Strange total energy results for a graphene with positive and negative charges.

[yige]

Hi, guys:

I have observed some strange total energy results for a charged graphene embedded in a Jellium background. My system is very simple, a periodic graphene layer in x-y plane and a vacuum layer in z direction. Three different heights of the vacuum layers (i.e., the distance between the charged slabs in z direction) are tried, H=60A, 80A and 100A, respectively.

Given a hole injection of 0.15e/C-atom, the total energy results are -30.797eV, -23.657eV, and -16.551eV, for H=60, 80, and 100A, respectively.
Given an electron injection of -0.15e/C-atom, the total energy results are -55.678eV, -55.678eV, and -55.646eV, for H=60, 80, and 100A, respectively.

In vasp manual, there is a discussion "It is important to emphasize that the total energy can not be corrected for charged slabs, since a charged slab results in an electrostatic potential that grows linearly with the distance from the slab (corresponding to a fixed electrostatic field). It is fairly simple to show that as a result of the interaction between the charged slab and the compensating background, the total energy depends linearly on the width of the vacuum. Presently, no simple a posteriori correction scheme is known or implemented in VASP. Total energies from charged slab calculations are hence useless, and can not be used to determine relative energies."

My understanding is that the linear dependence of total energy upon H is the consequence of the electrostatic interactions between the charged slabs and the Jellium background. If so, I expect a very similar change of total energy (with respect to vacuum layer height) in my two systems: a positively charged graphene in a negative Jellium, a negative charged graphene in a positive Jellium. But my vasp results are so different. There is a tiny change in total energy for negatively-charged-graphene/positive-Jellium as H changes from 60A to 100A, i.e., 30meV. While for the positively-charged-graphene/negative-Jellium, the total energy change (as H varying from 60A to 100A) is huge, i.e., 14eV. Something is wrong here? Does anyone has the theoretical formula to describe the linear relation of total energy as a function of H, as pointed out in VASP manual?

Thank you very much.

[tlchan]

For the negatively-charged graphene sheets, since you are using a very large vacuum space, the electrostatic potential in the vacuum region may be very low, you may want to check if there are electrons ejected from the graphene into the vacuum space. Maybe this gives rise to the different behaviour between the positively and negatively charged calculations.