Improving the exchange and correlation potential in density-functional approximations through constraints

Callow, Timothy J.; Pearce, Benjamin J.; Pitts, Tom; Lathiotakis, N. N.; Hodgson, M. J. P.; Gidopoulos, Nikitas I.

doi:10.1039/d0fd00069h

Cited by 7 publications

(10 citation statements)

References 42 publications

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“…In this case, approaching the atom inward from infinity, the decay of the outermost shell is substituted by the decay of the next, inner shell. The potential then experiences a step, which can be revealed, − particularly when using orbital-dependent, exact-exchange-based approximations, within the optimized effective potential (OEP) method; − however, this approach has known numerical difficulties which arise from the use of a finite basis set. ,,− Solutions have been proposed to overcome these numerical issues; ,,, however, the OEP method is yet to be adopted as a mainstream approximation within DFT owing to the numerically challenging nature of the approach.…”

Section: Properties Of the Exact Exchange-correlation Functionalmentioning

confidence: 99%

From Kohn–Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential

Kraisler

Hodgson

Gross

2021

J. Chem. Theory Comput.

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Accurately describing excited states within Kohn–Sham (KS) density functional theory (DFT), particularly those which induce ionization and charge transfer, remains a great challenge. Common exchange-correlation (xc) approximations are unreliable for excited states owing, in part, to the absence of a derivative discontinuity in the xc energy (Δ), which relates a many-electron energy difference to the corresponding KS energy difference. We demonstrate, analytically and numerically, how the relationship between KS and many-electron energies leads to the step structures observed in the exact xc potential in four scenarios: electron addition, molecular dissociation, excitation of a finite system, and charge transfer. We further show that steps in the potential can be obtained also with common xc approximations, as simple as the LDA, when addressed from the ensemble perspective. The article therefore highlights how capturing the relationship between KS and many-electron energies with advanced xc approximations is crucial for accurately calculating excitations, as well as the ground-state density and energy of systems which consist of distinct subsystems.

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Section: Properties Of the Exact Exchange-correlation Functionalmentioning

confidence: 99%

From Kohn–Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential

Kraisler

Hodgson

Gross

2021

J. Chem. Theory Comput.

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“…Obviously, either N or N + 1 is an odd number, and in the analysis of the derivative discontinuity it is assumed that it is possible to calculate the xc potential for an odd number of electrons accurately, without qualitative errors. With the present work, this assumption is justified, even for approximate xc potentials 7 .…”

Section: Introductionmentioning

confidence: 77%

“…We have implemented equations (5)(6)(7)(8)(9)(10)(11) in the Gaussian basis set code HIPPO 25 . The solution of finite-basis OEP equations hides non-analytic behaviour 26 , which leads to oscillations of the potential near the nuclei 27,28 .…”

Section: Resultsmentioning

confidence: 99%

Density functionals with spin-density accuracy for open shells

Callow

Pearce

Gidopoulos

2022

The Journal of Chemical Physics

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Electrons in zero external magnetic field can be studied with density functional theory (DFT) or with spin-DFT (SDFT). The latter is normally used for open shell systems because its approximations appear to model better the exchange and correlation (xc) functional, but also because so far the application of DFT implied a closed-shell-like approximation. Correcting this error for open shells allows the approximate DFT xc functionals to become as accurate as those in SDFT. In the limit of zero magnetic field, the Kohn-Sham equations of SDFT emerge as the generalised KS equations of DFT.

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“…For more detail on the computational implementation of the OEP equation please see Refs. [1] and [2]. Unless otherwise stated, all results use cc-pVTZ orbital bases and uncontracted cc-pVDZ auxiliary bases [5,23].…”

Section: Resultsmentioning

confidence: 99%

Density functionals with spin-density accuracy for open shells

Callow,

Pearce,

Gidopoulos

2021

Preprint

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Improving the exchange and correlation potential in density-functional approximations through constraints

Abstract:
We review and expand on our work to impose constraints on the effective Kohn Sham (KS) potential of local and semi-local density functional approximations. In this work, we relax a...

Cited by 7 publications

References 42 publications

From Kohn–Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential

From Kohn–Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential

Density functionals with spin-density accuracy for open shells

Density functionals with spin-density accuracy for open shells

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Product

Resources

About

Improving the exchange and correlation potential in density-functional approximations through constraints

Abstract: We review and expand on our work to impose constraints on the effective Kohn Sham (KS) potential of local and semi-local density functional approximations. In this work, we relax a...

Cited by 7 publications

References 42 publications

From Kohn–Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential

From Kohn–Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential

Density functionals with spin-density accuracy for open shells

Density functionals with spin-density accuracy for open shells

Contact Info

Product

Resources

About

Abstract:
We review and expand on our work to impose constraints on the effective Kohn Sham (KS) potential of local and semi-local density functional approximations. In this work, we relax a...