Exact-Exchange Kohn-Sham formalism applied to one-dimensional periodic electronic systems

TL;DR

This paper applies the exact-exchange Kohn-Sham formalism to one-dimensional periodic systems, demonstrating improved band gap predictions for trans-polyacetylene and showing the method's broad applicability without relying on specific symmetries.

Contribution

The paper introduces a symmetry-independent implementation of the EXX Kohn-Sham method for 1D periodic systems and validates it on trans-polyacetylene, achieving accurate band gaps compared to experiments.

Findings

EXX increases band gap estimates over LDA.

Correlation effects are negligible on bandstructure.

Bulk packing reduces the band gap by about 0.5 eV.

Abstract

The Exact-Exchange (EXX) Kohn-Sham formalism, which treats exchange interactions exactly within density-functional theory, is applied to one-dimensional periodic systems. The underlying implementation does not rely on specific symmetries of the considered system and can be applied to any kind of periodic structure in one to three dimensions. As a test system, $trans$-polyacetylene, both in form of an isolated chain and in the bulk geometry has been investigated. Within the EXX scheme, bandstructures and independent particle response functions are calculated and compared to experimental data as well as to data calculated by several other methods. Compared to results from the local-density approximation, the EXX method leads to an increased value for the band gap, in line with similar observations for three-dimensional semiconductors. An inclusion of correlation potentials within the local density approximation or generalized gradient approximations leads to only negligible effects in the bandstructure. The EXX band gaps are in good agreement with experimental data for bulk $trans$-polyacetylene. Packing effects of the chains in bulk $trans$-polyacetylene are found to lower the band gap by about 0.5 eV.