Exchange–correlation functionals from the strong interaction limit of DFT: applications to model chemical systems

Malet, Francesc; Mirtschink, André; Giesbertz, Klaas J. H.; Wagner, Lucas O.; Gori‐Giorgi, Paola

doi:10.1039/c4cp00407h

Cited by 36 publications

(78 citation statements)

References 42 publications

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“…As expected from the 1D model studied in ref 17 The NLR functional 19 results are very close to the ones from the KS SCE functional, showing that the former is a good approximation for the latter.…”

Section: Dissociationsupporting

confidence: 77%

See 1 more Smart Citation

Hydrogen Molecule Dissociation Curve with Functionals Based on the Strictly Correlated Regime

Vuckovic

Wagner

Mirtschink

et al. 2015

J. Chem. Theory Comput.

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112

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Using the dual Kantorovich formulation, we compute the strictly correlated electrons (SCE) functional (corresponding to the exact strong-interaction limit of density functional theory) for the hydrogen molecule along the dissociation curve. We use an exact relation between the Kantorovich potential and the optimal map to compute the comotion function, exploring corrections based on it. In particular, we analyze how the SCE functional transforms in an exact way the electron-electron distance into a one-body quantity, a feature that can be exploited to build new approximate functionals. We also show that the dual Kantorovich formulation provides in a natural way the constant in the Kohn-Sham potential recently introduced by Levy and Zahariev [Phys. Rev. Lett. 2014, 113, 113002] for finite systems.

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Section: Dissociationsupporting

confidence: 77%

“…Since the KS SCE energies are, as expected, 15,17 way too low around equilibrium, we have explored corrections beyond the KS SCE method. It turned out that a simple LDA correction to KS SCE performs very poorly, yielding energies that are higher than Hartree−Fock ones.…”

Section: Discussionmentioning

confidence: 99%

Hydrogen Molecule Dissociation Curve with Functionals Based on the Strictly Correlated Regime

Vuckovic

Wagner

Mirtschink

et al. 2015

J. Chem. Theory Comput.

Self Cite

112

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“…37,39,40,89 On the other hand, KS SCE treats moderately and weakly correlated systems very poorly, giving energies that are unacceptably too low. 37,88 A less drastic approximation is to construct a model, in such a way that its λ → ∞ limit is given by the exact or approximate value of , as done in the pioneering work of Seidl et al 58,59 Analogously, one can also model w λ ( r ), imposing that its λ → ∞ limit is given by w ∞ ( r ). This latter approach is the main object of the following sections.…”

Section: Modeling the Local Acmentioning

confidence: 99%

Exchange–Correlation Functionals via Local Interpolation along the Adiabatic Connection

Vuckovic

Irons

Savin

et al. 2016

J. Chem. Theory Comput.

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192

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The construction of density-functional approximations is explored by modeling the adiabatic connection locally, using energy densities defined in terms of the electrostatic potential of the exchange–correlation hole. These local models are more amenable to the construction of size-consistent approximations than their global counterparts. In this work we use accurate input local ingredients to assess the accuracy of a range of local interpolation models against accurate exchange–correlation energy densities. The importance of the strictly correlated electrons (SCE) functional describing the strong coupling limit is emphasized, enabling the corresponding interpolated functionals to treat strong correlation effects. In addition to exploring the performance of such models numerically for the helium and beryllium isoelectronic series and the dissociation of the hydrogen molecule, an approximate analytic model is presented for the initial slope of the local adiabatic connection. Comparisons are made with approaches based on global models, and prospects for future approximations based on the local adiabatic connection are discussed.

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“…In the development of density functionals for the exchange and/or correlation [2], a common approach is to exploit the properties of a known system, such as the homogeneous electron gas or the exchange and/or correlation hole. These properties can then be combined with exact constraints arising from, e.g., the Lieb-Oxford lower bound for the exchangecorrelation energy [3,4] or the limit of strictly correlated electrons [5,6]. Nevertheless, simple, scalable properties of the correlation energy are highly desirable.…”

Section: Introductionmentioning

confidence: 99%

Scaling in the correlation energies of atomic ions

2014

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We show through numerical investigations that the ground-state correlation energies of atomic ions follow an unexpectedly simple scaling relation, E c ≈ Z 4/3 f c (Z/N), where N is the number of electrons, Z is the atomic number, and f c is a universal function, for which an analytic expression with a one-parameter fit can be provided. The relation agrees well with several sets of correlation energies obtained from different methods for atomic ions with N = 2, . . . ,18 and Z = 2, . . . ,28. Moreover, our relation gives a good agreement with neutral atoms up to N ≈ 90. Our main result is readily applicable to estimating correlation energies of heavy elements, for which there are no available data in the literature. The simplicity of the relation may also have implications in the development of correlation functionals within density-functional theory.

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Exchange–correlation functionals from the strong interaction limit of DFT: applications to model chemical systems

Cited by 36 publications

References 42 publications

Hydrogen Molecule Dissociation Curve with Functionals Based on the Strictly Correlated Regime

Hydrogen Molecule Dissociation Curve with Functionals Based on the Strictly Correlated Regime

Exchange–Correlation Functionals via Local Interpolation along the Adiabatic Connection

Scaling in the correlation energies of atomic ions

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