Exact Hartree-Fock exchange in one-dimensional metals. II

A computational scheme is proposed for the evaluation of the Hartree-Fock (HF) exchange-energy contributions to the electronic band energies of one-dimensional (1D) periodic systems. The scheme is designed to cope with extremely slowly convergent exchange-energy lattice sums in metallic 1D systems. It is based on a multipole expansion of two-electron integrals, and makes use of the universal 1D lattice sums introduced in a previous paper [L. Z. Stolarczyk, M. Jeziorska, and H. J. Monkhorst, Phys. Rev. B 37, 10 646 (1988)]. The method is presented in a form that is suitable for ab initio linear combination of atomic orbitals crystal-orbital self-consistent-field calculations for infinite polymers. Its simplified version based on the Pariser-Parr-Pople model of {π}-electron polymers is also given. Test calculations performed for {π}-electron polymers with two identical atoms in the unit cell show that the proposed computational scheme is effective and provides very accurate values of the exchange contributions to band energies.