Can the Hartree–Fock kinetic energy exceed the exact kinetic energy?

Crisostomo, Steven; Levy, Mel; Burke, Kieron

doi:10.1063/5.0105684

Cited by 5 publications

(2 citation statements)

References 42 publications

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“…However, a realistic counter example has not been found. 78 Hence, we reach our final conclusion: The noninteracting kinetic energy obtained from a standard density functional is anticipated to exceed its HF counterpart. If this expectation is not met, it suggests that the underlying self-consistent density is excessively delocalized, and it is recommended to use the HF density instead.…”

Section: ■ the Kinetic Energy Indicatormentioning

confidence: 73%

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Simple and Efficient Route toward Improved Energetics within the Framework of Density-Corrected Density Functional Theory

Gräf

Thom

2023

J. Chem. Theory Comput.

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The crucial step in density-corrected Hartree–Fock density functional theory (DC(HF)-DFT) is to decide whether the density produced by the density functional for a specific calculation is erroneous and, hence, should be replaced by, in this case, the HF density. We introduce an indicator, based on the difference in noninteracting kinetic energies between DFT and HF calculations, to determine when the HF density is the better option. Our kinetic energy indicator directly compares the self-consistent density of the analyzed functional with the HF density, is size-intensive, reliable, and most importantly highly efficient. Moreover, we present a procedure that makes best use of the computed quantities necessary for DC(HF)-DFT by additionally evaluating a related hybrid functional and, in that way, not only “corrects” the density but also the functional itself; we call that procedure corrected Hartree–Fock density functional theory (C(HF)-DFT).

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Section: ■ the Kinetic Energy Indicatormentioning

confidence: 73%

“…It is also true that, contrary to the KS case, no universal proof exists that the HF kinetic energy needs to be smaller than (or equal to) the exact (interacting) kinetic energy; or in other words, that T c needs to be non-negative. However, a realistic counter example has not been found …”

Section: The Kinetic Energy Indicatormentioning

confidence: 99%

Simple and Efficient Route toward Improved Energetics within the Framework of Density-Corrected Density Functional Theory

Gräf

Thom

2023

J. Chem. Theory Comput.

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Seven useful questions in density functional theory

et al. 2023

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

Giarrusso

Pribram‐Jones

2022

The Journal of Chemical Physics

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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, Δ 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, Δ 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 site-occupation function theory spirit [Eq. (45) ]. 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 datasets. 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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Can the Hartree–Fock kinetic energy exceed the exact kinetic energy?

Cited by 5 publications

References 42 publications

Simple and Efficient Route toward Improved Energetics within the Framework of Density-Corrected Density Functional Theory

Simple and Efficient Route toward Improved Energetics within the Framework of Density-Corrected Density Functional Theory

Seven useful questions in density functional theory

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

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