Self-consistent Kohn-Sham calculations with adiabatic connection models

Śmiga, S.; Sala, F. Della; Gori-Giorgi, P.; Fabiano, E.

doi:10.48550/arxiv.2202.11531

Cited by 1 publication

(1 citation statement)

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“…In fact, an SCF implementation of these ACMs has been carried out only very recently and tested for few simple chemical species (Ne, CO and H 2 ). 45 Follow-up work, in which we present a detailed analysis of the adiabatic connection integrand corresponding to the HF reference [Eq (29)] 35 for the Hubbard dimer, is currently in progress.…”

Section: Discussionmentioning

confidence: 99%

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

Giarrusso,

Pribram-Jones

2022

Preprint

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The asymmetric Hubbard dimer is a model that allows for explicit expressions of the Hartree-Fock (HF) and Kohn-Sham (KS) states as analytical functions of the external potential, ∆v, and of the interaction strength, U. We use this unique circumstance to establish a rigorous comparison between the individual contributions to the correlation energies stemming from the two theories in the {U, ∆v} parameter space. Within this analysis of the Hubbard dimer, we observe a change in the sign of the HF kinetic correlation energy, compare the indirect repulsion energies, and derive an expression for the 'traditional' correlation energy, i.e. the one that corrects the HF estimate, in a pure siteoccupation function theory spirit [Eq. ( 43)]. Next, we test the performances of the Liu-Burke and the Seidl-Perdew-Levy functionals, which model the correlation energy based on its weak-and strong-interaction limit expansions and can be used for both the traditional and the KS correlation energies. Our results show that, in the Hubbard dimer setting, they typically work better for the HF reference, despite having been originally devised for KS. These conclusions are somewhat in line with prior assessments of these functionals on various chemical data sets. However, the Hubbard dimer model allows us to show the extent of the error that may occur in using the strong-interaction ingredient for the KS reference in place of the one for the HF reference, as has been carried out in most of the prior assessments.

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Section: Discussionmentioning

confidence: 99%