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

Alec F White1, Martin Head-Gordon1, C William McCurdy2

  • 1Department of Chemistry, University of California, Berkeley, California 94720, USA.

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|February 3, 2017
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Summary
This summary is machine-generated.

This study evaluates analytic continuation methods for calculating molecular shape resonances. Attenuated Coulomb potentials combined with specific analytic continuation techniques accurately determine resonance positions and widths.

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Area of Science:

  • Computational chemistry
  • Theoretical physics
  • Molecular spectroscopy

Background:

  • Analytic continuation of bound state energies is used to compute Siegert energies for molecular shape resonances.
  • Previous studies have applied various analytic continuation methods, but their accuracy and optimal conditions require further investigation.

Purpose of the Study:

  • To critically evaluate analytic continuation methods for shape resonances in polyatomic molecules.
  • To compare the effectiveness of different stabilizing potentials (Coulomb, Gaussian, attenuated Coulomb) in these calculations.
  • To assess the impact of Padé approximant order (type II vs. type III) on accuracy.

Main Methods:

  • Analytic continuation using low order (type III) and high order (type II) Padé approximants.
  • Application of Coulomb, Gaussian, and attenuated Coulomb stabilizing potentials.
  • Testing on a model potential with a known exact solution and the N2- (Πg2) shape resonance.

Main Results:

  • The choice of stabilizing potential and analytic continuation method significantly impacts the accuracy of computed resonance properties.
  • An attenuated Coulomb potential proved most effective for bound state analytic continuation.
  • Both evaluated Padé approximant methods showed potential for accurate results with appropriate potentials.

Conclusions:

  • Analytic continuation methods, particularly with attenuated Coulomb potentials, show significant promise for the algorithmic determination of molecular shape resonance positions and widths.
  • Further refinement of these computational techniques can advance the understanding of molecular resonances.