Derivation of von Weizsäcker Equation Based οn Green-Gauss Theorem

Romanowski, Zbigniew; Krukowski, S.

doi:10.12693/aphyspola.115.653

Cited by 4 publications

(9 citation statements)

References 19 publications

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“…This additional term does not alter the integral value of the kinetic energy because the integral of the Laplacian of the one‐electron density is zero . The improvement from this additional term in eq.…”

Section: The Enhancement Factormentioning

confidence: 99%

“…With the addition of this term we see that the kinetic energy value does not alter, because the integral of the Laplacian of the density is zero. [53] The improvements that this added term brings about on the approximate enhancement factor for the Na, Al, Ar, Fe, Ni and Kr atoms are shown in Figs. [1] through [6].…”

Section: Some Properties Of the Enhancement Factormentioning

confidence: 99%

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Study of some simple approximations to the non-interacting kinetic energy functional

Salazar

Guarderas

Ludeña

et al. 2016

Int. J. Quantum Chem.

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Within the framework of density functional theory, a study of approximations to the enhancement factor of the noninteracting kinetic energy functional T s [q] has been presented. For this purpose, the model of Parr (Liu and Parr, Phys Rev A 1997, 55, 1792) based on a series expansion of T s [q] involving powers of the density was employed. Application to 34 atoms, at the Hartree-Fock level has shown that the enhancement factors present peaks that are in excellent agreement with those of the exact ones and give an accurate description of the shell structure of these atoms. The application of Z-dependent expansions to represent some of the terms of these approximations for neutral atoms and for positive and negative ions, which allows T s [q] to be cast in a very simple form, is also explored. Indications are given as to how these functionals may be applied to molecules and clusters. V C

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Section: The Enhancement Factormentioning

confidence: 99%

Section: Some Properties Of the Enhancement Factormentioning

confidence: 99%

Study of some simple approximations to the non-interacting kinetic energy functional

Salazar

Guarderas

Ludeña

et al. 2016

Int. J. Quantum Chem.

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“…, l, requiring a special normalization as discussed below. In general, the real spherical harmonic function y m l ð; 'Þ is the normalized linear combination of complex spherical harmonics (or, simply, spherical harmonics) Y m l ð; 'Þ (Pinchon & Hoggan, 2007;Romanowski et al, 2008):…”

Section: Introductionmentioning

confidence: 99%

Density- and wavefunction-normalized Cartesian spherical harmonics forl≤ 20

Michael

Volkov

2015

Acta Cryst Sect A

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The widely used pseudoatom formalism [Stewart (1976). Acta Cryst. A32, 565-574; Hansen & Coppens (1978). Acta Cryst. A34, 909-921] in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens [Acta Cryst. (1988), A44, 6-7]. It was shown that the analytical form for normalization coefficients is available primarily for l ≤ 4 [Hansen & Coppens, 1978; Paturle & Coppens, 1988; Coppens (1992). International Tables for Crystallography, Vol. B, Reciprocal space, 1st ed., edited by U. Shmueli, ch. 1.2. Dordrecht: Kluwer Academic Publishers; Coppens (1997). X-ray Charge Densities and Chemical Bonding. New York: Oxford University Press]. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7 (Paturle & Coppens, 1988). In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle-Coppens (Paturle & Coppens, 1988) method in the Wolfram Mathematica software to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.

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“…Estas correcciones mejoran notablemente las predicciones del modelo original. La inclusión de estas correcciones a la teoría original se conoce como la teoría de Thomas-Fermi-Dirac-Weizsäcker (TFDW) [65,72]. La cual describiremos a continuación.…”

Section: El Modelo Thomas-fermi-dirac-weizsäcker Tfdwunclassified

“…Para deducir el término de corrección de Weizsäcker usaremos el enfoque presentado en el trabajo de Z. Romanowski y S. Krukowski [65] basado en el teorema de Green-Gauss.…”

Section: El Modelo Thomas-fermi-dirac-weizsäcker Tfdwunclassified

Estudio variacional de átomos multielectrónicos limitados espacialmente por fronteras cerradas y abiertas

Garcia

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Confinement effects on the ground-state energy of many-electron atoms located inside a penetrable prolate spheroidal cavity are studied within a variational treatment of the Thomas-Fermi-Dirac-Weizsäcker density functional scheme. Given a confining cavity size and shape as well as barrier height, isotropic and anisotropic confinement effects on the energy evolution, ionization potentials and pressure are discussed as well as their different conditions for electron escape. Comparison of the spheroidal box results for the energy evolution with corresponding ab initio calculations for endohedral confinement of Ne within the supermolecule approach Ne@Ne10 (He10) suggests that reasonable agreement between both types of calculation is achieved provided the atom-in-a-box model incorporates the mean size of surrounding atoms with nuclei positioned at the spheroidal baseline of the cavity and a realistic choice of the mean confining barrier height.

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Derivation of von Weizsäcker Equation Based οn Green-Gauss Theorem

Cited by 4 publications

References 19 publications

Study of some simple approximations to the non-interacting kinetic energy functional

Study of some simple approximations to the non-interacting kinetic energy functional

Density- and wavefunction-normalized Cartesian spherical harmonics forl≤ 20

Estudio variacional de átomos multielectrónicos limitados espacialmente por fronteras cerradas y abiertas

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