Confused about Effective Screening Medium for surfaces

Question

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?

Answer 1

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.