Communication: Effect of the orbital-overlap dependence in the meta generalized gradient approximation

Sun, Jianwei; Xiao, Bing; Ruzsinszky, Adrienn

doi:10.1063/1.4742312

Cited by 140 publications

(197 citation statements)

References 30 publications

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“…[45,96,137,139] This issue can be solved by considering only a KS as KED dependent ingredient. [148] Note that this problem is not very relevant in general, because the density regime with a KS % 0 and s % 0 is not common; however, it can be met in real systems (e.g., at the bond of the H 2 molecule). In finite systems, the exact exchange energy per particle [102] and potential [41,205] decay as:…”

Section: Order Of Limits Problemmentioning

confidence: 99%

“…The MS0 functional yields rather good solid-state results but it is not very accurate for molecular properties [67,148] (see also Section 4).…”

Section: The Regtpss Exchange-correlation Functional (2012)mentioning

confidence: 99%

“…[143][144][145][146][147] Moreover, a KS can distinguish and quantify the orbital overlap, [148] the nonlocality of the KED at the nuclear cusp, [133] in the tail of the density, [133,149] and in the quasi-two-dimensional regime. [150] Due to these remarkable features, a KS is the main KED dependent ingredient for recent nonempirical (or semi-empirical) [66,67,148,[151][152][153] and highly empirical [28] meta-GGA XC functionals. …”

Section: The a Ks Ingredientmentioning

confidence: 99%

“…The Meta-GGA Made-Simple (MGGA-MS; also known as MGGA-MS0, in this Review simply MS0) K-meta-GGA functional [67,148] has a simple exchange enhancement factor (Equation 5) of the form thus, it is not one-electron self-correlation free. The MS0 functional yields rather good solid-state results but it is not very accurate for molecular properties [67,148] (see also Section 4).…”

Section: The Regtpss Exchange-correlation Functional (2012)mentioning

confidence: 99%

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Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Sala

Fabiano

Constantin

2016

Int J of Quantum Chemistry

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We present the theory of semilocal exchange-correlation (XC) energy functionals which depend on the Kohn-Sham kinetic energy density (KED), including the relevant class of meta-generalized gradient approximation (meta-GGA) functionals. Thanks to the KED ingredient, meta-GGA functionals can satisfy different exact constraints for XC energy and can be made one-electron selfcorrelation free. This leads to a better accuracy over a wider range of properties with respect to GGAs, often reaching the accuracy of hybrid functionals, but at much reduced computational cost.An extensive survey of the relevant literature on existing KED dependent XC functionals is provided, considering nonempirical, semi-empirical, and fully empirical ones. A deeper analysis and a wide benchmark are presented for functionals derived considering only exact constraints and parameters obtained from model and/or atomic systems. K E Y W O R D Sdensity functional theory, kinetic energy, meta-GGA | I N T R O D U C T I O NKohn-Sham (KS)-density functional theory (DFT) [1][2][3][4][5] is nowadays one of the most popular computational approaches in quantum chemistry, solid-state physics, and materials science. [6][7][8][9][10][11] While the ground-state description of a real system of interacting electrons requires a complicate N-electron wavefunction, in KS-DFT this is mapped onto an auxiliary system of noninteracting electrons having the same ground-state density, which can be easily described using N single-particle KS orbitals. [1,2] The correspondence between the many-electron problem and the KS system is in principle exact [1,3] and it is based on the so called exchange-correlation (XC) energy functional, which collects all the quantum electron-electron interaction terms beyond the Hartree one. [12] Within the constrained-search formalism, [13] the XC energy functional is:E xc ½q 5 min W!q hWjT 1V ee jWi2T s ½q 2J½q 5E x ½q 1U c ½q 1T c ½q ;(1) where W is an N-electron ground-state wavefunction yielding the electron density q,T is the kinetic energy (KE) operator,V ee is the electron-electron interaction operator, T s is the KE of the noninteracting system, J is the Coulomb energy, E x is the exact exchange energy, and U c and T c represent, respectively, the potential and the kinetic contributions to the DFT correlation energy E c 5U c 1T c . The important point of Equation1 is that it is an universal functional of the electron density. However, its explicit functional form is not known, and any practical realization of KS-DFT is based on an approximated XC functional. The latter determines in practice the overall accuracy of the KS-DFT calculation.The study of the exact properties of the XC energy functional as well as the development of new and improved approximations have been hot research topics in DFT for more than three decades, and a large number of XC approximations has been proposed. [12,14,15] The different XC functionals are usually classified, according to their complexity, on the so called Jacob's ladder of DFT [14,16] whic...

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Section: Order Of Limits Problemmentioning

confidence: 99%

“…The MS0 functional yields rather good solid-state results but it is not very accurate for molecular properties [67,148] (see also Section 4).…”

Section: The Regtpss Exchange-correlation Functional (2012)mentioning

confidence: 99%

Section: The a Ks Ingredientmentioning

confidence: 99%

Section: The Regtpss Exchange-correlation Functional (2012)mentioning

confidence: 99%

See 2 more Smart Citations

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Sala

Fabiano

Constantin

2016

Int J of Quantum Chemistry

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“…Meta-generalized gradient approximations (meta-GGAs) [31][32][33][34][35][36][37][38][39][40][41][42] are the most sophisticated semilocal functionals, incorporating important exact conditions and having an improved overall accuracy with respect to the GGA functionals. The meta-GGA functionals use as an additional ingredient to the GGA ones the Kohn-Sham positive KE density:…”

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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MCML: Combining physical constraints with experimental data for a multi‐purpose meta‐generalized gradient approximation

et al. 2021

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The predictive power of density functional theory for materials properties can be improved without increasing the overall computational complexity by extending the generalized gradient approximation (GGA) for electronic exchange and correlation to density functionals depending on the electronic kinetic energy density in addition to the charge density and its gradient, resulting in a meta‐GGA. Here, we propose an empirical meta‐GGA model that is based both on physical constraints and on experimental and quantum chemistry reference data. The resulting optimized meta‐GGA MCML yields improved surface and gas phase reaction energetics without sacrificing the accuracy of bulk property predictions of existing meta‐GGA approaches.

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Communication: Effect of the orbital-overlap dependence in the meta generalized gradient approximation

Cited by 140 publications

References 30 publications

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Kinetic and Exchange Energy Densities near the Nucleus

MCML: Combining physical constraints with experimental data for a multi‐purpose meta‐generalized gradient approximation

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