Augmented potential, energy densities, and virial relations in the weak- and strong-interaction limits of DFT

Vuckovic, Stefan; Levy, Mel; Gori‐Giorgi, Paola

doi:10.1063/1.4997311

Cited by 29 publications

(47 citation statements)

References 71 publications

(146 reference statements)

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“…The electrostatic potential of the xc hole provides a definition (i.e., with the conventional DFT gauge 11,38,39 ) for the xc energy density: of the xc hole:…”

Section: A Basic Dft Backgroundmentioning

confidence: 99%

Range-separation and the multiple radii functional approximation inspired by the strongly interacting limit of density functional theory

Gould

Vuckovic

2019

The Journal of Chemical Physics

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The strongly-interacting limit of density functional theory has attracted considerable attention recently due to its ability to deal with the difficult strong correlation problem. Recent work [JPCL 8, 2799-2805 (2017)] introduced the "multiple radii functional" (MRF) approximation, inspired by this limit, which is designed to work well for strong correlations between dissociated fragments. Here, we analyse the MRF in exactly solvable one-dimensional molecules, to uncover how it matches, and deviates from, exact results; and use range-separation of the Coulomb potential in both exact and approximate theory to explore how this varies in space. Our work opens a path to new approximations incorporating the MRF, amongst other ingredients.

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“…The electrostatic potential of the xc hole provides a definition (i.e., with the conventional DFT gauge 11,38,39 ) for the xc energy density: of the xc hole:…”

Section: A Basic Dft Backgroundmentioning

confidence: 99%

Range-separation and the multiple radii functional approximation inspired by the strongly interacting limit of density functional theory

Gould

Vuckovic

2019

The Journal of Chemical Physics

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“…gauges) have been proposed for this quantity. [47][48][49][50] In the present work, we adhere to the definition of w λ (r) given in terms of the electrostatic potential of the xc hole: 22,43,44 w…”

Section: The Density-fixed Adiabatic Connectionmentioning

confidence: 99%

“…The energy density in the gauge of the electrostatic potential of the xc hole (eq 4) is wellestablished in the literature 22,35,43,44,51 and for more details on the advantage of this gauge choice over the other gauges for the construction of DFAs based on eqs 1 and 3, see ref 50.…”

Section: The Density-fixed Adiabatic Connectionmentioning

confidence: 99%

Fully Nonlocal Functionals Along the Adiabatic Connection of Density Functional Theory

Vuckovic¹

2019

Preprint

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Inspired by the exact form of the strongly interacting limit of density functional theory, Vuckovic and Gori Giorgi have recently proposed [J. Phys. Chem. Lett. 2017, 8, 2799] the multiple radii functional (MRF), a new framework for the construction of exchange-correlation (xc) energy approximations able to describe strong correlation electronic effects. To facilitate the construction of improved approximations based on the MRF functional, in the present work we use reverse engineering strategies to reveal the forms of the MRF functional which reproduce the exact xc functional for small atoms. We also develop a procedure that allows the MRF functional to be built on the top of exact exchange. Using the adiabatic connection representation of the xc functional, we also investigate routes for the construction of the correlation functional by combining information from the physical, weakly and strongly interacting regimes. We highlight the advantages of this approach over previous adiabatic connection-based approaches for the treatment of strong correlation and discuss how it can be used for recovering the presently missing kinetic component of the correlation energy in the MRF framework.<br> <pre><br></pre>

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“…Equation ( 2 ) can also be written in terms of real-space energy densities , which are, of course, not uniquely defined. For the purpose of building -interpolation models on energy densities, the choice of the gauge of the electrostatic potential of the exchange–correlation hole seems so far to be the most suitable [ 16 ], where is defined in terms of the pair density and the density (see also [ 34 ]), with obtained from , Energy density at . At , we have the Kohn–Sham or exchange hole, which yields in the case of a closed-shell singlet considered in this work (with real orbitals) where are the occupied KS spatial orbitals.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Local and global interpolations along the adiabatic connection of DFT: a study at different correlation regimes

Kooi

Gori‐Giorgi

2018

Theor Chem Acc

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Interpolating the exchange–correlation energy along the density-fixed adiabatic connection of density functional theory is a promising way to build approximations that are not biased toward the weakly correlated regime. These interpolations can be performed at the global (integrated over all spaces) or at the local level, using energy densities. Many features of the relevant energy densities as well as several different ways to construct these interpolations, including comparisons between global and local variants, are investigated here for the analytically solvable Hooke’s atom series, which allows for an exploration of different correlation regimes. We also analyze different ways to define the correlation kinetic energy density, focusing on the peak in the kinetic correlation potential.

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Augmented potential, energy densities, and virial relations in the weak- and strong-interaction limits of DFT

Cited by 29 publications

References 71 publications

Range-separation and the multiple radii functional approximation inspired by the strongly interacting limit of density functional theory

Range-separation and the multiple radii functional approximation inspired by the strongly interacting limit of density functional theory

Fully Nonlocal Functionals Along the Adiabatic Connection of Density Functional Theory

Local and global interpolations along the adiabatic connection of DFT: a study at different correlation regimes

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