The local potential determining the square root of the ground-state electron density of atoms and molecules from the Schrödinger equation

March, N. H.

doi:10.1016/0375-9601(86)90123-4

Cited by 165 publications

(78 citation statements)

References 14 publications

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“…In the Kohn-Sham scheme of the density functional theory, the non-interacting kinetic energy can be partitioned as a sum of the full Weizsäcker kinetic energy ( [20]) and the so-called Pauli energy T p [21][22][23]:…”

Section: Discussionmentioning

confidence: 99%

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Euler equation for descriptors of the spherically symmetric coulomb systems

Nagy

2016

Int J of Quantum Chemistry

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Section: Discussionmentioning

confidence: 99%

“…The appearence of the Pauli potential [21][22][23] in the Euler equation (31) is the consequence of the Pauli principle. The density is determined by a single equation (31).…”

Section: Discussionmentioning

confidence: 99%

Euler equation for descriptors of the spherically symmetric coulomb systems

Nagy

2016

Int J of Quantum Chemistry

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“…of the coefficients in the 1=Z expansion (23). e 0 N ð Þ was shown to have this property, and approximate forms for e 1 N ð Þ and e 2 N ð Þ were proposed.…”

Section: Ionization Potentials Calculated Via the 1=z Expansionmentioning

confidence: 99%

“…The theme of the present section concerns the potential V P introduced in eq. (35), [21][22][23][24] and now referred to as the Pauli potential. [23] Levy and G€ orling [20] also comment that the "seeds" for eq.…”

Section: The Pauli Potential In Dftmentioning

confidence: 99%

“…(35), [21][22][23][24] and now referred to as the Pauli potential. [23] Levy and G€ orling [20] also comment that the "seeds" for eq. (35) were provided by the observation of March and Murray [25] that the Euler equation of the von Weizs€ acker approximation [26,27] may be represented as a Schr€ odinger equation for the density amplitude ffiffiffiffiffiffiffiffi ffi q r ð Þ p .…”

Section: The Pauli Potential In Dftmentioning

confidence: 99%

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Chemical and ionization potentials: Relation via the Pauli potential and NOF theory

Piris

March

2015

Int J of Quantum Chemistry

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Hartree-Fock (HF) theory makes the prediction that for neutral atoms the chemical potential (l) is equal to minus the ionization potential (I). This has led us to inquire whether this intimate relation is sensitive to electron correlation. We present here therefore some discussion of the predictions for neutral atoms and atomic ions, and some homonuclear diatomic molecules. An account of fairly recent progress in obtaining the HF ionization potentials for the isoelectronic series of He, Be, Ne, Mg, and Ar-like atomic ions is first considered. The 1=Z expansion for total non-relativistic energy of atomic ions evokes that l52I is not very sensitive to the introduction of electron correlation. The connection between l and I for neutral atoms via the Pauli potential (V P ) is then examined. We focus on the relation of V P to more recent advances in density functional theory (DFT) plus low-order density matrix theory. In this context, the example of nonrelativistic Be-like atomic ions is treated. Afterward, we introduce the bosonized equation for the density amplitude ffiffiffi q p , which emphasizes the major role that plays dT W =dq in DFT. For spherical atomic densities, the bosonized potential argument strongly suggests also that l52I remains valid in the presence of electron correlation. Finally, numerical estimates of l and I from natural orbital functional (NOF) theory are presented for neutral atoms ranging from H to Kr. The predicted vertical I by means of the extended Koopmans' theorem are in good agreement with the corresponding experimental data. However, the NOF theory of l lowers the experimental values considerably as we approach to noble gas atoms though oscillatory behavior is in evidence. V C 2015 Wiley Periodicals, Inc. DOI: 10.1002/qua.25039 Ionization Potential and Asymptotic Large r Behavior of Ground-State Density of Spherical AtomsIt seems natural to begin this review relating to advances in density functional theory (DFT) with some account of fairly recent progress in obtaining the ground-state electron density q r ð Þ in some spherical atoms. Then, the nonrelativistic twoelectron He-like series of atomic ions with atomic number Z affords an appropriate starting point.Large r behavior of q r ð Þ in terms of I and Z It is well-known [1] that, in atomic units (a.u.), the ground-state density of rare gas atoms with spherical electron density q r ð Þ falls off at sufficiently large r as where I is the ionization potential. For sufficiently large Z, the expressions for constants n and A were found by March and Pucci [2] based on the early work of Schwartz, [3] namely, n % 2ð3=4ÞZ 21 and A5ð2Z 3 =pÞ½12ð3=4ZÞlnZ1OðZ 21 Þ . However, a more general relationship between n and I for arbitrary atomic number Z can be obtained using the DFT for the He-like series of atomic ions. [4] Consider V(r) is the one-body potential of DFT, then the constant chemical potential equation reads [5] l5 dT s q ½ dq 1V r ð Þwhere T s q ½ is the single-particle kinetic energy functional. While T s is still unknown for gener...

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Structure of the optimized effective Kohn?Sham exchange potential and its gradient approximations

Gritsenko

Leeuwen

Baerends

1996

Int. J. Quantum Chem.

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mAn analysis of the structure of the optimized effective Kohr-Sham exchange potential v, and its gradient approximations is presented. The potential is decomposed into the Slater potential us and the response of us to density variations, vresp. The latter exhibits peaks that reflect the atomic shell structure. Kohr-Sham exchange potentials derived from current gradient approaches for the exchange energy are shown to be quite reasonable for the Slater potential, but they fail to approximate the response part, which leads to poor overall potentials. Improved potentials are constructed by a direct fit of u, with a gradient-dependent Pad6 approximant form. The potentials obtained possess proper asymptotic and scaling properties and reproduce the shell structure of the exact vx.

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The local potential determining the square root of the ground-state electron density of atoms and molecules from the Schrödinger equation

Cited by 165 publications

References 14 publications

Euler equation for descriptors of the spherically symmetric coulomb systems

Euler equation for descriptors of the spherically symmetric coulomb systems

Chemical and ionization potentials: Relation via the Pauli potential and NOF theory

Structure of the optimized effective Kohn?Sham exchange potential and its gradient approximations

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