Self-consistent meta-generalized gradient approximation within the projector-augmented-wave method

Sun, Jianwei; Marsman, Martijn; Csonka, Gábor I.; Ruzsinszky, Adrienn; Pan, Hao; Kim, Yoon Suk; Kresse, Georg; Perdew, John P.

doi:10.1103/physrevb.84.035117

Cited by 202 publications

(198 citation statements)

References 71 publications

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“…This assessment provides therefore a thorough overview of the performance which can be expected by the various functionals in different applications. Our results are in good agreement with previous similar assessments of meta-GGA functionals, [31,286,301,306,308,309,329,361,363] but we extend them to several different systems and properties as well as to model systems.…”

Section: B E N C H M Ar K I Ng N O Ne M P I Ri C a L Exchang E-corrsupporting

confidence: 91%

“…In this case nonempirical meta-GGAs performs better than PBE and similar to the best GGA (PBEsol). [31,308,309] However, all these functionals are not able to predict reasonable cohesive energies results in Refs. [26] and the SSCE8 results in Ref.…”

Section: Results For Solid-state Systemsmentioning

confidence: 91%

“…[306] However, for properties of bulk solids, revTPSS usually improves over TPSS. [30,[307][308][309][310][311][312][313] For further details about the revTPSS performance see Section 4.…”

Section: The Revtpss Exchange-correlation Functional (2009)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: B E N C H M Ar K I Ng N O Ne M P I Ri C a L Exchang E-corrsupporting

confidence: 91%

Section: Results For Solid-state Systemsmentioning

confidence: 91%

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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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“…The considered functionals are LDA (7), PBEsol GGA (18), PBE GGA (11), B88 GGA (30), and MVS meta-GGA (this work). Table 2 compares the resulting meta-GGA (also denoted as MVS) against the PBEsol and PBE GGAs for heats of formation of the G3 set (43), barrier heights of the BH76 set (44,45), weak interactions of the S22 set (46), bond lengths of the T-96R set (47), and lattice constants of the LC20 set (48), where the first four are molecular test sets and the last is a solid-state test set. For computational details, see refs.…”

Section: Resultsmentioning

confidence: 99%

Semilocal density functional obeying a strongly tightened bound for exchange

Sun¹,

Perdew

Ruzsinszky³

2015

Proc. Natl. Acad. Sci. U.S.A.

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130

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Because of its useful accuracy and efficiency, density functional theory (DFT) is one of the most widely used electronic structure theories in physics, materials science, and chemistry. Only the exchange-correlation energy is unknown, and needs to be approximated in practice. Exact constraints provide useful information about this functional. The local spin-density approximation (LSDA) was the first constraint-based density functional. The LiebOxford lower bound on the exchange-correlation energy for any density is another constraint that plays an important role in the development of generalized gradient approximations (GGAs) and meta-GGAs. Recently, a strongly and optimally tightened lower bound on the exchange energy was proved for one-and twoelectron densities, and conjectured for all densities. In this article, we present a realistic "meta-GGA made very simple" (MGGA-MVS) for exchange that respects this optimal bound, which no previous beyond-LSDA approximation satisfies. This constraint might have been expected to worsen predicted thermochemical properties, but in fact they are improved over those of the Perdew-BurkeErnzerhof GGA, which has nearly the same correlation part. MVS exchange is however radically different from that of other GGAs and meta-GGAs. Its exchange enhancement factor has a very strong dependence upon the orbital kinetic energy density, which permits accurate energies even with the drastically tightened bound. When this nonempirical MVS meta-GGA is hybridized with 25% of exact exchange, the resulting global hybrid gives excellent predictions for atomization energies, reaction barriers, and weak interactions of molecules.density functional theory | exchange energy | lower bound D ensity functional theory (DFT) is a powerful tool for predicting structural, energetic, electronic, and magnetic properties of molecules, nanoparticles, surfaces, and solids in quantum chemistry, condensed matter physics, and materials science (1-3). It delivers in principle the exact ground-state energy and electron density for a system of electrons under an external potential, via self-consistent solution of auxiliary one-electron Schrödinger equations, the so-called Kohn-Sham equations. In practice, the density functional for the exchange-correlation energy, a typically small fraction of the total energy but a large fraction of the binding energy between atoms, has to be approximated. Because of their inexpensive computational cost and reasonable accuracy, semilocal approximations, which approximate the exact double integral for this energy with a single integral over 3D space, are widely used for a variety of properties, especially for large systems. They are also the bases for nonlocal corrections (4-6) that account for the nonlocality missing in the single integral. Nonlocal corrections are important for some systems and properties, e.g., strong correlation (4) and the long-range van der Waals interaction (6).Exact constraints on the exchange-correlation functional play essential roles in the development of ...

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“…It is known that BCC Fe is a ferromagnetic metal below its Curie point (1043 K) with a large local moment as 2.22 μ B per atom [58]. In this case, the local moment is underestimated by LSDA (1.94 μ B ).…”

Section: B Analysis Of the Effects Of The Exchange Enhancement Factormentioning

confidence: 98%

Testing the Jacob's ladder of density functionals for electronic structure and magnetism of rutileVO2

et al. 2014

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We employ semilocal density functionals (LSDA, PBE GGA, and meta-GGAs), LSDA+U, a nonlocal range-separated hybrid functional (HSE06), and the random phase approximation (RPA), to assess their performances for the groundstate magnetism and electronic structure of a strongly-correlated metal, rutile VO 2 . Using recent quantum Monte Carlo results as the benchmark, all tested semilocal and hybrid functionals as well as RPA (with PBE inputs) predict the correct magnetic ground states for R-VO 2 . The observed paramagnetism could arise from temperature-disordered local spin moments, or from the thermal destruction of these moments. All semilocal functionals also give the correct ground-state metallicity for R-VO 2 . However, in the ferromagnetic (FM) and anti-ferromagnetic (AFM) phases, LSDA+U and HSE06 incorrectly predict R-VO 2 to be a Mott-Hubbard insulator.

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Self-consistent meta-generalized gradient approximation within the projector-augmented-wave method

Cited by 202 publications

References 71 publications

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Semilocal density functional obeying a strongly tightened bound for exchange

Testing the Jacob's ladder of density functionals for electronic structure and magnetism of rutileVO2

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