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Orbital nodal surfaces: Topological challenges for density functionals
University of Bayreuth, Germany.
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-5571-0814
University of Bayreuth, Germany.
2017 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 95, no 24, 245118Article in journal (Refereed) Published
Abstract [en]

Nodal surfaces of orbitals, in particular of the highest occupied one, play a special role in Kohn-Sham density-functional theory. The exact Kohn-Sham exchange potential, for example, shows a protruding ridge along such nodal surfaces, leading to the counterintuitive feature of a potential that goes to different asymptotic limits in different directions. We show here that nodal surfaces can heavily affect the potential of semilocal density-functional approximations. For the functional derivatives of the Armiento-Kummel (AK13) [Phys. Rev. Lett. 111, 036402 (2013)] and Becke88 [Phys. Rev. A 38, 3098 (1988)] energy functionals, i.e., the corresponding semilocal exchange potentials, as well as the Becke-Johnson [J. Chem. Phys. 124, 221101 (2006)] and van Leeuwen-Baerends (LB94) [Phys. Rev. A 49, 2421 (1994)] model potentials, we explicitly demonstrate exponential divergences in the vicinity of nodal surfaces. We further point out that many other semilocal potentials have similar features. Such divergences pose a challenge for the convergence of numerical solutions of the Kohn-Sham equations. We prove that for exchange functionals of the generalized gradient approximation (GGA) form, enforcing correct asymptotic behavior of the potential or energy density necessarily leads to irregular behavior on or near orbital nodal surfaces. We formulate constraints on the GGA exchange enhancement factor for avoiding such divergences.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC , 2017. Vol. 95, no 24, 245118
National Category
Theoretical Chemistry
Identifiers
URN: urn:nbn:se:liu:diva-139184DOI: 10.1103/PhysRevB.95.245118ISI: 000403355300004OAI: oai:DiVA.org:liu-139184DiVA: diva2:1120187
Note

Funding Agencies|German-Israeli Foundation for Scientific Research and Development; University of Bayreuth Graduate School; Swedish Research Council (VR) [2016-04810]; Swedish e-Science Research Centre (SeRC)

Available from: 2017-07-05 Created: 2017-07-05 Last updated: 2017-11-29

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