In this case it is important to consider the real physics of the problem. How do the extra electrons end up in the central region, what is the physical mechanism that keeps them there? If it's some local potential, you can apply a local shift to individual atoms (or a group of atoms) to simulate this effect, by constructing a potential well for the electrons, localized in space. This can also be achieved by inserting a metallic gate and applying a potential to it.