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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); Army Research Laboratory (ARL); 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. https://doi.org/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. https://doi.org/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 = {Mon Nov 27 00:00:00 EST 2017},
month = {Mon Nov 27 00:00:00 EST 2017}
}

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Cited by: 5 works
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Works referenced in this record:

A multicenter numerical integration scheme for polyatomic molecules
journal, February 1988

  • Becke, A. D.
  • The Journal of Chemical Physics, Vol. 88, Issue 4
  • DOI: 10.1063/1.454033

Cross section and asymmetry parameter calculation for sulfur 1s photoionization of SF6
journal, September 1999

  • Natalense, Alexandra P. P.; Lucchese, Robert R.
  • The Journal of Chemical Physics, Vol. 111, Issue 12
  • DOI: 10.1063/1.479794

Dynamics of dissociative electron attachment to ammonia
journal, May 2016


Self‐consistent molecular orbital methods. XVII. Geometries and binding energies of second‐row molecules. A comparison of three basis sets
journal, June 1976

  • Collins, John B.; von R. Schleyer, Paul; Binkley, J. Stephen
  • The Journal of Chemical Physics, Vol. 64, Issue 12
  • DOI: 10.1063/1.432189

Dissociative excitation of HeH + by electron impact
journal, October 1991


Unambiguous observation of F-atom core-hole localization in CF 4 through body-frame photoelectron angular distributions
journal, January 2017


The influence of polarization functions on molecular orbital hydrogenation energies
journal, January 1973

  • Hariharan, P. C.; Pople, J. A.
  • Theoretica Chimica Acta, Vol. 28, Issue 3
  • DOI: 10.1007/BF00533485

R-matrix calculation of low-energy electron collisions with uracil
journal, April 2009

  • Dora, Amar; Tennyson, Jonathan; Bryjko, Lilianna
  • The Journal of Chemical Physics, Vol. 130, Issue 16
  • DOI: 10.1063/1.3119667

A new basis set method for quantum scattering calculations
journal, June 1987

  • Miller, William H.; Jansen op de Haar, Bernadette M. D. D.
  • The Journal of Chemical Physics, Vol. 86, Issue 11
  • DOI: 10.1063/1.452459

Self‐Consistent Molecular‐Orbital Methods. I. Use of Gaussian Expansions of Slater‐Type Atomic Orbitals
journal, September 1969

  • Hehre, W. J.; Stewart, R. F.; Pople, J. A.
  • The Journal of Chemical Physics, Vol. 51, Issue 6
  • DOI: 10.1063/1.1672392

What will it take to observe processes in 'real time'?
journal, February 2014

  • Leone, Stephen R.; McCurdy, C. William; Burgdörfer, Joachim
  • Nature Photonics, Vol. 8, Issue 3
  • DOI: 10.1038/nphoton.2014.48

Molpro: a general-purpose quantum chemistry program package: Molpro
journal, July 2011

  • Werner, Hans-Joachim; Knowles, Peter J.; Knizia, Gerald
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 2
  • DOI: 10.1002/wcms.82

Calculation of low‐energy elastic cross sections for electron‐CF 4 scattering
journal, May 1994

  • Gianturco, F. A.; Lucchese, R. R.; Sanna, N.
  • The Journal of Chemical Physics, Vol. 100, Issue 9
  • DOI: 10.1063/1.467237

Ab initio study of low-energy electron-methane scattering
journal, October 1991


Hole-Cutting for Three-Dimensional Overlapping Grids
journal, January 1999


Molecular frame photoelectron angular distributions for core ionization of ethane, carbon tetrafluoride and 1,1-difluoroethylene
journal, February 2016

  • Menssen, A.; Trevisan, C. S.; Schöffler, M. S.
  • Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 49, Issue 5
  • DOI: 10.1088/0953-4075/49/5/055203

Electron-molecule close coupling with correlated target wave functions: Application to impact dissociation of F 2
journal, September 1991


Variational Methods in Nuclear Collision Problems
journal, December 1948


Effects of interchannel coupling on the photoionization cross sections of carbon dioxide
journal, April 1990

  • Lucchese, Robert R.
  • The Journal of Chemical Physics, Vol. 92, Issue 7
  • DOI: 10.1063/1.457778

