Modeling electron dynamics coupled to continuum states in finite volumes with absorbing boundaries

  • Umberto De Giovannini
  • Ask Hjorth Larsen
  • Angel Rubio
Regular Article

Abstract

Absorbing boundaries are frequently employed in real-time propagation of the Schrödinger equation to remove spurious reflections and efficiently emulate outgoing boundary conditions. These conditions are a fundamental ingredient for the calculation of observables involving infinitely extended continuum states in finite volumes. In the literature, several boundary absorbers have been proposed. They mostly fall into three main families: mask function absorbers, complex absorbing potentials, and exterior complex-scaled potentials. To date none of the proposed absorbers is perfect, and all present a certain degree of reflections. Characterization of such reflections is thus a critical task with strong implications for time-dependent simulations of atoms and molecules. We introduce a method to evaluate the reflection properties of a given absorber and present a comparison of selected samples for each family of absorbers. Further, we discuss the connections between members of each family and show how the same reflection curves can be obtained with very different absorption schemes.

Keywords

Computational Methods 

References

  1. 1.
    B. Boudaïffa, P. Cloutier, D. Hunting, M.A. Huels, L. Sanche, Science 287, 1658 (2000)CrossRefADSGoogle Scholar
  2. 2.
    Introducing Molecular Electronics, Lecture Notes in Physics, edited by G. Cuniberti, K. Richter, G. Fagas (Springer, Berlin, Heidelberg, 2006), Vol. 680Google Scholar
  3. 3.
    M. Meckel et al., Science 320, 1478 (2008)CrossRefADSGoogle Scholar
  4. 4.
    Y. Huismans et al., Science 331, 61 (2011)CrossRefADSGoogle Scholar
  5. 5.
    R.M. Lock, S. Ramakrishna, X. Zhou, H.C. Kapteyn, M.M. Murnane, T. Seideman, Phys. Rev. Lett. 108, 133901 (2012)CrossRefADSGoogle Scholar
  6. 6.
    R.R. Lucchese, G. Raseev, V. McKoy, Phys. Rev. A 25, 2572 (1982)Google Scholar
  7. 7.
    I. Sánchez, F. Martín, J. Phys. B 30, 679 (1997)CrossRefADSGoogle Scholar
  8. 8.
    H. Bachau, E. Cormier, P. Decleva, J.E. Hansen, F. Martín, Rep. Prog. Phys. 64, 1815 (2001)CrossRefADSGoogle Scholar
  9. 9.
    A. Dora, J. Tennyson, L. Bryjko, T. van Mourik, J. Chem. Phys. 130, 164307 (2009)CrossRefADSGoogle Scholar
  10. 10.
    P. Descouvemont, D. Baye, Rep. Prog. Phys. 73, 036301 (2010)CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    A. Ermolaev, I. Puzynin, A. Selin, S. Vinitsky, Phys. Rev. A 60, 4831 (1999)CrossRefADSGoogle Scholar
  12. 12.
    J. Inglesfield, J. Phys.: Condens. Matter 20, 095215 (2008)ADSGoogle Scholar
  13. 13.
    J.E. Inglesfield, J. Phys.: Condens. Matter 23, 305004 (2011)Google Scholar
  14. 14.
    T. Nakatsukasa, K. Yabana, J. Chem. Phys. 114, 2550 (2001)CrossRefADSGoogle Scholar
  15. 15.
    S. Kurth, G. Stefanucci, C.O. Almbladh, A. Rubio, E.K.U. Gross, Phys. Rev. B 72, 035308 (2005)CrossRefADSGoogle Scholar
