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Horáček, J.; Mach, Pavel; Urban, Ján

doi:10.1103/physreva.82.032713

Cited by 31 publications

(30 citation statements)

References 38 publications

(46 reference statements)

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“…8), and λ 0 is the value of the stabilizing parameter λ at which the bound state becomes unstable. A concrete method, in addition, needs a function that has the right analytical structure and can be fitted to the data, for which in the ACCC method a Padé approximant is used.…”

Section: Extrapolation Methodsmentioning

confidence: 99%

“…Apart from the Padé parameters, the crossing point λ 0 is also unknown and must be determined through a fit, which leads to a two-level fitting procedure: an internal fit of the Padé parameters and an external fit of λ 0 . 8 Owing to the highly non-linear nature of this scheme, one frequently encounters convergence difficulties up to convergence failures-especially for higher Padé orders beyond [1,1] (see Refs. 8 and 9 and below)-and the same is Table II).…”

Section: Extrapolation Methodsmentioning

confidence: 99%

“…[8][9][10] In this context, two additional approximations were introduced: The formula for angular momentum l = 1 was used, since the sought temporary states are-as a rule-of π * character, 8 and a long-range Coulomb potential was used to generate the input data. While it is not straightforward to overcome the former approximation (although perhaps an l-wave analysis of the bound state could be extrapolated back to vanishing stabilization), the Coulomb stabilization was essentially chosen for the ease of implementation into standard ab initio codes, and can be replaced by adding a short-range potential to the one-electron Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

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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%

Section: Extrapolation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…Complex coordinate methods 4,[16][17][18][19][20][21] compute the Siegert energy as an eigenvalue of a transformed, non-Hermitian, Hamiltonian operator. Bound state extrapolation 22,23 or analytic continuation 24,25 methods rely on the analytic continuation of bound-state energies to find resonance parameters. The focus of this study is this final class of methods; in particular, we focus on the method of analytic continuation in the coupling constant (ACCC) for shape resonances in molecules.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, these two methods have been combined and applied to molecular shape resonances. 25,[27][28][29][30] In most of these studies, a Coulomb potential is used to bind the resonance as in the method of scaled nuclear charges. The exception is the manifestly short-range Voronoi potential suggested by Sommerfeld et al 28 Sommerfeld and coworkers noted that the long-range Coulomb potential is not formally applicable and obtained much more consistent results with their Voronoi potential.…”

Section: Introductionmentioning

confidence: 99%

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

White

Head‐Gordon

McCurdy

2017

The Journal of Chemical Physics

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The computation of Siegert energies by analytic continuation of bound state energies has recently been applied to shape resonances in polyatomic molecules by several authors. We critically evaluate a recently proposed analytic continuation method based on low order (type III) Padé approximants as well as an analytic continuation method based on high order (type II) Padé approximants. We compare three classes of stabilizing potentials: Coulomb potentials, Gaussian potentials, and attenuated Coulomb potentials. These methods are applied to a model potential where the correct answer is known exactly and to the 2 Π g shape resonance of N − 2 which has been studied extensively by other methods. Both the choice of stabilizing potential and method of analytic continuation prove to be important to the accuracy of the results. We conclude that an attenuated Coulomb potential is the most effective of the three for bound state analytic continuation methods. With the proper potential, such methods show promise for algorithmic determination of the positions and widths of molecular shape resonances.

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Analytical continuation in coupling constant method; application to the calculation of resonance energies and widths for organic molecules: Glycine, alanine and valine and dimer of formic acid

Papp¹,

Matejčík²,

Mach³

et al. 2013

Chemical Physics

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Calculation ofS-matrix poles by means of analytic continuation in the coupling constant: Application to the2Πgstate of

Cited by 31 publications

References 38 publications

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

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

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

Analytical continuation in coupling constant method; application to the calculation of resonance energies and widths for organic molecules: Glycine, alanine and valine and dimer of formic acid

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