Unambiguous exchange-correlation energy density

Burke, Kieron; Cruz, Federico G.; Lam, Kin‐Chung

doi:10.1063/1.477479

Cited by 125 publications

(128 citation statements)

References 47 publications

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“…10,22 The CF reflects the so-called ''gauge problem'', which arises from a fundamental ambiguity in the definition of exchange-energy densities (in fact of any energy density). 10,[22][23][24] By definition, a CF integrates to zero ð G s ðrÞdr ¼ 0:…”

Section: Introductionmentioning

confidence: 99%

New approaches for the calibration of exchange-energy densities in local hybrid functionals

Maier

Haasler

Arbuznikov

et al. 2016

Phys. Chem. Chem. Phys.

123

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The ambiguity of exchange-energy densities is a fundamental challenge for the development of local hybrid functionals, or of other functionals based on a local mixing of exchange-energy densities. In this work, a systematic construction of semi-local calibration functions (CFs) for adjusting the exchangeenergy densities in local hybrid functionals is provided, which directly links a given CF to an underlying semi-local exchange functional, as well as to the second-order gradient expansion of the exchange hole. Using successive steps of integration by parts allows the derivation of correction terms of increasing order, resulting in more and more complicated but also more flexible CFs. We derive explicit first-and second-order CFs (pig1 and pig2) based on B88 generalized-gradient approximation (GGA) exchange, and a first-order CF (tpig1) based on t-dependent B98 meta-GGA exchange. We combine these CFs with different long-range damping functions and evaluate them for calibration of LDA, B88 GGA, and TPSS meta-GGA exchange-energy densities. Based on a minimization of unphysical nondynamical correlation contributions in three noble-gas dimer potential-energy curves, free parameters in the CFs are optimized, and performance of various approaches in the calibration of different exchangeenergy densities is compared. Most notably, the second-order pig2 CF provides the largest flexibility with respect to the diffuseness of the damping function. This suggests that higher-order CFs based on the present integration-by-parts scheme may be particularly suitable for the flexible construction of local hybrid functionals.

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Section: Introductionmentioning

confidence: 99%

New approaches for the calibration of exchange-energy densities in local hybrid functionals

Maier

Haasler

Arbuznikov

et al. 2016

Phys. Chem. Chem. Phys.

123

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“…For a similar reason, the MVS meta-GGA shows an even smaller enhancement factor, which even displays a pronounced de-enhancement for large s. Note that for a KS 50 and small values of s all the functionals show a flat exchange enhancement factor. This is a consequence of the nuclear cusp condition of Equation 68. For a KS 51 all functionals give F x 51, to satisfy the HEG limit: actually all functionals satisfy the GE4 condition (see Equation 53), but MS0 and MVS which are limited to GE2.…”

Section: Enhancement Factors Of Nonempirical Exchangecorrelation Mementioning

confidence: 99%

“…We recall, however, that e xc is not univocally defined, as any function which integrates to zero can be added to the integrand, without changing the total energy. [68,69] The GGA (rq) and meta-GGA (r 2 q,s KS ) basic quantities are usually not employed directly into the functional, but are instead used to construct input ingredients that respect basic scaling constraints. Section 2.1 provides a full list of such input ingredients as well as a detailed review of their properties.…”

mentioning

confidence: 99%

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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“…In general, the xc energy can be expressed (ambiguously [85,109,110]) as E xc = n(r)e xc (r) d 3 r, with e xc (r) denoting the xc energy density per particle. Here, we highlight two related, yet fundamentally different concepts of incorporating the EXX energy density per particle e ex x (r) into practical density-functional approximations.…”

Section: Counteracting Electronic Self-interaction With Hybrid Functimentioning

confidence: 99%

The Influence of One-Electron Self-Interaction on d-Electrons

Schmidt

Kümmel

2016

Computation

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Abstract:We investigate four diatomic molecules containing transition metals using two variants of hybrid functionals. We compare global hybrid functionals that only partially counteract self-interaction to local hybrid functionals that are designed to be formally free from one-electron self-interaction. As d-orbitals are prone to be particularly strongly influenced by self-interaction errors, one may have expected that self-interaction-free local hybrid functionals lead to a qualitatively different Kohn-Sham density of states than global hybrid functionals. Yet, we find that both types of hybrids lead to a very similar density of states. For both global and local hybrids alike, the intrinsic amount of exact exchange plays the dominant role in counteracting electronic self-interaction, whereas being formally free from one-electron self-interaction seems to be of lesser importance.

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Unambiguous exchange-correlation energy density

Cited by 125 publications

References 47 publications

New approaches for the calibration of exchange-energy densities in local hybrid functionals

New approaches for the calibration of exchange-energy densities in local hybrid functionals

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

The Influence of One-Electron Self-Interaction on d-Electrons

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