Comparing Bader charge difference with z-averaged charge difference

[somil]

Hi,

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?

cheers,
somil