Convergence rates of supercell calculations in the reduced Hartree-Fock model (Q2830703)

The principal goal of this work is to prove rigorously that the replacement of the periodic system describing the electronic structure in regular crystals (semiconductors and insulators) by the discrete numerical model operating with a supercell (i.e. a sufficiently large box, which contains a large but finite number of periods) is actually valid and to estimate the convergence rate for such a replacement. It is proven within the reduced Hartree-Fock model, which neglects by the exchange term and shown that the supercell electronic density converges exponentially fast to the periodic electronic density in the whole space under this assumption. This result is a more practically useful estimation in comparison with the previously known convergence rate expressed as an inverse length of the supercell.