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Timothy J Callow1, Benjamin J Pearce, Tom Pitts

  • 1Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK. timothy.callow@durham.ac.uk b.j.pearce@durham.ac.uk tom.pitts@durham.ac.uk matthew.j.hodgson@durham.ac.uk nikitas.gidopoulos@durham.ac.uk.

Faraday Discussions
|September 17, 2020
PubMed
Summary
This summary is machine-generated.

We developed a robust method to optimize the effective Kohn-Sham (KS) potential in density-functional approximations. This approach corrects potential behavior and enables accurate prediction of band-gaps in solids.

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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Materials Science

Background:

  • Density-functional approximations (DFAs) are crucial for electronic structure calculations.
  • Accurate prediction of electronic band-gaps in solids is a significant challenge for semi-local DFAs.
  • The exact Kohn-Sham (KS) potential exhibits properties like derivative discontinuity that are difficult to capture.

Purpose of the Study:

  • To review and expand on imposing constraints on the effective KS potential.
  • To demonstrate the numerical robustness of the optimized effective potential (OEP) equations.
  • To show that constrained OEP can improve the accuracy of DFAs for solid-state properties.

Main Methods:

  • Constraining the minimization of approximate total energy density-functionals.
  • Solving the resulting optimized effective potential (OEP) equations.
  • Applying constraints to the 'screening charge' corresponding to the Hartree, exchange, and correlation potential.

Main Results:

  • The OEP equations are numerically robust despite known mathematical issues with finite basis sets.
  • Constraining the screening charge corrects the asymptotic behavior of the KS potential.
  • The constrained KS potential exhibits a non-zero derivative discontinuity.

Conclusions:

  • Constrained OEP provides a viable route to improve DFAs.
  • This method accurately captures essential features of the exact KS potential.
  • The approach is promising for accurate band-gap prediction in solids.