Sum-rules of the response potential in the strongly-interacting limit of DFT

Giarrusso, Sara; Gori‐Giorgi, Paola; Giesbertz, Klaas J. H.

doi:10.1140/epjb/e2018-90301-8

Cited by 7 publications

(10 citation statements)

References 46 publications

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“…It is evident that, in order to correctly describe how this potential behaves around its maximum, we need to include also the knowledge of how the comotion function diverges, while this information is not needed in the case of the maximum of the SCE Hartree XC potential. Nonetheless, our modeled SCE response potential correctly integrates to exactly one as it should, fulfilling a recently derived sum-rule . Moreover, excluding for a moment the point f mod ( a r ) = ∞ from our model comotion function, we can evaluate the analytical behavior of the step structure of the modeled SCE response potential, v resp,mod SCE , that is, the difference from its left and right limits toward a R , getting which differs from the exact step height in the model by the factor .…”

Section: Analytical 1d Model For V Hxc Sce and V Resp Sce In The Diss...mentioning

confidence: 70%

Exchange-Correlation Energy Densities and Response Potentials: Connection between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

Giarrusso

Gori‐Giorgi

2020

J. Phys. Chem. A

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We analyze in depth two widely used definitions (from the theory of conditional probability amplitudes and from the adiabatic connection formalism) of the exchange-correlation energy density and of the response potential of Kohn−Sham density functional theory. We introduce a local form of the couplingconstant-dependent Hohenberg−Kohn functional, showing that the difference between the two definitions is due to a corresponding local first-order term in the coupling constant, which disappears globally (when integrated over all space), but not locally. We also design an analytic representation for the response potential in the strong-coupling limit of density functional theory for a model single stretched bond.

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Section: Analytical 1d Model For V Hxc Sce and V Resp Sce In The Diss...mentioning

confidence: 70%

Exchange-Correlation Energy Densities and Response Potentials: Connection between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

Giarrusso

Gori‐Giorgi

2020

J. Phys. Chem. A

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“…We first consider two types of simple exponential basis functions (13) in the HL model, with exponents corresponding to the ionization energies obtained with our model Hamiltonian. So in the equations for x ± peak (16) and v kin (x ± peak ) (17), which are for exponential basis functions, we use the two values for a = 2 √ 2 I A with I A = − A according to cases 1 and 2 above, and the corresponding two values for b. This yields HL estimates for both the values at and the locations of the maxima, see option 1 and option 2 for exponential basis functions in Tab.…”

Section: B Numerical Resultsmentioning

confidence: 99%

“…This feature has received further interest in the literature. [11][12][13][14][15][16][17][18][19] In Ref. 4, it was demonstrated that such step structure (with height ∆I = I A − I B if A has higher ionization potential) is due to the response potential v resp .…”

Section: Introductionmentioning

confidence: 99%

Secondary kinetic peak in the Kohn-Sham potential and its connection to the response step

Giarrusso¹,

Neugarten²,

Baerends³

et al. 2022

Preprint

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We consider a prototypical 1D model Hamiltonian for a stretched heteronuclear molecule and construct individual components of the corresponding KS potential, namely: the kinetic, the N − 1, and the conditional potentials. These components show very special features, such as peaks and steps, in regions where the density is drastically low. Some of these features are quite well known, whereas others, such as a secondary peak in the kinetic potential or a second bump in the conditional potential, are less or not known at all. We discuss these features building on the analytical model treated in J. Chem. Theory Comput. 14, 4151 (2018). In particular, we provide an explanation for the underlying mechanism which determines the appearance of both peaks in the kinetic potential and elucidate why these peaks delineate the region over which the plateau structure, due to the N − 1 potential, stretches. We assess the validity of the Heitler-London Ansatz at large but finite internuclear distance, showing that, if optimal orbitals are used, this model is an excellent approximation to the exact wavefunction. Notably, we find that the second natural orbital presents an extra node very far out on the side of the more electronegative atom.

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“…Nonetheless, our modelled SCE response potential correctly integrates to exactly one as it should, fulfilling a recently derived sum-rule. 62 Moreover, excluding for a moment the point f mod (a r ) = ∞ from our model co-motion function, we can evaluate the analytical behaviour of the step structure of the modelled SCE response potential, v SCE resp,mod , i.e. the difference from its left and right limits towards a R , getting…”

Section: Response Potential From the Coupling-constant Integrationmentioning

confidence: 99%

Exchange-Correlation Energy Densities and Response Potentials: Connection Between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

Giarrusso¹,

Gori‐Giorgi²

2019

Preprint

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We analyze in depth two widely used definitions (from the theory of conditional probablity amplitudes and from the adiabatic connection formalism) of the exchange-correlation energy density and of the response potential of Kohn-Sham density functional theory. We introduce a local form of the coupling-constant-dependent Hohenberg-Kohn functional, showing that the difference between the two definitions is due to a corresponding local first-order term in the coupling constant, which disappears globally (when integrated over all space), but not locally. We also design an analytic representation for the response potential in the strong-coupling limit of density functional theory for a model single stretched bond.<br>

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Sum-rules of the response potential in the strongly-interacting limit of DFT

Cited by 7 publications

References 46 publications

Exchange-Correlation Energy Densities and Response Potentials: Connection between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

Exchange-Correlation Energy Densities and Response Potentials: Connection between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

Secondary kinetic peak in the Kohn-Sham potential and its connection to the response step

Exchange-Correlation Energy Densities and Response Potentials: Connection Between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

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