Kinetic and Exchange Energy Densities near the Nucleus

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

doi:10.3390/computation4020019

Cited by 25 publications

(28 citation statements)

References 91 publications

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“…It is seen in Figure that a closer fit is provided by the shell‐by‐shell optimized functional. In addition, the exact asymptotic behavior at the nucleus is not fulfilled either by these expansions which show a slight negative deviation at the nucleus.…”

Section: Calculation and Resultsmentioning

confidence: 88%

The Liu‐Parr power series expansion of the Pauli kinetic energy functional with the incorporation of shell‐inducing traits: Atoms

Ludeña

Salazar

Cornejo

et al. 2018

Int J of Quantum Chemistry

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An approximate expression for the Pauli kinetic energy functional Tp is advanced in terms of the Liu‐Parr expansion [S. Liu, R.G. Parr, Phys. Rev. A 1997, 55, 1792] which involves a power series of the one‐electron density. We use this explicit functional for Tp to compute the value of the noninteracting kinetic energy functional Ts of 34 atoms, from Li to Kr (and their positive and negative monoions). In particular, we examine the effect that a shell‐by‐shell mean‐square optimization of the expansion coefficients has on the kinetic energy values and explore the effect that the size of the expansion, given by the parameter n, has on the accuracy of the approximation. The results yield a mean absolute percent error Δabs=(1/N)∑i=1NΔi for 34 neutral atoms of 0.15, 0.08, 0.04, 0.03, and 0.01 for expansions with n = 3, 4, 5, 6, and 7, respectively (where Δi=100|Tnormalsapp(i)−TnormalsHF(i)|/TnormalsHF(i)). We show that these results, which are the most accurate ones obtained to date for the representation of the noninteracting kinetic energy functional, stem from the imposition of shell‐inducing traits. We also compare these Liu‐Parr functionals with the exact but nonexplicit functional generated in the local‐scaling transformation version of DFT.

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Section: Calculation and Resultsmentioning

confidence: 88%

The Liu‐Parr power series expansion of the Pauli kinetic energy functional with the incorporation of shell‐inducing traits: Atoms

Ludeña

Salazar

Cornejo

et al. 2018

Int J of Quantum Chemistry

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“…Constantin et al [10] investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. They propose non-local density-dependent ingredients that allow a proper description in this special region.…”

Section: Contentmentioning

confidence: 99%

Special Issue “50th Anniversary of the Kohn–Sham Theory—Advances in Density Functional Theory”

Nagy

Schwarz

2016

Computation

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“…For real atoms, this expression is not exact but it is a good approximation because the 1s-shell gives the main contribution to nuclear properties: for an atom with an infinite number of electrons we have s % 0:3534, see Ref. [112].…”

Section: Input Ingredients Of Meta-gga Functionals 211 | Inhomogementioning

confidence: 99%

“…[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. [132] At the nuclear cusp s KS behaves as [133] s KS 5s W 13s W ½q P ; [112] In the density tail asymptotic region of finite systems we have (to first order) [5,134] …”

Section: The Positive-defined Ks Kinetic Energy Densitymentioning

confidence: 99%

“…Conversely, for Be the tail region originates from the nondegenerate s-type HOMO, thus a KS ! 0; in a similar way, at the bond of Be 2 , a KS is close to zero.At the nuclear cusp, it can be shown that a KS 0:0286, see Refs.[133] and [112].We recall that 1= 11ða KS Þ 2 h i is the electron localization function (ELF), often used in the characterization of chemical bonds. [143][144][145][146][147] Moreover, a KS can distinguish and quantify the orbital overlap, [148] the nonlocality of the KED at the nuclear cusp, [133] in the tail of the density, [133,149] and in the quasi-two-dimensional regime.…”

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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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Kinetic and Exchange Energy Densities near the Nucleus

Cited by 25 publications

References 91 publications

The Liu‐Parr power series expansion of the Pauli kinetic energy functional with the incorporation of shell‐inducing traits: Atoms

The Liu‐Parr power series expansion of the Pauli kinetic energy functional with the incorporation of shell‐inducing traits: Atoms

Special Issue “50th Anniversary of the Kohn–Sham Theory—Advances in Density Functional Theory”

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

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