A thermochemically competitive local hybrid functional without gradient corrections

Bahmann, Hilke; Rodenberg, Alexander; Arbuznikov, Alexei V.; Kaupp, Martin

doi:10.1063/1.2429058

Cited by 131 publications

(170 citation statements)

References 33 publications

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“…As for the 'pig2' CF above, we may thus choose one of these three terms for partitioning and treatment according to eqn (12). Taking, e.g., the second term of eqn (37) without prefactor and partitioning it as…”

Section: B98-based ''Meta-gga'' Calibration Functionmentioning

confidence: 99%

“…We will apply integration by parts to them in the same way as done above for the original energy density (14). That is, we (i) apply a partitioning (11), thus (ii) building (when possible) a new CF according to eqn (12) and (18).…”

Section: Second-and Higher-order Gga Calibration Functionsmentioning

confidence: 99%

“…While much of the attention in the development of local hybrids during the last years has focused on the LMF, 12 so-called calibration function (CF) G s [eqn (1) and (3)], which is the central topic of the present work, has been studied less. 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).…”

Section: Introductionmentioning

confidence: 99%

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

Maier

Haasler

Arbuznikov

et al. 2016

Phys. Chem. Chem. Phys.

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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: B98-based ''Meta-gga'' Calibration Functionmentioning

confidence: 99%

Section: Second-and Higher-order Gga Calibration Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Maier

Haasler

Arbuznikov

et al. 2016

Phys. Chem. Chem. Phys.

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123

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“…Unfortunately, its thermochemical performance is rather poor. 14 Later, Kaupp and co-workers 16,17,20 showed that parametrized mixing functions including…”

Section: ͑1͒mentioning

confidence: 99%

“…Most subsequent thermochemical tests of local hybrids have been performed non-self-consistently. 16,17,[19][20][21]23 In this work, we present self-consistent GKS calculations using the screened and LC local hybrid functionals defined in Eqs. ͑10͒ and ͑11͒.…”

Section: ͑14͒mentioning

confidence: 99%

Self-consistent generalized Kohn-Sham local hybrid functionals of screened exchange: Combining local and range-separated hybridization

Janesko

Krukau

Scuseria

2008

The Journal of Chemical Physics

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We present local hybrid functionals that incorporate a position-dependent admixture of short-range ͑screened͒ nonlocal exact ͓Hartree-Fock-type ͑HF͔͒ exchange. We test two limiting cases: screened local hybrids with no long-range HF exchange and long-range-corrected local hybrids with 100% long-range HF exchange. Long-range-corrected local hybrids provide the exact asymptotic exchange-correlation potential in finite systems, while screened local hybrids avoid the problems inherent to long-range HF exchange in metals and small-bandgap systems. We treat these functionals self-consistently using the nonlocal exchange potential constructed from Kohn-Sham orbital derivatives. Generalized Kohn-Sham calculations with screened and long-range-corrected local hybrids can provide accurate molecular thermochemistry and kinetics, comparable to existing local hybrids of full-range exchange. Generalized Kohn-Sham calculations with existing full-range local hybrids provide results consistent with previous non-self-consistent and "localized local hybrid" calculations. These new functionals appear to provide a promising extension of existing local and range-separated hybrids.

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Approximate Density Functionals: Which Should I Choose?

Rappoport

Crawford

Furche

et al. 2005

Encyclopedia of Inorganic Chemistry

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Density functional methods have a long tradition in inorganic and bioinorganic chemistry. We introduce the density functional machinery and give an overview of most popular approximate exchange‐correlation (XC) functionals. We present comparisons of density functionals for energies, structures, and reaction barriers of inorganic and bioinorganic systems, giving guidance on the title question. New development directions and current trends in density functional theory (DFT) are reviewed.

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A thermochemically competitive local hybrid functional without gradient corrections

Cited by 131 publications

References 33 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

Self-consistent generalized Kohn-Sham local hybrid functionals of screened exchange: Combining local and range-separated hybridization

Approximate Density Functionals: Which Should I Choose?

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