Extrapolating bound state data of anions into the metastable domain

Feuerbacher, Sven; Sommerfeld, Thomas; Cederbaum, Lorenz S.

doi:10.1063/1.1792031

Cited by 28 publications

(17 citation statements)

References 41 publications

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“…In the quantum chemistry community, the energies were typically extrapolated directly (without transformation); 1,22-25 however, choosing the specific data range for the extrapolation is non-trivial, since the state in question undergoes avoided crossings with discretized continuum solutions. 22,25 Consequently, the functional forms typically employed are robust linear or quadratic fits, and energy-extrapolation approaches always have the taste of semi-quantitative schemes.…”

Section: Extrapolation Methodsmentioning

confidence: 99%

Short-range stabilizing potential for computing energies and lifetimes of temporary anions with extrapolation methods

Sommerfeld

Ehara

2015

The Journal of Chemical Physics

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The energy of a temporary anion can be computed by adding a stabilizing potential to the molecular Hamiltonian, increasing the stabilization until the temporary state is turned into a bound state, and then further increasing the stabilization until enough bound state energies have been collected so that these can be extrapolated back to vanishing stabilization. The lifetime can be obtained from the same data, but only if the extrapolation is done through analytic continuation of the momentum as a function of the square root of a shifted stabilizing parameter. This method is known as analytic continuation of the coupling constant, and it requires--at least in principle--that the bound-state input data are computed with a short-range stabilizing potential. In the context of molecules and ab initio packages, long-range Coulomb stabilizing potentials are, however, far more convenient and have been used in the past with some success, although the error introduced by the long-rang nature of the stabilizing potential remains unknown. Here, we introduce a soft-Voronoi box potential that can serve as a short-range stabilizing potential. The difference between a Coulomb and the new stabilization is analyzed in detail for a one-dimensional model system as well as for the (2)Πu resonance of CO2(-), and in both cases, the extrapolation results are compared to independently computed resonance parameters, from complex scaling for the model, and from complex absorbing potential calculations for CO2(-). It is important to emphasize that for both the model and for CO2(-), all three sets of results have, respectively, been obtained with the same electronic structure method and basis set so that the theoretical description of the continuum can be directly compared. The new soft-Voronoi-box-based extrapolation is then used to study the influence of the size of diffuse and the valence basis sets on the computed resonance parameters.

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Section: Extrapolation Methodsmentioning

confidence: 99%

Short-range stabilizing potential for computing energies and lifetimes of temporary anions with extrapolation methods

Sommerfeld

Ehara

2015

The Journal of Chemical Physics

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“…The negative ions are resonances, with negative electron affinity of the chain, captured by the finite basis set. But the resonance can evolve smoothly(35) to a bound state with positive electron affinity as the chain length grows. In contrast to the situation for atoms and molecules, the resonant one-electron states of bulk solids can be converged with respect to basis set.Ref 36.…”

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confidence: 99%

Understanding band gaps of solids in generalized Kohn–Sham theory

Perdew

Yang

Burke

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

509

311

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The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. However, the gap in the band structure of the exact multiplicative Kohn-Sham (KS) potential substantially underestimates the fundamental gap, a major limitation of KS densityfunctional theory. Here, we give a simple proof of a theorem: In generalized KS theory (GKS), the band gap of an extended system equals the fundamental gap for the approximate functional if the GKS potential operator is continuous and the density change is delocalized when an electron or hole is added. Our theorem explains how GKS band gaps from metageneralized gradient approximations (meta-GGAs) and hybrid functionals can be more realistic than those from GGAs or even from the exact KS potential. The theorem also follows from earlier work. The band edges in the GKS one-electron spectrum are also related to measurable energies. A linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations. T he most basic property of a periodic solid is its fundamental energy gap G, which vanishes for a metal but is positive for semiconductors and other insulators. G dominates many properties. As the unbound limit of an exciton series, G is an excitation energy of the neutral solid, but it is defined here as a difference of ground-state energies: If EðMÞ is the ground-state energy for a solid with a fixed number of nuclei and M electrons, and if M = N for electrical neutrality, thenis the difference between the first ionization energy IðNÞ and the first electron affinity AðNÞ of the neutral solid. Whereas I and A can be measured for a macroscopic solid, they can be computed directly (as ground-state energy differences) either by starting from finite clusters and extrapolating to infinite cluster size or (for I-A) by starting from a finite number of primitive unit cells, with periodic boundary condition on the surface of this finite collection, and extrapolating to an infinite number. Here we shall follow both approaches, which have been discussed in a recent study (1). (The energy to remove an electron to infinite separation cannot depend upon the crystal face through which it is removed, although the energy to remove an electron to a macroscopic separation, but much smaller than the dimensions of that face, may so depend. The gap is of course a bulk property.) Band-Gap Problem in Kohn-Sham Density-Functional TheoryKohn-Sham density-functional theory (2, 3) is a formally exact way to compute the ground-state energy and electron density of M interacting electrons in a multiplicative external potential. This theory sets up a fictitious system of noninteracting electrons with the same ground-state density as the real interacting system, found by solving self-consistent one-electron Schrödinger equations. These electrons move in a multiplicative effective Kohn-Sham (KS) potential, the sum of the external and Hartree potentials and the derivative of the density functional for...

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“…In particular, the conventional methods will yield inappropriate lowest unoccupied molecular orbital (LUMO), and orbitals in the valence region corresponding to a freeelectron, which cannot be trusted for the computations of EAs (see the next section). Such temporary anions can though be characterized, while employing the conventional quantum mechanics, for example, through the orbital exponent stabilization method [25] and also through a much simpler nuclear-charge stabilization method [22,23]. In the present study, the metastability of the deprotonated anionic species of benzene is addressed through the nuclear-charge Page 3 of 25 99 stabilization method.…”

Section: Computational Detailsmentioning

confidence: 99%