Effect of electronic correlation on the energy bands of insulating crystals. Application to argon

A study has been made of the effect of electronic correlation on the electronic states of insulating solids. This study is based upon a many-body theory first developed by Hedin and used in semiconductors by Brinlanan and Goodman. In order to test the theory, band-structure calculations for argon were made using the orthogonalized-plane-wave method. For comparison, calculations were made using a Slater exchange, using a Hartree-Fock exchange, and including correlations at various symmetry points of the first Brillouin zone. In the Hartree-Fock calculation the exchange potential was treated in a nearly exact manner, but no iterations toward self-consistency were performed. Among the most interesting results are as follows: (a) A Hartree-Fock exchange given an energy gap which is too large; (b) a calculation with correlation yields an energy gap within 5% of experiment; (c) correlation has the effect of lowering the band gap by 3.5 eV, a relatively large number, as suggested some time ago by Fowler; (d) the internal structure of the energy bands changes little with different potentials, but the band gap varies considerably as one goes from, e.g., Slater to Hartree-Fock; and (e) the width of the valence bands is relatively large.