the origin and end up on the right side, which is not desired. I am not familiar with details of the Berry phase implementation in VASP, but I suspect this can cause some pi-wrapping artefacts (jumps) in polarization. In 3D you can imagine a set of 3 planes going through R_center that should not be crossed by any atoms during deformation. In practice, you can set R_center = 0 0 0, provided no atoms cross walls of the unit cell.

I hope my interpretation is correct
Oleg

[wxiaom86]

The dipole moment of a periodical set of charges is not well defined. It depends on the choice of origin. When Berry phase calculations are preformed, one is typically interested in a _difference_ in dipole moments. Unlike the moment itself, the difference is well defined.

Now back to your question: Let's first look at 1D problem. In this case "on the same side" means that no atoms should cross the R_center as illustrated below with two sets of atoms "a" and "b" displaced along the x-axis as a result of some structural deformation.

----a---b-------> x
Before displacement

-------a---b----> x
After displacement

  |
Good position of the R_center

     |
Bad position for the R_center

In the last case, the a-atom starts on the left side of the origin and end up on the right side, which is not desired. I am not familiar with details of the Berry phase implementation in VASP, but I suspect this can cause some pi-wrapping artefacts (jumps) in polarization. In 3D you can imagine a set of 3 planes going through R_center that should not be crossed by any atoms during deformation. In practice, you can set R_center = 0 0 0, provided no atoms cross walls of the unit cell.

I hope my interpretation is correct
Oleg

Hi Oleg,

Thanks for your nice explanation. It seems very clear to me now. I have one more question about the result of the polarization.
With regard to the wrapping (to eliminate the polarization quantum), for the electronic polarization, it is obvious that the result is either modulo eR/Omega or 2eR/Omega (2 is spin degeneracy) depending on ISPIN. However, for the ionic contribution, what's the correct denominator? Does it depend on the core charges in the potential file of each species?

Best,
Xiaoming

[wxiaom86]

Btw, does VASP consider the pi-wrapping when printing the final polarization?

Best,

Xiaoming

[rubel]

Hello Xiaomin,

the ionic contribution should include Z - number of core electrons
For the ionic polarization please check Eqs. (4) - (8) in http://olegrubel.mcmaster.ca/publicatio ... 4_2013.pdf
Regarding pi wrapping I would suggest you posting the output file as I did not have much experience with Berry phase in VASP.

Thank you
Oleg

[wxiaom86]

Hello Xiaomin,

the ionic contribution should include Z - number of core electrons
For the ionic polarization please check Eqs. (4) - (8) in http://olegrubel.mcmaster.ca/publicatio ... 4_2013.pdf
Regarding pi wrapping I would suggest you posting the output file as I did not have much experience with Berry phase in VASP.

Thank you
Oleg

Thanks Oleg,

It can happen that one cannot find a DIPOL to satisfy the 'on the same side' condition for all the atoms. Unfortunately, I cannot find such a position for my system. Then, how to deal with this case? Do you or any others have any idea?

Best,
Xiaoming

[rubel]

It is possible to evaluate the polarization change as long as the initial structure (lambda=0) can be "smoothly" transformer into the final structure (lambda =1). In this case it is necessary to generate intermediate structures with 0<lambda<1, and evaluate the Berry phases (electronic and ionic) as a function of lambda. The goal is to make sure that the phase evolves smoothly as you go from lambda=0 to lambda=1. Any sudden jumps in the phase would be related to pi-wrapping and need to be (manually) subtracted. Once you know how the phase changes between initial and the final states, the polarization change can be calculated. If structural changes are large, the phase change can exceed 2pi easily. I would keep R_center fixed throughout the calculations.

I hope it will help
Oleg