Comparing Bader charge difference with z-averaged charge difference
I am currently studying clustered metal-semiconductor interfaces. I am assessing the charge transferred to the metal in such a case.
One of the ways to find charge transfer occuring at the interface is to use the total cell charge averaged in the x- and y-directions, as a function of the direction perpendicular to the interface (say, rho(z)). Then the quantity of interest is: rho_interface(z) - rho_metal(z)- rho_sc(z). This way one gets the "charge density" of the cell as a function of z-direction.
Another way, one could do is the "bader charge difference" of these cells, i.e. BADER_CHG_interface - BADER_CHG_metal - BADER_CHG_sc. To compare the two approaches I wrote the difference in bader charges of atoms as a function of z (z-coordinate of a bader-analysed atom), as well.
What I am looking for is a qualitative agreement between the two approaches. That means the region in which the first method goes negative/positive I would like to see the bader charge differences to be negative/positive as well. However, I do not find a qualitative agreement for a handful of the studied cases. In fact in some case, these two approaches show opposite signs. Does anyone know, why should this qualitative agreement be missing in some cases?