# Confused about Effective Screening Medium for surfaces

Using Quantum ESPRESSO I want to perform a slab calculation with a charged ligand ($$\ce{H3O+}$$), in order to avoid dipole effects across the cell I am using the "Effective Screening Medium":

assume_isolated = "esm"
esm_bc          = "bc1"


I find the documentation a little bit confusing about the esm_w keyword, it is said that the screening will start at $$z = \pm[L_z/2 + \mathrm{esm}_w]$$ and that my slab should be centered around $$z = 0$$.

After some research, it seems that when esm is activated the cell is shifted so that $$L_z/2$$ is the top edge and $$-L_z/2$$ is bottom edge, is that right?

• I gave my +1 long ago, but just realized now that you might have been asking two questions in one post, which makes it a bit more difficult for users to be inclined to write an answer. I commented out what seemed to be the second question, which I hope helps! You can probably ask that question as a follow-up to an answer, or in a new post! Feb 24, 2022 at 3:40
• How did this go? Have you found an answer now? It would be nice to get this out of the unanswered queue since it's been there for more than 11 months now! Please update us! Sep 7, 2022 at 13:45
• @NikeDattani Thank you for the reminder. When working with ESM using Quantum Espresso the slab must be centered around z = 0, everything described above is right. Sep 7, 2022 at 14:00
• Does that mean you've figured out the answer to the question? If so, could you please write a self-answer? I think it would be useful for future users! Sep 7, 2022 at 14:01

The Effective Screening Medium (ESM) is a method that allows performing calculations in a 2D framework. The method is using Green functions, depending on the boundary conditions of these functions, different conditions can be imposed within the unit cell:

• "bc1" Vacuum-Slab-Vacuum
• "bc2" Metal-Slab-Metal
• "bc3" Vacuum-Slab-Metal

As you might have guessed, the method focuses on electrochemistry and can be used to perform grand-canonical DFT. The authors put an emphasis on two advantages: With ESM the electrostatic potential is not ill-defined anymore even in a plane-wave code, and the method gives the correct "image charge contribution" (if someone in the comment could give more details about this...)

Practically in Quantum Espresso one has to activate the ESM with assume_isolated = "esm" and specify the boundary condition with esm_bc = "bcX". When activated the unit cell will not span from $$[0 ; z]$$ but from $$[-z/2 ; z/2]$$. The slab must be centred around 0, which in this case is the centre of the cell. You still need enough vacuum on both sides for the electronic density to decay to 0 before reaching the screening medium. (~ 10 Å of vacuum)

To my understanding, this is some kind of improved "dipole correction" because you get completely rid of the periodicity along one dimension. But if someone could precise what are the advantage over a regular dipole correction this would be much appreciated.

• This is largely correct. Regarding the difference between ESM and conventional dipole-corrections, the results are similar for neutral systems. One added benefit of ESM is that potential along the z-direction is truly decoupled since the Poisson equation is solved with open BCs, rather than correcting the periodic Poisson solution with added dipole. This also speaks to the proper treatment of image charges (no periodic artifacts). For charged systems, ESM introduces special BCs as you pointed out that aid electrochemical modeling (i.e., you can treat the system as a parallel plate capacitor). Sep 22, 2022 at 17:48
• +1. Just now I got a bit confused because both the question and answer were posted (byt the same person) on Sept 22 but comments existed on Sept 7, which was confusing, until I finally noticed that the year was different! I came here because you mentioned electrochemistry, and wondered whether or not you might have any input about this question: mattermodeling.stackexchange.com/q/10208/5 Jan 10 at 20:17