Exact Hartree-Fock exchange in one-dimensional metals

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Abstract
The Hartree-Fock (HF) band model employing the nonlocal HF exchange operator is applied in studies of model one-dimensional (1D) metals: a simple monatomic chain and an equidistant trans-polyacetylene chain. The Pariser-Parr-Pople approximation is used, with the (long-range) electron repulsion described by a modified Mataga-Nishimoto formula. For each of the (infinite) chains we derive expressions for the band-energy function, density-of-states function, and total π-electron energy per atom. The derivation makes use of closed-form expressions found for some slowly convergent 1D lattice sums which are of universal character for 1D periodic systems. Anomalies of the HF exchange contributions to band structures of metallic systems are identified and discussed. It is pointed out that adhoc screening of Coulomb interactions, as in the Hubbard model, leads to arbitrary results for energy bands.