Electron density theory of atoms and molecules

March, N. H.

doi:10.1021/j100209a022

Cited by 111 publications

(67 citation statements)

References 3 publications

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“…[1][2][3][4][5][6] The DFT is based on the earlier fundamental work of Hohenberg and Kohn 7 and Kohn and Sham. 8 In the Kohn-Sham DFT formalism, 8 the electron density is decomposed into a set of orbitals, leading to a set of one-electron Schrödinger-type equations to be solved self-consistently.…”

Section: Introductionmentioning

confidence: 99%

Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields

Chu¹

2005

The Journal of Chemical Physics

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A critical re-assignment of the Rydberg states of iodomethane based on new polarization data J. Chem. Phys. 138, 134308 (2013) In this paper, we present a short account of some recent developments of self-interaction-free density-functional theory ͑DFT͒ and time-dependent density-functional theory ͑TDDFT͒ for accurate and efficient treatment of the electronic structure, and time-dependent quantum dynamics of many-electron atomic and molecular systems. The conventional DFT calculations using approximate and explicit exchange-correlation energy functional contain spurious self-interaction energy and improper long-range asymptotic potential, preventing reliable treatment of the excited, resonance, and continuum states. We survey some recent developments of DFT/TDDFT with optimized effective potential ͑OEP͒ and self-interaction correction ͑SIC͒ for both atomic and molecular systems for overcoming some of the above mentioned difficulties. These DFT ͑TDDFT͒/ OEP-SIC approaches allow the use of orbital-independent single-particle local potential which is self-interaction free. In addition we discuss several numerical techniques recently developed for efficient and high-precision treatment of the self-interaction-free DFT/TDDFT equations. The usefulness of these procedures is illustrated by a few case studies of atomic, molecular, and condensed matter processes of current interests, including ͑a͒ autoionizing resonances, ͑b͒ relativistic OEP-SIC treatment of atomic structure ͑Z = 2-106͒, ͑c͒ shell-filling electronic structure in quantum dots, ͑d͒ atomic and molecular processes in intense laser fields, including multiphoton ionization, and very-high-order harmonic generation, etc. For the time-dependent processes, an alternative Floquet formulation of TDDFT is introduced for time-independent treatment of multiphoton processes in intense periodic or quasiperiodic fields. We conclude this paper with some open questions and perspectives of TDDFT.

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Section: Introductionmentioning

confidence: 99%

Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields

Chu¹

2005

The Journal of Chemical Physics

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“…[14], we obtain the following expression for the kinetic energy Our task of expressing the kinetic energy as a functional of the one-particle density can be accomplished by introducing eq. [4] into eq. [17].…”

Section: Explicit Kinetic Energy Density Functionalsmentioning

confidence: 99%

Approximate kinetic energy density functionals generated by local-scaling transformations

Ludeña¹,

López-Boada²,

Pino³

1996

Can. J. Chem.

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Different stages in the development of density functional theory are succinctly reviewed for the purpose of tracing the origin of the local-scaling transformation version of density functional theory. Explicit kinetic energy functionals are generated within this theory. These functionals are analyzed in terms of several approximations to the local-scaling function and are applied to a few selected first-row atoms.Key words: density functional theory, kinetic energy density functionals, local-scaling transformations, explicit kinetic energy functionals, kinetic energy of first-row atoms.RCsumC : On fait une revue succincte des divers stades du dCveloppement de la thCorie de la fonctionnelle de densit6 dans le but de diterminer l'origine de la version de la thCorie de la fonctionnelle de densit6 bas6e sur la transformation d'tchelle locale. Des fonctionnelles explicites de l1Cnergie cinktique sont gCnCrCes I'intCrieur de cette thCorie. On analyse ces fonctionnelles en termes de plusieurs approximations 2 la fonction d'ichelle locale et on les applique a quelques ClCments choisis de la premikre pCriode.Mots c l b : thCorie de la fonctionnelle de densitC, fonctionnelles de densit6 de 1'Cnergie cinCtique, transformations d'Cchelle locale, fonctionnelles explicites de 1'Cnergie cinktique, Cnergie cinCtique des ClCments de la premitre pkriode.[Traduit par la redaction]

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“…(2) is readily derived from eq. (3), one finds the well-known von Weizs€ acker equation [6] l5 jrqj 2 8q 2 Dq 4q 1V r ð Þ…”

Section: Behavior Of Ground-state Density Of Spherical Atomsmentioning

confidence: 99%

“…(6) in the asymptotic form (1), the ionization potential has to be expressed as a function of atomic number Z. A quadratic fit of the ionization potentials obtained by the difference between 2Z 2 =2 (energy of the one-electron ion) and the diffusion quantum Monte Carlo (DMC) energy of the twoelectron system, in terms of Z, in the range Z c Z 2, gives the following result [4] :…”

Section: Behavior Of Ground-state Density Of Spherical Atomsmentioning

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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Electron density theory of atoms and molecules

Cited by 111 publications

References 3 publications

Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields

Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields

Approximate kinetic energy density functionals generated by local-scaling transformations

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

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