Correlated electron densities, experimental ionisation potentials, and experimental electron affinities are used to investigate the homogeneity of the exchange–correlation and non-interacting kinetic energy functionals of Kohn–Sham density functional theory under density scaling. Results are presented for atoms and small molecules, paying attention to the influence of the integer discontinuity and the choice of the electron affinity. For the exchange–correlation functional, effective homogeneities are highly system-dependent on either side of the integer discontinuity. By contrast, the average homogeneity—associated with the potential that averages over the discontinuity—is generally close to 4/3 when the discontinuity is computed using positive affinities for systems that do bind an excess electron and negative affinities for those that do not. The proximity to 4/3 becomes increasingly pronounced with increasing atomic number. Evaluating the discontinuity using a zero affinity in systems that do not bind an excess electron instead leads to effective homogeneities on the electron abundant side that are close to 4/3. For the non-interacting kinetic energy functional, the effective homogeneities are less system-dependent and the effect of the integer discontinuity is less pronounced. Average values are uniformly below 5/3. The study provides information that may aid the development of improved exchange–correlation and non-interacting kinetic energy functionals.
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21 January 2012
Research Article|
January 17 2012
Effective homogeneity of the exchange–correlation and non-interacting kinetic energy functionals under density scaling
Alex Borgoo;
Alex Borgoo
a)
1Department of Chemistry,
Durham University
, South Road, Durham DH1 3LE, United Kingdom
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Andrew M. Teale;
Andrew M. Teale
2Department of Chemistry, Centre for Theoretical and Computational Chemistry,
University of Oslo
, P.O. Box 1033, Blindern, Oslo N-0315, Norway
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David J. Tozer
David J. Tozer
b)
1Department of Chemistry,
Durham University
, South Road, Durham DH1 3LE, United Kingdom
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a)
Electronic mail: a.j.borgoo@durham.ac.uk.
b)
Electronic mail: d.j.tozer@durham.ac.uk.
J. Chem. Phys. 136, 034101 (2012)
Article history
Received:
October 24 2011
Accepted:
December 19 2011
Citation
Alex Borgoo, Andrew M. Teale, David J. Tozer; Effective homogeneity of the exchange–correlation and non-interacting kinetic energy functionals under density scaling. J. Chem. Phys. 21 January 2012; 136 (3): 034101. https://doi.org/10.1063/1.3676722
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