Erratum: Properties of constraint-based single-point approximate kinetic energy functionals [Phys. Rev. B<b>80</b>, 245120 (2009)]

Karasiev, Valentin V.; Jones, R. S.; Trickey, S. B.; Harris, Frank E.

doi:10.1103/physrevb.87.239903

Cited by 29 publications

(61 citation statements)

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“…One result has been the emergence of active research on orbital-free DFT (OFDFT), that is, approximate functionals for the ingredients of the KS free energy, namely the KS kinetic energy (KE) T s , entropy S s , and XC free energy F xc or their ground-state counterparts. Almost all of this effort has been for ground-state OFKE functionals [43][44][45][46] . (Note that most of the OFKE literature invokes the KS separation of the KE in order to use existing E xc approximations consistently.)…”

Section: Introductionmentioning

confidence: 99%

Temperature-dependent behavior of confined many-electron systems in the Hartree-Fock approximation

2012

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Many-electron systems confined at substantial finite temperatures and densities present a major challenge to density functional theory. In particular, there is comparatively little systematic knowledge about the behavior of free-energy density functionals for temperatures and pressures of interest, for example, in the study of warm dense matter. As with ground-state functionals, development of approximate free-energy functionals is faced with significant needs for reliable assessment and calibration data. Here we address, in part, this need for detailed results on well-characterized systems. We present results on a comparatively simple, well-defined, computationally feasible but previously unexplored model, the thermal Hartree-Fock approximation. We discuss the main technical tasks (defining a suitable basis and evaluation of the required matrix elements) and give an illustrative initial application which probes both the content of the model and the solution techniques: a system of eight one-electron atoms with nuclei at fixed, arbitrary positions in a hard-walled box. Even this simple system produces physical behavior different from that produced by simple ground state density functionals used at finite temperature (a common approximation in the study of WDM).

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Section: Introductionmentioning

confidence: 99%

Temperature-dependent behavior of confined many-electron systems in the Hartree-Fock approximation

2012

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“…P92 20 and E00 21 tested by X-C) and our GGAs (VT84F, PBE2) is that the former do not predict binding in small molecules at all, while the latter do predict semi-quantitatively correct binding in those molecules and simple solids 6,17,18 . This categorical distinction and the broad utility of these GGAs is suggestive of having achieved a universal functional (though certainly not a proof).…”

Section: And References Therein X-c's Numerical Exploration Of G([n]mentioning

confidence: 99%

“…(For reference, the calculated equi- X-C also note that the near-nucleus density from PBE2 is peculiar. This is almost inevitable with any properly positive-definite GGA 17 . A singularity at the origin in the Pauli potential causes the artifact.…”

Section: And References Therein X-c's Numerical Exploration Of G([n]mentioning

confidence: 99%

Comment on “Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation”

2015

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“…[126]. At the nuclear cusp of any atom the reduced gradient is quite small (s<0:4), so that all the common GGA exchange enhancement factors behave as F x % 11ls 2 , to satisfy some gradient expansion: thus L % 2ql which diverges at the nuclear cusp as q, see Section 2.1, instead of being finite.…”

Section: Nuclear Cusp Problemmentioning

confidence: 99%

“…In general, modeling s KS using density ingredients only (i.e., s and q) is a very difficult problem [60,126] because of its strong nonlocality even for light atoms. [129] In fact, s KS has been evaluated as a functional of the density using a machine-learning technique with about one hundred thousands empirical parameters, for onedimensional systems, [130,131] as well as for real molecules.…”

Section: The Positive-defined Ks Kinetic Energy Densitymentioning

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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Erratum: Properties of constraint-based single-point approximate kinetic energy functionals [Phys. Rev. B80, 245120 (2009)]

Abstract: Erratum: Properties of constraint-based single-point approximate kinetic energy functionals [Phys. Rev. B 80, 245120 (2009)]

Cited by 29 publications

References 1 publication

Temperature-dependent behavior of confined many-electron systems in the Hartree-Fock approximation

Temperature-dependent behavior of confined many-electron systems in the Hartree-Fock approximation

Comment on “Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation”

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

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