English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The asymmetric Hubbard dimer is a model that allows for explicit expressionsof the Hartree-Fock (HF) and Kohn-Sham (KS) states as analytical functions ofthe external potential, $\Delta v$, and of the interaction strength, $U$. Weuse this unique circumstance to establish a rigorous comparison between theindividual contributions to the correlation energies stemming from the twotheories in the $\{U,\Delta v\}$ parameter space. Within this analysis of theHubbard dimer, we observe a change in the sign of the HF kinetic correlationenergy, compare the indirect repulsion energies, and derive an expression forthe 'traditional' correlation energy, i.e. the one that corrects the HFestimate, in a pure site-occupation function theory spirit [Eq. (43)]. Next, wetest the performances of the Liu-Burke and the Seidl-Perdew-Levy functionals,which model the correlation energy based on its weak- and strong-interactionlimit expansions and can be used for both the traditional and the KScorrelation energies. Our results show that, in the Hubbard dimer setting, theytypically work better for the HF reference, despite having been originallydevised for KS. These conclusions are somewhat in line with prior assessmentsof these functionals on various chemical data sets. However, the Hubbard dimermodel allows us to show the extent of the error that may occur in using thestrong-interaction ingredient for the KS reference in place of the one for theHF reference, as has been carried out in most of the prior assessments.

Comparing correlation components and approximations in Hartree-Fock and Kohn-Sham theories via an analytical test case study