A Simple Local Correlation Energy Functional for Spherically Confined Atoms from ab Initio Correlation Energy Density

Vyboishchikov, Sergei F.

doi:10.1002/cphc.201700774

Cited by 11 publications

(13 citation statements)

References 37 publications

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“…It is furthermore notable that the correlation energy density for He is quite similar to the one obtained by Vyboishchikov's 'local 2e-integral' approach, despite the different mathematical ansatz. 61 From a DFT perspective, the more interesting dependence is between CC c (r) and ρ (Fig. 3).…”

Section: Resultsmentioning

confidence: 99%

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Towards density functional approximations from coupled cluster correlation energy densities

Margraf

Künkel

Reuter

2019

The Journal of Chemical Physics

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Semi-)local density functional approximations (DFAs) are the workhorse electronic structure methods in condensed matter theory and surface science. The correlation energy density c (r) (a spatial function that yields the correlation energy E c upon integration) is central to defining such DFAs. Unlike E c , c (r) is not uniquely defined, however. Indeed, there are infinitely many functions that integrate to the correct E c for a given electron density ρ. The challenge for constructing useful DFAs is thus to find a suitable connection between c (r) and ρ. Herein, we present a new such approach by deriving c (r) directly from the coupledcluster (CC) energy expression. The corresponding energy densities are analyzed for prototypical two-electron systems. To explore their usefulness for designing DFAs, we construct a semilocal functional to approximate the numerical CC correlation energy densities. Importantly, the energy densities are not simply used as reference data, but guide the choice of the functional form, leading to a remarkably simple and accurate correlation functional for the Helium isoelectronic series.

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Section: Resultsmentioning

confidence: 99%

“…51 More recently, Vyboishchikov used modified "local" twoelectron integrals to calculate the correlation energy density c (r) at the MP2 and CISD level. 61 These functions were used to construct a simple local correlation functional for spherically confined atoms.…”

Section: B Correlation Energy Densities From Wftmentioning

confidence: 99%

Towards density functional approximations from coupled cluster correlation energy densities

Margraf

Künkel

Reuter

2019

The Journal of Chemical Physics

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“…Moreover, spherical confinement was used in the comparative study (taking the free-ion limit as reference) of the behavior of spin potential and the pairing energy of first row transition metal cations within the KS model [57]. A detailed analysis of the correlation energy, the performance of several commonly used functionals, electron density, as well as the XC potential in some constrained atoms have been reported [58,59]. The calculation of the static polarizability of confined He and Ne atoms was done through time-dependent DFT in [60].…”

Section: Introductionmentioning

confidence: 99%

Shannon Entropy in Confined He-Like Ions within a Density Functional Formalism

Majumdar

Roy

2020

Quantum Reports

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Shannon entropy in position ( S r ) and momentum ( S p ) spaces, along with their sum ( S t ) are presented for unit-normalized densities of He, Li + and Be 2 + ions, spatially confined at the center of an impenetrable spherical enclosure defined by a radius r c . Both ground, as well as some selected low-lying singly excited states, viz., 1sns (n = 2–4) 3S, 1snp (n = 2–3) 3P, 1s3d 3D, are considered within a density functional methodology that makes use of a work function-based exchange potential along with two correlation potentials (local Wigner-type parametrized functional, as well as the more involved non-linear gradient- and Laplacian-dependent Lee-Yang-Parr functional). The radial Kohn-Sham (KS) equation is solved using an optimal spatial discretization scheme via the generalized pseudospectral (GPS) method. A detailed systematic analysis of the confined system (relative to the corresponding free system) is performed for these quantities with respect to r c in tabular and graphical forms, with and without electron correlation. Due to compression, the pattern of entropy in the aforementioned states becomes characterized by various crossovers at intermediate and lower r c regions. The impact of electron correlation is more pronounced in the weaker confinement limit and appears to decay with the rise in confinement strength. The exchange-only results are quite good to provide a decent qualitative discussion. The lower bounds provided by the entropic uncertainty relation hold well in all cases. Several other new interesting features are observed.

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“…It is furthermore notable that the correlation energy density for He is quite similar to the one obtained by Vyboishchikov's 'local 2e-integral' approach, despite the different mathematical ansatz. 66 In the supporting information we also include the respective plots for the PBE and LDA correlation functionals (Figs. S1 and S2).…”

Section: Resultsmentioning

confidence: 99%

Towards Density Functional Approximations from Coupled Cluster Correlation Energy Densities

Margraf¹,

Künkel²,

Reuter³

2019

Preprint

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<div> <div> <div> <p>(Semi-)local density functional approximations (DFAs) are the workhorse electronic structure methods in condensed matter theory and surface science. The correlation energy density εc(r) (a spatial function that yields the correlation energy Ec upon integration) is central to defining such DFAs. Unlike Ec, εc(r) is not uniquely defined, however. Indeed, there are infinitely many functions that integrate to the correct Ec for a given electron density ρ. The challenge for constructing useful DFAs is thus to find a suitable connection between εc(r) and ρ. Herein, we present a new such approach by deriving εc(r) directly from the coupled- cluster (CC) energy expression. The corresponding energy densities are analyzed for prototypical two-electron systems. To explore their usefulness for designing DFAs, we construct a semilocal functional to approximate the numerical CC correlation energy densities. Importantly, the energy densities are not simply used as reference data, but guide the choice of the functional form, leading to a remarkably simple and accurate correlation functional for the Helium isoelectronic series. </p> </div> </div> </div>

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A Simple Local Correlation Energy Functional for Spherically Confined Atoms from ab Initio Correlation Energy Density

Cited by 11 publications

References 37 publications

Towards density functional approximations from coupled cluster correlation energy densities

Towards density functional approximations from coupled cluster correlation energy densities

Shannon Entropy in Confined He-Like Ions within a Density Functional Formalism

Towards Density Functional Approximations from Coupled Cluster Correlation Energy Densities

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