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

Vuckovic, Stefan; Wagner, Lucas O.; Mirtschink, André; Gori‐Giorgi, Paola

doi:10.1021/acs.jctc.5b00387

Cited by 47 publications

(117 citation statements)

References 65 publications

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“…50 We would expect that the two-legged representation would capture the given local AC very well, but even a single line segment approximation, w λ ( r ) ≈ w ∞ ( r ), this time coming from the strong coupling limit, would be highly accurate for the stretched H 2 . 37 In contrast to the local AC curves of the stretched and H 2 at equilibrium, the curvature of the local AC curve at the intermediate bond length is highly pronounced. The shapes of the local AC curves at the nuclei mirror the difference in correlation regimes present in the hydrogen molecule at different bond lengths.…”

Section: Resultsmentioning

confidence: 96%

“…The overall accuracy of KS-SCE for H 2 dissociation can be substantially improved by the addition of nonlocal corrections. 37 …”

Section: Resultsmentioning

confidence: 99%

“…For atomic densities with N > 2 it could be either a very good approximation for the true minimum of eq 34 or, again, the exact result. 64,98 For the H 2 molecule we have used the results of ref (37), where the SCE energy density has been computed by obtaining the comotion function from the dual Kantorovich formulation 91,100 of the SCE problem.…”

Section: Modeling the Local Acmentioning

confidence: 99%

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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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Section: Resultsmentioning

confidence: 96%

“…The overall accuracy of KS-SCE for H 2 dissociation can be substantially improved by the addition of nonlocal corrections. 37 …”

Section: Resultsmentioning

confidence: 99%

Section: Modeling the Local Acmentioning

confidence: 99%

See 1 more Smart Citation

Exchange–Correlation Functionals via Local Interpolation along the Adiabatic Connection

Vuckovic

Irons

Savin

et al. 2016

J. Chem. Theory Comput.

Self Cite

192

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show abstract

“…To show this, we calculate the nonlocal functional for real 3D atoms-self-consistently for two electrons, and non-self-consistently for more-where the KS-SCE functional has also been evaluated [49]. We also treat the 3D hydrogen molecule non-self-consistently, which has only recently been treated by the exact KS-SCE functional [40,50]. In comparing the KS-NLR and KS-SCE methods, we also consider a simplified 1D universe, as in Ref.…”

Section: Introductionmentioning

confidence: 99%

Electron avoidance: A nonlocal radius for strong correlation

Wagner

Gori‐Giorgi

2014

Phys. Rev. A

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We present here a model of the exchange-correlation hole for strongly correlated systems using a simple nonlocal generalization of the Wigner-Seitz radius. The model behaves similarly to the strictly correlated electron approach, which gives the infinitely correlated limit of density functional theory. Unlike the strictly correlated method, however, the energies and potentials of this model can be presently calculated for arbitrary geometries in three dimensions. We discuss how to evaluate the energies and potentials of the nonlocal model, and provide results for many systems where it is also possible to compare to the strictly correlated electron treatment.

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“…Refs [55][56][57][58] give examples in a KS context, and in a DMFT context they are commonplace [59][60][61][62][63][64]. A genuine density functional treatment of strongly correlated electrons, which is exact in the limiting case of dissociated H 2 , is provided by the strictly correlated electrons (SCE) functional [65][66][67][68].…”

Section: Nonlocality and Dissociation Of An Electron Pair Bondmentioning

confidence: 99%

On derivatives of the energy with respect to total electron number and orbital occupation numbers. A critique of Janak's theorem

Baerends

2019

Molecular Physics

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The relation between the derivative of the energy with respect to occupation number and the orbital energy, ∂E/∂ni = i, was first introduced by Slater for approximate total energy expressions such as Hartree-Fock and exchange-only LDA, and his derivation holds for hybrid functionals as well. We argue that Janak's extension of this relation to (exact) Kohn-Sham density functional theory is not valid. The reason is the nonexistence of systems with noninteger electron number, and therefore of the derivative of the total energy with respect to electron number, ∂E/∂N . How to handle the lack of a defined derivative ∂E/∂N at the integer point, is demonstrated using the Lagrange multiplier technique to enforce constraints. The well-known straight-line behavior of the energy as derived from statistical physical considerations [1] for the average energy of a molecule in a macroscopic sample ("dilute gas") as a function of average electron number is not a property of a single molecule at T = 0. One may choose to represent the energy of a molecule in the nonphysical domain of noninteger densities by a straight-line functional, but the arbitrariness of this choice precludes the drawing of physical conclusions from it.

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

Cited by 47 publications

References 65 publications

Exchange–Correlation Functionals via Local Interpolation along the Adiabatic Connection

Exchange–Correlation Functionals via Local Interpolation along the Adiabatic Connection

Electron avoidance: A nonlocal radius for strong correlation

On derivatives of the energy with respect to total electron number and orbital occupation numbers. A critique of Janak's theorem

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