Variational treatment of electron–polyatomicmolecule scattering calculations using adaptive overset grids
Abstract
In this paper, the complex Kohn variational method for electron–polyatomicmolecule scattering is formulated using an oversetgrid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense atomcentered 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 freeparticle Green's function and potential ${\hat{G}}_{0}^{+}\hat{V}$ on the overset grid in a BornArnoldi 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 ${\mathrm{CF}}_{4}$ in the staticexchange approximation and compared in detail with calculations performed with the numerical Schwinger variational approach based on singlecenter expansions. Finally, an efficient procedure for operating with the freeparticle Green's function and exchange operators (to which no approximation is made) is also described.
 Authors:

 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Chemical Sciences Division; Univ. of California, Davis, CA (United States). Dept. of Chemistry
 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); Texas A & M Univ., College Station, TX (United States); Univ. of California, Davis, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22); Army Research Lab. (ARL) (United States); US Army Research Office (ARO)
 OSTI Identifier:
 1458505
 Alternate Identifier(s):
 OSTI ID: 1410395
 Grant/Contract Number:
 AC0205CH11231; SC0012198; W911NF1410383
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review A
 Additional Journal Information:
 Journal Volume: 96; Journal Issue: 5; Journal ID: ISSN 24699926
 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–polyatomicmolecule 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–polyatomicmolecule 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–polyatomicmolecule 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–polyatomicmolecule 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–polyatomicmolecule scattering is formulated using an oversetgrid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense atomcentered 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 freeparticle Green's function and potential G^ 0+V^ on the overset grid in a BornArnoldi 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 staticexchange approximation and compared in detail with calculations performed with the numerical Schwinger variational approach based on singlecenter expansions. Finally, an efficient procedure for operating with the freeparticle 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},
issn = {24699926},
number = 5,
volume = 96,
place = {United States},
year = {2017},
month = {11}
}
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