Effective homogeneity of the exchange–correlation and non-interacting kinetic energy functionals under density scaling

Borgoo, Alex; Teale, Andrew M.; Tozer, David J.

doi:10.1063/1.3676722

Cited by 26 publications

(58 citation statements)

References 37 publications

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“…The coordinate and particlenumber scaling [72] defines, for different values of the parameter b, a whole family of scalings that do not preserve the particle number. The most important members of this scaling family are: the Thomas-Fermi scaling [73,74] (b51=3) which is relevant for the semiclassical theory of the nonrelativistic atom [73] ; the homogeneous density scaling [75][76][77][78] (b 5 0) that is related to the self-interaction problem [75] ; the uniformelectron-gas scaling (b521=3), that is important in the semiclassical theory of metallic clusters [79] ; and the strong-correlation scaling (b521 and k ) 1) that is important to describe the strong correlation limit. [72] APPENDIX C: FUNCTIONAL DERIVATIVES Let us consider the calculation of the functional derivative of a general functional of the form …”

Section: Appendix B: Density Scalingsmentioning

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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Section: Appendix B: Density Scalingsmentioning

confidence: 99%

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Sala

Fabiano

Constantin

2016

Int J of Quantum Chemistry

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“…If the value of k is system-independent, then the functional is homogeneous of degree k. If the value of k is system-dependent, then the functional is inhomogeneous and the degree of system-dependence provides a measure of the degree of inhomogeneity. In a recent study, 38 we used Eq. (4) to study the density scaling properties of the exchange-correlation functional.…”

Section: A Density Scaling and Influence Of The Integer Discontinuitymentioning

confidence: 99%

System-dependent exchange–correlation functional with exact asymptotic potential and εHOMO ≈ − I

Gledhill

Tozer

2015

The Journal of Chemical Physics

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Density scaling considerations are used to derive an exchange–correlation explicit density functional that is appropriate for the electron deficient side of the integer and which recovers the exact r → ∞ asymptotic behaviour of the exchange–correlation potential. The functional has an unconventional mathematical form with parameters that are system-dependent; the parameters for an N-electron system are determined in advance from generalised gradient approximation (GGA) calculations on the N- and (N − 1)-electron systems. Compared to GGA results, the functional yields similar exchange–correlation energies, but HOMO energies that are an order of magnitude closer to the negative of the vertical ionisation potential; for anions, the HOMO energies are negative, as required. Rydberg excitation energies are also notably improved and the exchange–correlation potential is visibly lowered towards the near-exact potential. Further development is required to improve valence excitations, static isotropic polarisabilities, and the shape of the potential in non-asymptotic regions. The functional is fundamentally different to conventional approximations.

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“…Thus, for the uniform-electron-gas and the ThomasFermi scalings 95,96 , where the γ → ∞ limit is important, large values of η u are relevant; on the opposite, for the homogeneous and fractional-particle scalings 95,97,98 , where γ → 0, small values of η u are important. These considerations will be significant to analyze the behavior of an η u -dependent enhancement factor in different conditions.…”

Section: Construction Of the U-meta-gga Exchange Functionalmentioning

confidence: 99%

Hartree potential dependent exchange functional

Constantin

Fabiano

Sala

2016

The Journal of Chemical Physics

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We introduce a novel non-local ingredient for the construction of exchange density functionals: the reduced Hartree parameter, which is invariant under the uniform scaling of the density and represents the exact exchange enhancement factor for one-and two-electron systems. The reduced Hartree parameter is used together with the conventional meta-generalized gradient approximation (meta-GGA) semilocal ingredients (i.e. the electron density, its gradient and the kinetic energy density) to construct a new generation exchange functional, termed u-meta-GGA. This u-meta-GGA functional is exact for the exchange of any one-and two-electron systems, is size-consistent and non-empirical, satisfies the uniform density scaling relation, and recovers the modified gradient expansion derived from the semiclassical atom theory. For atoms, ions, jellium spheres, and molecules, it shows a good accuracy, being often better than meta-GGA exchange functionals. Our construction validates the use of the reduced Hartree ingredient in exchange-correlation functional development, opening the way to an additional rung in the Jacob's ladder classification of non-empirical density functionals.

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Effective homogeneity of the exchange–correlation and non-interacting kinetic energy functionals under density scaling

Cited by 26 publications

References 37 publications

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

System-dependent exchange–correlation functional with exact asymptotic potential and εHOMO ≈ − I

Hartree potential dependent exchange functional

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