The authors derive formulas for the general four-center integral and its Bloch sum within the basis of optimally localized muffin-tin orbitals in the atomic spheres approximation. As an example of application the Hartree and exchange energies of silicon are calculated and the cohesive energy determined in the local-density and Hartree-Fock approximations.
 

Physical Review B, 34 5512-17, 1986.