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Title: Variational treatment of electron–polyatomic-molecule scattering calculations using adaptive overset grids

Abstract

In this paper, the complex Kohn variational method for electron–polyatomic-molecule scattering is formulated using an overset-grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense atom-centered subgrids that allow the simultaneous spherical expansions of the wave function about multiple centers. Scattering boundary conditions are enforced by using a basis formed by the repeated application of the free-particle Green's function and potential G ^ 0 + V ^ on the overset grid in a Born-Arnoldi solution of the working equations. The theory is shown to be equivalent to a specific Padé approximant to the T matrix and has rapid convergence properties, in both the number of numerical basis functions employed and the number of partial waves employed in the spherical expansions. The method is demonstrated in calculations on methane and CF 4 in the static-exchange approximation and compared in detail with calculations performed with the numerical Schwinger variational approach based on single-center expansions. Finally, an efficient procedure for operating with the free-particle Green's function and exchange operators (to which no approximation is made) is also described.

Authors:
 [1];  [2];  [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Chemical Sciences Division; Univ. of California, Davis, CA (United States). Dept. of Chemistry
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Chemical Sciences Division; Texas A & M Univ., College Station, TX (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); Army Research Lab. (ARL) (United States); US Army Research Office (ARO)
OSTI Identifier:
1458505
Alternate Identifier(s):
OSTI ID: 1410395
Grant/Contract Number:  
AC02-05CH11231; SC0012198; W911NF-14-1-0383
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 96; Journal Issue: 5; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; electron & positron scattering; scattering theory

Citation Formats

Greenman, Loren, Lucchese, Robert R., and McCurdy, C. William. Variational treatment of electron–polyatomic-molecule scattering calculations using adaptive overset grids. United States: N. p., 2017. Web. doi:10.1103/PhysRevA.96.052706.
Greenman, Loren, Lucchese, Robert R., & McCurdy, C. William. Variational treatment of electron–polyatomic-molecule scattering calculations using adaptive overset grids. United States. doi:10.1103/PhysRevA.96.052706.
Greenman, Loren, Lucchese, Robert R., and McCurdy, C. William. Mon . "Variational treatment of electron–polyatomic-molecule scattering calculations using adaptive overset grids". United States. doi:10.1103/PhysRevA.96.052706. https://www.osti.gov/servlets/purl/1458505.
@article{osti_1458505,
title = {Variational treatment of electron–polyatomic-molecule scattering calculations using adaptive overset grids},
author = {Greenman, Loren and Lucchese, Robert R. and McCurdy, C. William},
abstractNote = {In this paper, the complex Kohn variational method for electron–polyatomic-molecule scattering is formulated using an overset-grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense atom-centered subgrids that allow the simultaneous spherical expansions of the wave function about multiple centers. Scattering boundary conditions are enforced by using a basis formed by the repeated application of the free-particle Green's function and potential G^ 0+V^ on the overset grid in a Born-Arnoldi solution of the working equations. The theory is shown to be equivalent to a specific Padé approximant to the T matrix and has rapid convergence properties, in both the number of numerical basis functions employed and the number of partial waves employed in the spherical expansions. The method is demonstrated in calculations on methane and CF4 in the static-exchange approximation and compared in detail with calculations performed with the numerical Schwinger variational approach based on single-center expansions. Finally, an efficient procedure for operating with the free-particle Green's function and exchange operators (to which no approximation is made) is also described.},
doi = {10.1103/PhysRevA.96.052706},
journal = {Physical Review A},
number = 5,
volume = 96,
place = {United States},
year = {2017},
month = {11}
}

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