Clarification on parabolic pbc correction

[Mauro Sgroi]

Dear developers,

I'd like to receive a clarification on the PBC correction.

Environ gives this warning:

WARNING: you are using the parabolic pbc correction;  the potential shift above must be added to band and Fermi energies.

Should I add the shift also to the total energy?

Or this is already taken into account by the software?

Thanks a lot and best regards,

Mauro Sgroi.

Centro Ricerche FIAT.

[andr...@gmail.com]

Thanks Mauro, 

this is a very important point, which is probably not so clear in the documentation. In a periodic plane-wave simulations, for a neutral system, a shift in the potential will not change the energy of the system: if you think at the total electrostatic energy as being the integral of potential times charge, if you expand this in reciprocal space the G=0 contribution cancels out because the G=0 component of the charge is zero for a neutral system, regardless of the value of V(G=0).  By default plane wave codes set V(G=0)=0, which is a way to impose that the term that depends on the total charge is equal to zero and can be though of as adding a uniform (G=0) compensating charge background to the system. 

However this means that the average of the potential is fixed to zero, but the alignment of the electrostatic potential in a system will change as we change the size of the simulation cell or any other property of the system. In Environ the potential is shifted so as to go to zero infinitely far from the QM system. This allows to have a fixed and reasonable reference for the electrostatic potential in your calculations, e.g. you can directly use the Fermi energy to estimate the potential of zero charge of the system and it will not depend on the amount of vacuum you have in your simulation or other numerical details. The only catch is that, for the way Environ deals with electrostatics, there is a constant shift that needs to be included due to the fact that nuclear charges are modeled as gaussian instead of point-like. This shift is constant (it does not depend on the positions of the atoms, but only depends on the charges of the atoms and the cell size) and needs to be included only for quantities that are defined with respect to the reference potential, such as the potential drop in the system and the band alignment. 

In principles the above discussion is only valid for a neutral system, for a charges system instead the energy will depend on the absolute value of the shift. In practice we never want to deal with 2D charged systems, as they would have an infinite energy anyway. In case you are simulating a charged slab, you should also probably adding a diffuse layer somewhere to flatten the electrostatic potential at infinity. 

I hope this helps,

Best,

Oliviero