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

Janesko, Benjamin G.; Krukau, Aliaksandr V.; Scuseria, Gustavo E.

doi:10.1063/1.2980056

Cited by 72 publications

(68 citation statements)

References 94 publications

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“…This approach has an increasing popularity ("generalized KohnSham" approach) due to its relative simplicity compared to the rigorous optimized effective potential method. 29 All the terms of the B05 potential matrix, F, are readily available except those coming from the ND correlation components, Eqs. (8) and (9), μ and ν below are basis function indices …”

Section: Dealing With the Discontinuities In The B05 Functional Amentioning

confidence: 99%

Improved self-consistent and resolution-of-identity approximated Becke'05 density functional model of nondynamic electron correlation

Proynov

Liu

Shao

et al. 2012

The Journal of Chemical Physics

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In a recent letter [E. Proynov, Y. Shao, and J. Kong, Chem. Phys. Lett. 493, 381 (2010)], Becke's B05 model of nondynamic electron correlation in density functional theory was implemented selfconsistently with computational efficiency (the "SCF-RI-B05" scheme). Important modifications of the algorithm were done in order to make the self-consistency feasible. In the present work, we give a complete account of the SCF-RI-B05 algorithm, including all the formulae for the analytical representation of the B05 functional and for its self-consistent field (SCF) potential. The average performance of the SCF-RI-B05 method reported in the above letter was somewhat less accurate, compared to the original B05 implementation, mainly because the parameters of the original B05 model were optimized with post-local-spin-density calculations. In this work, we report improved atomization energies with SCF-RI-B05, based on a SCF re-optimization of its four linear parameters. The re-optimized SCF-RI-B05 scheme is validated also on reaction barriers, and on the subtle energetics of NO dimer, an exemplary system of strong nondynamic correlation. It yields both the binding energy and the singlet-triplet splitting of the NO dimer correctly, and close to the benchmarks reported in the literature.

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Section: Dealing With the Discontinuities In The B05 Functional Amentioning

confidence: 99%

Improved self-consistent and resolution-of-identity approximated Becke'05 density functional model of nondynamic electron correlation

Proynov

Liu

Shao

et al. 2012

The Journal of Chemical Physics

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“…[42,51] (2) Position dependence: in local hybrid functionals developed by Scuseria et al, the mixing parameter is determined as a function of the electron density at each point in space, thereby avoiding the need of empirical parameters. [52][53][54][55] (3) Perturbation theory: the mixing parameter used in the Perdew-Burke-Ernzerhof hybrid functional (PBE0) and the Heyd−Scuseria−Ernzerhof (HSE) functional (an approximation of the former) is 25%, [45,56] which was determined analytically via perturbation theory. [57,58] Subsequent benchmarks showed that HSE predicts accurate thermochemical properties for molecular test sets (G2), [45] and good band gaps for simple semiconductors such as C, Si, BN, BP, SiC, β-GaN, GaP, and MgO with a mean absolute error (MAE) of 0.2 eV, which is much better than either LDA and PBE (MAE: ~1.4 eV).…”

Section: Introductionmentioning

confidence: 99%

Calibrating transition-metal energy levels and oxygen bands in first-principles calculations: Accurate prediction of redox potentials and charge transfer in lithium transition-metal oxides

2015

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Transition metal (TM) oxides play an increasingly important role in technology today including applications such as catalysis, solar energy harvesting, and energy storage. In many of these applications, the details of their electronic structure near the Fermi level are critically important for their properties. We propose a first-principles based computational methodology for the accurate prediction of oxygen charge transfer in TM oxides and lithium TM (Li-TM) oxides. To obtain accurate electronic structures, the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional is adopted and the amount of exact Hartree-Fock exchange (mixing parameter) is adjusted to reproduce reference band gaps.We show that the HSE06 functional with optimal mixing parameter yields not only improved electronic densities of states but also better energetics (Li-intercalation voltages) for LiCoO 2 and LiNiO 2 as compared to GGA, GGA+U and standard HSE06.We find that the optimal mixing parameters for TM oxides are system-specific and correlate with the covalency (ionicity) of the TM species. Strong covalent (ionic) nature of TM-O bonding leads to lower (higher) optimal mixing parameters. We find that optimized HSE06 functionals predict stronger hybridization of the Co 3d and O 2p orbitals than GGA, resulting in a greater contribution from oxygen states to charge compensation upon delithiation in LiCoO 2 . We also find that the band gaps of Li-TM oxides increase linearly with the mixing parameter, enabling the straightforward determination of optimal mixing parameters based on GGA (α = 0.0) and HSE06 (α = 0.25) calculations. Our results also show that G 0 W 0 @GGA+U band gaps of TM oxides (MO, M = Mn, Co, Ni) and LiCoO 2 agree well with experimental references, suggesting that G 0 W 0 calculations can be used as a reference for the calibration of the mixing parameter in case no experimental band gap has been reported. 3

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“…Perdew et al [42] pointed out that such behavior hinders the correct description of space dependent phenomena. To overcome this shortcoming the so called local hybrids were suggested [43][44][45][46][47][48][49].…”

Section: Introductionmentioning

confidence: 99%

Theoretical unification of hybrid-DFT andDFT + Umethods for the treatment of localized orbitals

et al. 2014

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Hybrid functionals serve as a powerful practical tool in different fields of computational physics and quantum chemistry. On the other hand, their applicability for the case of correlated d and f orbitals is still questionable and needs more considerations. In this article we formulate the on-site occupation dependent exchange correlation energy and effective potential of hybrid functionals for localized states and connect them to the on-site correction term of the DFT + U method. The resultant formula indicates that the screening of the onsite electron repulsion is governed by the ratio of the exact exchange in hybrid functionals. Our derivation provides a theoretical justification for adding a DFT + U -like on-site potential in hybrid-DFT calculations to resolve issues caused by overscreening of localized states. The resulting scheme, hybrid DFT + V w , is tested for chromium impurity in wurtzite AlN and vanadium impurity in 4H-SiC, which are paradigm examples of systems with different degrees of localization between host and impurity orbitals.

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

Cited by 72 publications

References 94 publications

Improved self-consistent and resolution-of-identity approximated Becke'05 density functional model of nondynamic electron correlation

Improved self-consistent and resolution-of-identity approximated Becke'05 density functional model of nondynamic electron correlation

Calibrating transition-metal energy levels and oxygen bands in first-principles calculations: Accurate prediction of redox potentials and charge transfer in lithium transition-metal oxides

Theoretical unification of hybrid-DFT andDFT + Umethods for the treatment of localized orbitals

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