Semilocal Approximations for the Kinetic Energy

Tran, Fabien; Wesołowski, Tomasz Adam

doi:10.1142/9789814436731_0016

Cited by 21 publications

(26 citation statements)

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“…For the kinetic term standard semilocal approximations can be employed [19,20,[39][40][41]43]. For the XC part, instead, two main possibilities can be envisaged: i) As a first simple option it is possible to use for E xc the GGA functional "most similar" to the meta-GGA functional used for subsystems calculations.…”

Section: B Non-additive Embedding Contributionsmentioning

confidence: 99%

“…For a recent review of all KE functionals see Ref. 43. Moreover, several works have extended the subsystem formulation of DFT beyond the conventional Kohn-Sham (KS) framework, considering e.g., hybrid functionals [44], embedded interacting wave functions [45], orbital-dependent effective exact exchange methods [21,46], or density matrix [47].…”

Section: Introductionmentioning

confidence: 99%

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Subsystem density functional theory with meta-generalized gradient approximation exchange-correlation functionals

Śmiga

Fabiano

Laricchia

et al. 2015

The Journal of Chemical Physics

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We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes the problem and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method.

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Section: B Non-additive Embedding Contributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Subsystem density functional theory with meta-generalized gradient approximation exchange-correlation functionals

Śmiga

Fabiano

Laricchia

et al. 2015

The Journal of Chemical Physics

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“…An important and long‐enduring problem in the quantum mechanical description of many‐particle systems is how to represent adequately the noninteracting kinetic energy,

T_{normals} [ρ]

, as a functional of the one‐particle density . In the early development of quantum theory, such as is embodied in the Thomas‐Fermi approximation, the kinetic energy was given as a functional of

normalρ,

T_{TF} [ρ] = C_{normalF} \int d r {normalρ}^{5 / 3} (r) .

…”

Section: Introductionmentioning

confidence: 99%

The Liu‐Parr power series expansion of the Pauli kinetic energy functional with the incorporation of shell‐inducing traits: Atoms

Ludeña

Salazar

Cornejo

et al. 2018

Int J of Quantum Chemistry

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An approximate expression for the Pauli kinetic energy functional Tp is advanced in terms of the Liu‐Parr expansion [S. Liu, R.G. Parr, Phys. Rev. A 1997, 55, 1792] which involves a power series of the one‐electron density. We use this explicit functional for Tp to compute the value of the noninteracting kinetic energy functional Ts of 34 atoms, from Li to Kr (and their positive and negative monoions). In particular, we examine the effect that a shell‐by‐shell mean‐square optimization of the expansion coefficients has on the kinetic energy values and explore the effect that the size of the expansion, given by the parameter n, has on the accuracy of the approximation. The results yield a mean absolute percent error Δabs=(1/N)∑i=1NΔi for 34 neutral atoms of 0.15, 0.08, 0.04, 0.03, and 0.01 for expansions with n = 3, 4, 5, 6, and 7, respectively (where Δi=100|Tnormalsapp(i)−TnormalsHF(i)|/TnormalsHF(i)). We show that these results, which are the most accurate ones obtained to date for the representation of the noninteracting kinetic energy functional, stem from the imposition of shell‐inducing traits. We also compare these Liu‐Parr functionals with the exact but nonexplicit functional generated in the local‐scaling transformation version of DFT.

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“…Similar shortcomings as for the XE density near the nucleus affect also many KE functionals at the GGA level [51][52][53][54][55] or at the Laplacian level [56]; for a recent review of semilocal functionals, see [57]. The KE density is usually defined in terms of the KE enhancement factor:…”

Section: Introductionmentioning

confidence: 99%

Kinetic and Exchange Energy Densities near the Nucleus

2016

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Abstract:We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the semiclassical limit of large non-relativistic neutral atoms. We show that a model based on the helium iso-electronic series is very accurate, as also confirmed by numerical calculations on real atoms up to two thousands electrons. Based on this model, we propose non-local density-dependent ingredients that are suitable for the description of the kinetic and exchange energy densities in the region close to the nucleus. These non-local ingredients are invariant under the uniform scaling of the density, and they can be used in the construction of non-local exchange-correlation and kinetic functionals.

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Semilocal Approximations for the Kinetic Energy

Cited by 21 publications

References 1 publication

Subsystem density functional theory with meta-generalized gradient approximation exchange-correlation functionals

Subsystem density functional theory with meta-generalized gradient approximation exchange-correlation functionals

The Liu‐Parr power series expansion of the Pauli kinetic energy functional with the incorporation of shell‐inducing traits: Atoms

Kinetic and Exchange Energy Densities near the Nucleus

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