[QE-users] Total energy of charged slabs

[Zhenyao Fang]

Dear pwscf users,

I am performing some calculations on negatively charged slabs (with one additional electron), and I’m mainly focusing on the energy difference between charged system and neutral system. With ions fixed, I found that the charged system has a higher energy than the neutral system, instead of being lower. 

The energy difference dE = E(q=-1) - E(q=0) is around 3.944 eV. The LUMO position of the neutral slab is 3.462 eV, and the vacuum level for the neutral slab is 7.654 eV. Besides, by inspecting the charge difference plots, the additional charge is localized inside the slab. I understand that there could be problems about jellium background, so I used the package “sxdefectalign2d” to correct the interactions due to periodic images, and the total energy of the charged slab remains the same as the size of vacuum increases. 

I’m quite confused by the fact that the total energy would increase with one more electron. Since the additional charge is mainly inside the slab, it should lower the energy and be stabilised inside the slab. Therefore, I was wondering how I can reconcile these controversies. Besides, another related question is how we define the zero energy in QE? In other words, does LUMO larger or smaller than zero possibly imply the stability of the system?

I am looking forward to your replies. Thanks in advance.

Best,
Zhenyao Fang