Hartree‐fock exchange and LCAO approximation in the band structure calculations of solids

It is shown that the use of the simple cubature formula for the approximate calculation of the density matrix Qrr in the non‐local Hartree‐Fock exchange for crystals leads to a non‐physical divergence of the lattice sums. To overcome this difficulty it is proposed to introduce a weight function in the cubature formula for the numerical integration over the Brillouin zone in calculating non‐local exchange. It is discussed the simple way to choose the nodes of the numerical integration which is based on the large unit cell transformation in the direct and reciprocal lattices. This choice allows to extend the special point technique of the Brillouin zone integration to the non‐local exchange calculation.