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

Abstract

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. Here, 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 2Π 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 then 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.

Authors:
 [1];  [1]; ORCiD logo [2]
  1. Univ. of California, Berkeley, CA (United States). Dept. of Chemistry; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Chemical Sciences
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Chemical Sciences; Univ. of California, Davis, CA (United States). Dept. of Chemistry
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1379693
Alternate Identifier(s):
OSTI ID: 1361751
Grant/Contract Number:
AC02-05CH11231
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 146; Journal Issue: 4; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

White, Alec F., Head-Gordon, Martin, and McCurdy, C. William. Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules. United States: N. p., 2017. Web. doi:10.1063/1.4974761.
White, Alec F., Head-Gordon, Martin, & McCurdy, C. William. Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules. United States. doi:10.1063/1.4974761.
White, Alec F., Head-Gordon, Martin, and McCurdy, C. William. Mon . "Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules". United States. doi:10.1063/1.4974761. https://www.osti.gov/servlets/purl/1379693.
@article{osti_1379693,
title = {Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules},
author = {White, Alec F. and Head-Gordon, Martin and McCurdy, C. William},
abstractNote = {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. Here, 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 2Πg 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 then 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.},
doi = {10.1063/1.4974761},
journal = {Journal of Chemical Physics},
number = 4,
volume = 146,
place = {United States},
year = {Mon Jan 30 00:00:00 EST 2017},
month = {Mon Jan 30 00:00:00 EST 2017}
}

Journal Article:
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  • We propose a new approach to the dynamics of systems of several particles, based on analytic continuation in the coupling constant by the use of Pade approximants of the second kind. In the present paper this approach is used to construct a theory of resonant states in nuclei by means of analytic continuation in the coupling constant of the attractive part of the interaction. A technique for finding the parameters of resonances is described; these include the energies, widths, and wave functions of Gamow states and the corresponding quantities for antibound (virtual) states of real and complex Hamiltonians. The samemore » technique of analytic extrapolation is used to calculate matrix elements involving resonance wave functions. It is shown that this theory leads to a procedure for regularizing resonance matrix elements which is exactly equivalent in its result to the well known Zel'dovich regularization but is much simpler than that method in practice. The possibility is discussed of applying this formalism to a shell model with two particles in the continuum and to the theory of many-particle resonances.« less
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