Rungs 1 to 4 of DFT Jacob’s ladder: Extensive test on the lattice constant, bulk modulus, and cohesive energy of solids

Tran, Fabien; Stelzl, Julia; Blaha, Peter

doi:10.1063/1.4948636

Cited by 229 publications

(209 citation statements)

References 185 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%

“…[329] 3.2.9 | The SCAN exchange-correlation functional (2015) The Strongly Constrained and Appropriately Normed (SCAN) K-meta-GGA functional [152] has the following exchange enhancement factor (see Equation 5): [70] and bðr s Þ is defined in Equation 83. As for the exchange, The SCAN functional contains several constants, 9 AM-parameters, and at least 2 BS-parameters (from Ar 2 fitting).…”

Section: The Mgga-ms1 and Mgga-ms2 Exchangecorrelation Functionals 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: The Mgga-ms1 and Mgga-ms2 Exchangecorrelation Functionals mentioning

confidence: 99%

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Sala

Fabiano

Constantin

2016

Int J of Quantum Chemistry

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“…These systems are not dominated by dispersion effects and they are well described by the original SG4 functional [26,27]. Nevertheless, it is important to check that the addition of the rVV10m correction is not worsening this accuracy for these materials, in order to verify the broad applicability of the method.…”

Section: Sg4-rvv10mmentioning

confidence: 99%

Solid-State Testing of a Van-Der-Waals-Corrected Exchange-Correlation Functional Based on the Semiclassical Atom Theory

et al. 2018

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Abstract:We extend the SG4 generalized gradient approximation, developed for covalent and ionic solids with a nonlocal van der Waals functional. The resulting SG4-rVV10m functional is tested, considering two possible parameterizations, for various kinds of bulk solids including layered materials and molecular crystals as well as regular bulk materials. The results are compared to those of similar methods, PBE + rVV10L and rVV10. In most cases, SG4-rVV10m yields a quite good description of systems (from iono-covalent to hydrogen-bond and dispersion interactions), being competitive with PBE + rVV10L and rVV10 for dispersion-dominated systems and slightly superior for iono-covalent ones. Thus, it shows a promising applicability for solid-state applications. In a few cases, however, overbinding is observed. This is analysed in terms of gradient contributions to the functional.

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“…[14][15][16] Our test set of 22 bulk crystals includes main-group metals Li, K, Al, semiconductors diamond, Si, β-SiC, Ge, BP, AlP, AlAs, GaN, GaP, GaAs, ionic crystals NaCl, NaF, LiCl, LiF, MgO, MgS, and transition metals Cu, Pd, Ag. Calculations on these solids were performed using a locally modified version 10 of the Gaussian program 17 with periodic boundary conditions (PBC).…”

Section: Lattice Constantsmentioning

confidence: 99%

Assessment of the Tao-Mo nonempirical semilocal density functional in applications to solids and surfaces

Car

Staroverov

et al. 2017

Phys. Rev. B

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Recently, Tao and Mo developed a new semilocal exchange-correlation density functional. The exchange part of this functional is derived from a density matrix expansion corrected to reproduce the fourth-order gradient expansion in the slowly-varying-density limit, while the correlation part is based on the TPSS correlation functional with a modification for the low-density limit. In the present work, the Tao-Mo functional is assessed by computing various properties of solids and jellium surfaces. This includes 22 lattice constants and bulk moduli, 30 band gaps, 7 cohesive energies, and jellium surface exchange and correlation energies for the density parameter r s in the range from 2 to 3 bohrs. Our calculations show that the Tao-Mo meta-generalized gradient approximation can yield consistently high accuracy for most properties considered here, with mean absolute errors of 0.025 Å for lattice constants, 7.0 GPa for bulk moduli, 0.08 eV/atom for cohesive energies, and 35 erg/cm 2 for surface exchange-correlation energies.The mean absolute error in band gaps is larger than that of TPSS, but slightly smaller than the errors of LSDA, PBE, and revTPSS. However, band gaps are still underestimated, particularly for large-gap semiconductors, compared to the HSE06 nonlocal screened hybrid functional.

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Rungs 1 to 4 of DFT Jacob’s ladder: Extensive test on the lattice constant, bulk modulus, and cohesive energy of solids

Cited by 229 publications

References 185 publications

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Solid-State Testing of a Van-Der-Waals-Corrected Exchange-Correlation Functional Based on the Semiclassical Atom Theory

Assessment of the Tao-Mo nonempirical semilocal density functional in applications to solids and surfaces

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