The quantum defect: The true measure of time-dependent density-functional results for atoms

Faassen, Meta van; Burke, Kieron

doi:10.1063/1.2173252

Cited by 17 publications

(30 citation statements)

References 37 publications

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“…The same is true for the deviations between the perturbative RPA energies on EXX-only basis and the self-consistent RPA results. This result is expected to hold quite generally, as long as one does not examine a quantity which is particularly sensitive to the correlation potential (as, for instance, the quantum defect of high Rydberg states 61 ). In fact, Table IV indicates that even a perturbative treatment of both the exact exchange and the RPA may be legitimate for very complex systems, in which even self-consistent calculations with the exact exchange are too expensive.…”

Section: A Sensitivity To Form Of Ks Orbitalsmentioning

confidence: 96%

Random-phase-approximation-based correlation energy functionals: Benchmark results for atoms

Jiang

Engel²

2007

The Journal of Chemical Physics

112

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The random phase approximation (RPA) for the correlation energy functional of density functional theory has recently attracted renewed interest. Formulated in terms of the Kohn-Sham (KS) orbitals and eigenvalues, it promises to resolve some of the fundamental limitations of the local density and generalized gradient approximations, as for instance their inability to account for dispersion forces. First results for atoms, however, indicate that the RPA overestimates correlation effects as much as the orbital-dependent functional obtained by a second order perturbation expansion on the basis of the KS Hamiltonian. In this contribution, three simple extensions of the RPA are examined, (a) its augmentation by an LDA for short-range correlation, (b) its combination with the second order exchange term, and (c) its combination with a partial resummation of the perturbation series including the second order exchange. It is found that the ground state and correlation energies as well as the ionization potentials resulting from the extensions (a) and (c) for closed sub-shell atoms are clearly superior to those obtained with the unmodified RPA. Quite some effort is made to ensure highly converged RPA data, so that the results may serve as benchmark data. The numerical techniques developed in this context, in particular for the inherent frequency integration, should also be useful for applications of RPA-type functionals to more complex systems.

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Section: A Sensitivity To Form Of Ks Orbitalsmentioning

confidence: 96%

Random-phase-approximation-based correlation energy functionals: Benchmark results for atoms

Jiang

Engel²

2007

The Journal of Chemical Physics

112

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“…7 is shallow and short-ranged, and so has no Rydberg series. Exact exchange or SIC functionals take care of this [98]; Fig. 8 shows how accurate the LDA-SIC potential is in comparison.…”

Section: B Tddft Approximationsmentioning

confidence: 99%

“…For example, it is the response of the two non-interacting KS electrons sitting in the KS potential of Fig. 2, and ω q are the The differences between the KS eigenvalues obtained using the exact potential [98].…”

Section: A Time-dependent Dftmentioning

confidence: 99%

Density functional calculations of nanoscale conductance

Koentopp

Chang

Burke

et al. 2008

J. Phys.: Condens. Matter

Self Cite

141

156

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Density functional calculations for the electronic conductance of single molecules are now common. We examine the methodology from a rigorous point of view, discussing where it can be expected to work, and where it should fail. When molecules are weakly coupled to leads, local and gradientcorrected approximations fail, as the Kohn-Sham levels are misaligned. In the weak bias regime, XC corrections to the current are missed by the standard methodology. For finite bias, a new methodology for performing calculations can be rigorously derived using an extension of time-dependent current density functional theory from the Schrödinger equation to a Master equation. Contents

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“…As |R| → ∞, the results coincide with those of standard KS-DFT. For higher-energy resonances, TDDFT is needed as a matter of principle [9,10].First, we note that as |R| → ∞, the complex density n θ (r) associated with the LER ofbecomes equal to the complex densityñ θ (r) associated toṽ(re iθ ). In Eq.…”

mentioning

confidence: 99%

“…As |R| → ∞, the results coincide with those of standard KS-DFT. For higher-energy resonances, TDDFT is needed as a matter of principle [9,10].…”

mentioning

confidence: 99%

Density Functional Resonance Theory of Unbound Electronic Systems

Whitenack

Wasserman

2011

Phys. Rev. Lett.

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Density Functional Resonance Theory (DFRT) is a complex-scaled version of ground-state Density Functional Theory (DFT) that allows one to calculate the resonance energies and lifetimes of metastable anions. In this formalism, the exact energy and lifetime of the lowest-energy resonance of unbound systems is encoded into a complex "density" that can be obtained via complex-coordinate scaling. This complex density is used as the primary variable in a DFRT calculation just as the ground-state density would be used as the primary variable in DFT. As in DFT, there exists a mapping of the N -electron interacting system to a Kohn-Sham system of N non-interacting particles in DFRT. This mapping facilitates self consistent calculations with an initial guess for the complex density, as illustrated with an exactly-solvable model system. Whereas DFRT yields in principle the exact resonance energy and lifetime of the interacting system, we find that neglecting the complex-correlation contribution leads to errors of similar magnitude to those of standard scattering close-coupling calculations under the bound-state approximation.Density Functional Theory (DFT) [1][2][3] provides one of the most accurate and reliable methods to calculate the ground-state electronic properties of molecules, clusters, and materials from first principles. It is one of the workhorses of computational quantum chemistry [4]. In addition, DFT's time-dependent extension (TDDFT) [5] can now be applied to a wealth of excited-state and time-dependent properties in both linear and non-linear regimes [6]. When the N -electron system of interest has no bound ground state, however, neither DFT nor TDDFT can be applied in a straightforward way. A correct DFT calculation converges to the true ground state by ionizing the system, thus leaving no reliable starting point for a subsequent TDDFT calculation on the Nelectron system. In practice, a finite simulation box or basis set can make the system artificially bound [7,8], but information about the relevant lifetimes is lost in the process.We address here this fundamental limitation of groundstate DFT, and propose a solution.Consider a system of N interacting electrons in an external potentialṽ(r), with ground-state densityñ(r). The potential is set to be everywhere positive and go to a positive constant C as |r| → ∞. The ground-state energy isẼ > 0. We start by asking how the gound state density changes when a smooth step is added toṽ(r) at a radius |R| that is larger than the range ofṽ(r). The step is such that the new potential v(r) coincides with v(r) for |r| < |R| but goes to zero at infinity. Sinceṽ(r) is everywhere positive, all N electrons tunnel out and v(r) supports no bound states. The correct ground state energy is now E = 0, and the new density n(r) is delocalized through all space. In practical calculations, however, v(r) andṽ(r) cannot be distinguished if |R| is beyond the size of the simulation box. The result provided by ground-state DFT using the exact exchange-correlation functional is not E, b...

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The quantum defect: The true measure of time-dependent density-functional results for atoms

Cited by 17 publications

References 37 publications

Random-phase-approximation-based correlation energy functionals: Benchmark results for atoms

Random-phase-approximation-based correlation energy functionals: Benchmark results for atoms

Density functional calculations of nanoscale conductance

Density Functional Resonance Theory of Unbound Electronic Systems

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