A density difference based analysis of orbital-dependent exchange-correlation functionals

Abstract

We present a density difference based analysis for a range of orbital-dependent Kohn–Sham functionals. Results for atoms, some members of the neon isoelectronic series and small molecules are reported and compared with ab initio wave function calculations. Particular attention is paid to the quality of approximations to the exchange-only optimised effective potential (OEP) approach: we consider both the localised Hartree–Fock as well as the Krieger–Li–Iafrate methods. Analysis of density differences at the exchange-only level reveals the impact of the approximations on the resulting electronic densities. These differences are further quantified in terms of the ground state energies, frontier orbital energy differences and highest occupied orbital energies obtained. At the correlated level, an OEP approach based on a perturbative second-order correlation energy expression is shown to deliver results comparable with those from traditional wave function approaches, making it suitable for use as a benchmark against which to compare standard density functional approximations.

Keywords:

• optimised effective potential method
• localised Hartree–Fock
• electron correlation
• density functional theory
• ab initio DFT

Acknowledgements

It is a pleasure to dedicate this work to Prof. Rodney J. Bartlett on the occasion of his 70th birthday. We would like to thank Rod for sharing his ideas, many stimulating discussions, and for giving two of us (I. Grabowski and S. Śmiga) the opportunity to work together at the Quantum Theory Project. A.M. Teale gratefully acknowledges support via the Royal Society University Research Fellowship scheme. We thank TURBOMOLE GmbH for providing the TURBOMOLE program package and M. Margarito for technical support.

Additional information

Funding

This work was partially supported by the Polish Committee for Scientific Research MNiSW [grant number N N204 560839]; National Science Center [Grant No. DEC-2012/05/N/ST4/02079]; European Research Council (ERC) Starting Grant FP7 Project DEDOM [grant number 207441] and European Research Council (ERC) Advanced Grant FP7 Project ABACUS [grant number 267683].