Beyond the local approximation to exchange and correlation: The role of the Laplacian of the density in the energy density of Si

Cancio, Antonio C.; Chou, M. Y.

doi:10.1103/physrevb.74.081202

Cited by 21 publications

(26 citation statements)

References 30 publications

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“…[47][48][49][50] Nekovee and co-workers 47,48 used the Variational Quantum Monte Carlo (VMC) method to investigate the xc energy density e xc (r) = n(r) xc (r) of strongly inhomogeneous electron gases subject to sinusoidal external potentials. Subtracting the xc energy density obtained by VMC from the one obtained by using LDA, e LDA xc − e VMC xc , negative errors were shown to arise in the center of the quantum wells, which is consistent with our results for HO gas.…”

Section: The Elf As An Index Of Confinement Physicsmentioning

confidence: 99%

Using the electron localization function to correct for confinement physics in semi-local density functional theory

Feng¹,

Armiento²,

Mattsson³

2014

The Journal of Chemical Physics

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We have previously proposed that further improved functionals for density functional theory can be constructed based on the Armiento-Mattsson subsystem functional scheme if, in addition to the uniform electron gas and surface models used in the Armiento-Mattsson 2005 functional, a model for the strongly confined electron gas is also added. However, of central importance for this scheme is an index that identifies regions in space where the correction provided by the confined electron gas should be applied. The electron localization function (ELF) is a well-known indicator of strongly localized electrons. We use a model of a confined electron gas based on the harmonic oscillator to show that regions with high ELF directly coincide with regions where common exchange energy functionals have large errors. This suggests that the harmonic oscillator model together with an index based on the ELF provides the crucial ingredients for future improved semi-local functionals. For a practical illustration of how the proposed scheme is intended to work for a physical system we discuss monoclinic cupric oxide, CuO. A thorough discussion of this system leads us to promote the cell geometry of CuO as a useful benchmark for future semi-local functionals. Very high ELF values are found in a shell around the O ions, and take its maximum value along the Cu-O directions. An estimate of the exchange functional error from the effect of electron confinement in these regions suggests a magnitude and sign that could account for the error in cell geometry. © 2014 AIP Publishing LLC. [http://dx

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Section: The Elf As An Index Of Confinement Physicsmentioning

confidence: 99%

Using the electron localization function to correct for confinement physics in semi-local density functional theory

Feng¹,

Armiento²,

Mattsson³

2014

The Journal of Chemical Physics

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“…This class of functionals have been also quite largely investigated. [54][55][56][57][58][59][60][61] As previously stated, L-meta-GGA are explicit-density functionals, in contrast to all the functionals which depend on s KS . Due to the aforementioned numerical problems with the Laplacian, L-metaGGAs can, in some cases, be transformed in simple GGAs, eliminating the Laplacian term by an integration by parts (see, e.g., the…”

Section: Fig Urementioning

confidence: 99%

“…Because of these properties, q is a crucial ingredient for modeling the exact exchange [58] and kinetic [64,120] energy densities. Nevertheless, despite its good features, the reduced Laplacian displays an important drawback that limited its application in DFT development.…”

Section: Input Ingredients Of Meta-gga Functionals 211 | Inhomogementioning

confidence: 99%

“…However, recent studies have reinvigorated the use of the Laplacian of the density. [58,59,61,[425][426][427][428] Moreover, other additional ingredients, that is, the square kinetic energy density, [429] which involves the Laplacian of KS orbitals, can be further investigated to develop more accurate exchange and/or correlation functionals.…”

Section: Onc Lusion S a Nd Pe Rspe Ctivesmentioning

confidence: 99%

“…However, we note that, in an all-electron calculation, a bond between two atoms (e.g., aligned in z direction) is a saddle point, where d 2 q=dz 2 >0 while d 2 q=dx 2 <0 and d 2 q=dy 2 <0, thus, the actual sign and value of the Laplacian depend on the bond type. [117][118][119] The properties of q are summarized in the third line of Table 1.Because of these properties, q is a crucial ingredient for modeling the exact exchange [58] and kinetic [64,120] energy densities. Nevertheless, despite its good features, the reduced Laplacian displays an important drawback that limited its application in DFT development.…”

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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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