Developers Manual:Ion-Ion interaction
The ion-ion interaction term is tricky to treat, as is an inifinte sum with a finite result. The standard way to handle it is through an Ewald sum, however in Octopus this is done in a slighlty different way.
The energy term (per volume unit) is:
is a sum over atoms inside the cell, only over atoms outside and is over all the atoms.
The first separation that is
as the first term is the energy of a finite system, the second can be seen as the interaction of the particles in the cell with the potential generated by the particles outside, we will call it .