Semiclassical Neutral Atom as a Reference System in Density Functional Theory

Constantin, Lucian A.; Fabiano, Eduardo; Laricchia, Savio; Sala, Fabio Della

doi:10.1103/physrevlett.106.186406

Cited by 129 publications

(184 citation statements)

References 31 publications

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“…Equation 56 is based on the ThomasFermi scaling (Appendix B) and it has been used in the construction of GGA [95,189] and meta-GGA [152,153] functionals. Moreover, modified GE2 [73,104] and modified GE4 [189] (MGE2 and MGE4, respectively) have been derived from the semiclassical theory of atoms.…”

Section: Exchange Energy Of the Semiclassical Neutral Atommentioning

confidence: 99%

“…The semiclassical theory of neutral atoms [73,95,123,124,[183][184][185][186][187][188] provides the large-Z asymptotic expansion of the exchange energy [104] E x 5E HEG …”

Section: Exchange Energy Of the Semiclassical Neutral Atommentioning

confidence: 99%

“…The APBE functional [95] that uses l50:26, which was determined from the semiclassical atom theory (Equation 57). Moreover, to guarantee the correct LDA linear response constraint (Equation 107) it uses for correlation b50:079.…”

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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: Exchange Energy Of the Semiclassical Neutral Atommentioning

confidence: 99%

“…The semiclassical theory of neutral atoms [73,95,123,124,[183][184][185][186][187][188] provides the large-Z asymptotic expansion of the exchange energy [104] E x 5E HEG …”

Section: Exchange Energy Of the Semiclassical Neutral Atommentioning

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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“…Moreover, we recall that while in real atoms the electrons far from the nucleus experience a screened nuclear charge so that the corresponding orbitals differ from the hydrogenic ones, for large atoms or very positive ions, this screening effect becomes vanishingly small, and the simple model of hydrogenic orbitals becomes exact [69]. This model system has been largely used in DFT [68,[70][71][72], is very important for semiclassical physics [70,73,74] and has been used as a main reference system in recent GGA functionals [20,55].…”

Section: Kinetic and Exchange Energy Densities At The Nuclear Cusp Inmentioning

confidence: 99%

Kinetic and Exchange Energy Densities near the Nucleus

2016

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Abstract:We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the semiclassical limit of large non-relativistic neutral atoms. We show that a model based on the helium iso-electronic series is very accurate, as also confirmed by numerical calculations on real atoms up to two thousands electrons. Based on this model, we propose non-local density-dependent ingredients that are suitable for the description of the kinetic and exchange energy densities in the region close to the nucleus. These non-local ingredients are invariant under the uniform scaling of the density, and they can be used in the construction of non-local exchange-correlation and kinetic functionals.

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“…(11). The first has c 1 = 0; c 2 = 0, and so represents a Thomas-Fermi-von Weizsäcker form; this form will hereafter be denoted the 'two-term' form, defined by a single parameter, c 1 .…”

Section: Approximate T S [ρ] Functionalsmentioning

confidence: 99%

Molecular Binding in Post-Kohn–Sham Orbital-Free DFT

Borgoo

Green

Tozer

2014

J. Chem. Theory Comput.

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. For a series of 11 molecules, the binding broadly improves as the effective homogeneity improves, although the extent to which it improves is dependent on the accuracy of the non-interacting kinetic energy; optimal binding appears to require both to be accurate simultaneously. The use of a Thomas-Fermi-von Weizsäcker form, augmented with a second gradient correction, goes some way towards achieving this, exhibiting molecular * To whom correspondence should be addressed † Oslo University ‡ Durham University 1 binding on average. The findings are discussed in terms of the non-interacting kinetic potential and the Hellmann-Feynman theorem. The extent to which the functionals can reproduce the system-dependence of the near-exact effective homogeneity is quantified and potential energy curves are presented for selected molecules. The study provides impetus for including density scaling homogeneity considerations in the design of noninteracting kinetic energy functionals.

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Semiclassical Neutral Atom as a Reference System in Density Functional Theory

Cited by 129 publications

References 31 publications

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Kinetic and Exchange Energy Densities near the Nucleus

Molecular Binding in Post-Kohn–Sham Orbital-Free DFT

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