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 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 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 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:
-
- 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)
- 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}
}
Web of Science
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
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
Dynamics of dissociative electron attachment to ammonia
journal, May 2016
- Rescigno, T. N.; Trevisan, C. S.; Orel, A. E.
- Physical Review A, Vol. 93, Issue 5
Padé-approximant corrections to general variational expressions of scattering theory: Application to photoionization of carbon monoxide
journal, September 1983
- Lucchese, Robert R.; McKoy, Vincent
- Physical Review A, Vol. 28, Issue 3
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
Dissociative excitation of by electron impact
journal, October 1991
- Orel, A. E.; Rescigno, T. N.; Lengsfield, B. H.
- Physical Review A, Vol. 44, Issue 7
Unambiguous observation of F-atom core-hole localization in through body-frame photoelectron angular distributions
journal, January 2017
- McCurdy, C. W.; Rescigno, T. N.; Trevisan, C. S.
- Physical Review A, Vol. 95, Issue 1
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
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
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
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
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
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
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
Ab initio study of low-energy electron-methane scattering
journal, October 1991
- Lengsfield, B. H.; Rescigno, T. N.; McCurdy, C. W.
- Physical Review A, Vol. 44, Issue 7
Hole-Cutting for Three-Dimensional Overlapping Grids
journal, January 1999
- Petersson, N. Anders
- SIAM Journal on Scientific Computing, Vol. 21, Issue 2
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
Electron-molecule close coupling with correlated target wave functions: Application to impact dissociation of
journal, September 1991
- Lengsfield, B. H.; Rescigno, T. N.
- Physical Review A, Vol. 44, Issue 5
Variational Methods in Nuclear Collision Problems
journal, December 1948
- Kohn, W.
- Physical Review, Vol. 74, Issue 12
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
Resonance partial widths and partial photodetachment rate using the rotated-coordinate method
journal, June 1980
- Noro, T.; Taylor, H. S.
- Journal of Physics B: Atomic and Molecular Physics, Vol. 13, Issue 12
Schwinger variational principle and Padé approximants
journal, June 1972
- Garibotti, C. R.
- Annals of Physics, Vol. 71, Issue 2
Discrete variable representations and sudden models in quantum scattering theory
journal, July 1982
- Lill, J. V.; Parker, G. A.; Light, J. C.
- Chemical Physics Letters, Vol. 89, Issue 6
Iterative approach to the Schwinger variational principle applied to electron—molecular-ion collisions
journal, August 1981
- Lucchese, Robert R.; McKoy, Vincent
- Physical Review A, Vol. 24, Issue 2
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
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
Electronic excitation of 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
Resonant interactions of slow electrons with DNA constituents
journal, October 2008
- Winstead, Carl; McKoy, Vincent
- Radiation Physics and Chemistry, Vol. 77, Issue 10-12
High-order Newton-Cotes integration methods in scattering theory
journal, August 1988
- Basden, Bryan; Lucchese, Robert R.
- Journal of Computational Physics, Vol. 77, Issue 2
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
Convergence of Padé Approximants for the Bethe-Salpeter Amplitude
journal, May 1967
- Nuttall, J.
- Physical Review, Vol. 157, Issue 5
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
Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses
journal, October 2014
- Calegari, F.; Ayuso, D.; Trabattoni, A.
- Science, Vol. 346, Issue 6207
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
Collisions of electrons with polyatomic molecules: Electron-methane scattering by the complex Kohn variational method
journal, May 1989
- McCurdy, C. William; Rescigno, Thomas N.
- Physical Review A, Vol. 39, Issue 9
Electron–molecule collision calculations using the R-matrix method
journal, June 2010
- Tennyson, Jonathan
- Physics Reports, Vol. 491, Issue 2-3
Observation of the dynamics leading to a conical intersection in dissociative electron attachment to water
journal, September 2011
- Haxton, D. J.; Adaniya, H.; Slaughter, D. S.
- Physical Review A, Vol. 84, Issue 3
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
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
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
Numerical grid methods for quantum-mechanical scattering problems
journal, August 2000
- Rescigno, T. N.; McCurdy, C. W.
- Physical Review A, Vol. 62, Issue 3
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
Works referencing / citing this record:
Perfect control of photoelectron anisotropy for randomly oriented ensembles of molecules by XUV REMPI and polarization shaping
text, January 2019
- Goetz, R. Esteban; Koch, Christiane P.; Greenman, Loren
- arXiv
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