Efficient calculation of the exact exchange energy in periodic systems using a truncated Coulomb potential

We present a scheme for calculating the exact exchange energy in periodic solids within a Kohn--Sham or Hartree--Fock approach, which removes the need to treat the integrable singularities via an auxiliary function. In the exchange integrals, we use a modified Coulomb potential, which tends to the exact potential as the number of k points increases yet has no singularities, and which is also very simple to implement. We compare this approach to the auxiliary function scheme for diamond, graphite, and two allotropes of silicon carbide and show that it converges more rapidly with the number of wave vectors.