Own definition of solid: A solid is a substance that does not flow, it is hard when looking at it at the macro scale. The atoms are tightly bound together.
The electron and proton would be called a dipole. With the wall in between, these are still two dipoles, but they are shielded from eachothers radiation.
Without the wall, this is now a configuration of two hydrogen atoms. A H_2 molecule.
The optimal distance d, would be zero, as the energy would go to – infinity.