The three remaining terms in the many-body Hamiltonian are the electron-electron, electron-ion and ion-ion electrostatic interactions. When studying atomic and molecular systems, the evaluation of these terms simply involves summing up all the pairwise interactions present.
In a solid system, the situation is complicated by the use of periodic boundary conditions. Now the sum of pairwise interactions includes the infinite number of periodic images of each particle. The methods used to deal with these sums over periodic images are described in the following chapter, which deals with the details of performing QMC calculations on solids.