Resonance partial widths and partial photodetachment rate using the rotated-coordinate method
journal, June 1980


Schwinger variational principle and Padé approximants
journal, June 1972


Discrete variable representations and sudden models in quantum scattering theory
journal, July 1982


Iterative approach to the Schwinger variational principle applied to electron—molecular-ion collisions
journal, August 1981


Interchannel coupling and ground state correlation effects in the photoionization of CO
journal, October 1993

  • Rescigno, T. N.; Lengsfield, B. H.; Orel, A. E.
  • The Journal of Chemical Physics, Vol. 99, Issue 7
  • DOI: 10.1063/1.466010

Self‐consistent molecular orbital methods. XXIII. A polarization‐type basis set for second‐row elements
journal, October 1982

  • Francl, Michelle M.; Pietro, William J.; Hehre, Warren J.
  • The Journal of Chemical Physics, Vol. 77, Issue 7, p. 3654-3665
  • DOI: 10.1063/1.444267

Electronic excitation of H 2 by electron impact: Close-coupling calculations using the complex Kohn variational method
journal, April 1991

  • Parker, Steven D.; McCurdy, C. William; Rescigno, Thomas N.
  • Physical Review A, Vol. 43, Issue 7
  • DOI: 10.1103/PhysRevA.43.3514

Resonant interactions of slow electrons with DNA constituents
journal, October 2008


High-order Newton-Cotes integration methods in scattering theory
journal, August 1988


Imaging molecular shapes with molecular-frame photoelectron angular distributions from core hole ionization
journal, September 2012

  • Trevisan, C. S.; McCurdy, C. W.; Rescigno, T. N.
  • Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 45, Issue 19
  • DOI: 10.1088/0953-4075/45/19/194002

Convergence of Padé Approximants for the Bethe-Salpeter Amplitude
journal, May 1967


Signatures of bond formation and bond scission dynamics in dissociative electron attachment to methane
journal, January 2015

  • Douguet, N.; Slaughter, D. S.; Adaniya, H.
  • Physical Chemistry Chemical Physics, Vol. 17, Issue 38
  • DOI: 10.1039/C5CP04178C

Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses
journal, October 2014


Ion-momentum imaging of dissociative attachment of electrons to molecules
journal, October 2016

  • Slaughter, D. S.; Belkacem, A.; McCurdy, C. W.
  • Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 49, Issue 22
  • DOI: 10.1088/0953-4075/49/22/222001

Collisions of electrons with polyatomic molecules: Electron-methane scattering by the complex Kohn variational method
journal, May 1989


Electron–molecule collision calculations using the R-matrix method
journal, June 2010


Observation of the dynamics leading to a conical intersection in dissociative electron attachment to water
journal, September 2011


Interrelation between variational principles for scattering amplitudes and generalized R -matrix theory
journal, September 1987

  • McCurdy, C. William; Rescigno, Thomas N.; Schneider, Barry I.
  • Physical Review A, Vol. 36, Issue 5
  • DOI: 10.1103/PhysRevA.36.2061

Dynamics of the Dissociating Uracil Anion Following Resonant Electron Attachment
journal, October 2014

  • Kawarai, Y.; Weber, Th.; Azuma, Y.
  • The Journal of Physical Chemistry Letters, Vol. 5, Issue 21
  • DOI: 10.1021/jz501907d

Velocity slice imaging study on dissociative electron attachment to CF4
journal, April 2014

  • Ómarsson, Frímann H.; Szymańska, Ewelina; Mason, Nigel J.
  • The European Physical Journal D, Vol. 68, Issue 4
  • DOI: 10.1140/epjd/e2014-40804-5

Numerical grid methods for quantum-mechanical scattering problems
journal, August 2000


Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules
journal, March 1972

  • Hehre, W. J.; Ditchfield, R.; Pople, J. A.
  • The Journal of Chemical Physics, Vol. 56, Issue 5, p. 2257-2261
  • DOI: 10.1063/1.1677527

Works referencing / citing this record:

Perfect control of photoelectron anisotropy for randomly oriented ensembles of molecules by XUV REMPI and polarization shaping
journal, August 2019

  • Goetz, R. Esteban; Koch, Christiane P.; Greenman, Loren
  • The Journal of Chemical Physics, Vol. 151, Issue 7
  • DOI: 10.1063/1.5111362