  16. 16.
    G. Stefanucci, S. Kurth, A. Rubio, E.K.U. Gross, Phys. Rev. B 77, 075339 (2008)CrossRefADSGoogle Scholar
  17. 17.
    J. Krause, K. Schafer, K. Kulander, Phys. Rev. A 45, 4998 (1992)CrossRefADSGoogle Scholar
  18. 18.
    K. Kulander, F. Mies, K. Schafer, Phys. Rev. A 53, 2562 (1996)Google Scholar
  19. 19.
    M. Lein, J. Marangos, P. Knight, Phys. Rev. A 66 (2002)Google Scholar
  20. 20.
    S. Chelkowski, C. Foisy, A.D. Bandrauk, Phys. Rev. A 57, 1176 (1998)Google Scholar
  21. 21.
    R. Grobe, S. Haan, J. Eberly, Comput. Phys. Commun. 117, 200 (1999)Google Scholar
  22. 22.
    U. De Giovannini, D. Varsano, M.A.L. Marques, H. Appel, E.K.U. Gross, A. Rubio, Phys. Rev. A 85, 062515 (2012)CrossRefADSGoogle Scholar
  23. 23.
    U. De Giovannini, G. Brunetto, A. Castro, J. Walkenhorst, A. Rubio, ChemPhysChem 14, 1363 (2013)CrossRefGoogle Scholar
  24. 24.
    A. Crawford-Uranga, U. De Giovannini, D.J. Mowbray, S. Kurth, A. Rubio, J. Phys. B 47, 124018 (2014)CrossRefADSGoogle Scholar
  25. 25.
    D. Neuhauser, M. Baer, J. Chem. Phys. 91, 4651 (1989)CrossRefADSGoogle Scholar
  26. 26.
    R. Santra, L.S. Cederbaum, Chem. Phys. 368, 1 (2002)Google Scholar
  27. 27.
    K. Varga, S. Pantelides, Phys. Rev. Lett. 98, 076804 (2007)CrossRefADSGoogle Scholar
  28. 28.
    B.D. Wibking, K. Varga, Phys. Lett. A 376, 365 (2012)CrossRefADSMATHMathSciNetGoogle Scholar
  29. 29.
    J. Muga, J.P. Palao, B. Navarro, I.L. Egusquiza, Phys. Rep. 395, 357 (2004)CrossRefADSMathSciNetGoogle Scholar
  30. 30.
    J. Aguilar, J. Combes, Commun. Math. Phys. 22, 269 (1971)CrossRefADSMATHMathSciNetGoogle Scholar
  31. 31.
    E. Balslev, J.M. Combes, Commun. Math. Phys. 22, 280 (1971)CrossRefADSMATHMathSciNetGoogle Scholar
  32. 32.
    J.L. Sanz-Vicario, E. Lindroth, N. Brandefelt, Phys. Rev. A 66, 052713 (2002)Google Scholar
  33. 33.
    D.L. Whitenack, A. Wasserman, Phys. Rev. Lett. 107, 163002 (2011)CrossRefADSGoogle Scholar
  34. 34.
    A.H. Larsen, U. De Giovannini, D.L. Whitenack, A. Wasserman, A. Rubio, J. Phys. Chem. Lett. 4, 2734 (2013)CrossRefGoogle Scholar
  35. 35.
    B. Simon, Ann. Math. 97, 247 (1973)CrossRefMATHGoogle Scholar
  36. 36.
    B. Simon, Phys. Lett. A 71, 211 (1979)CrossRefADSGoogle Scholar
  37. 37.
    C. McCurdy, C. Stroud, M. Wisinski, Phys. Rev. A 43, 5980 (1991)Google Scholar
  38. 38.
    U.V. Riss, H.D. Meyer, J. Phys. B 28, 1475 (1995)CrossRefADSGoogle Scholar
  39. 39.
    N. Moiseyev, J. Phys. B 31, 1431 (1999)CrossRefADSGoogle Scholar
  40. 40.
    O. Shemer, D. Brisker, N. Moiseyev, Phys. Rev. A 71, 032716 (2005)Google Scholar
  41. 41.
    A. Scrinzi, Phys. Rev. A 81, 053845 (2010)CrossRefADSGoogle Scholar
  42. 42.
    D. Macias, S. Brouard, J.G. Muga, Chem. Phys. Lett. 228, 672 (1994)Google Scholar
  43. 43.
    Á. Vibók, G.J. Halász, Phys. Chem. Chem. Phys. 3, 3048 (2001)CrossRefGoogle Scholar
  44. 44.
    D.E. Manolopoulos, J. Chem. Phys. 117, 9552 (2002)CrossRefADSGoogle Scholar
  45. 45.
    J.P. Palao, J. Muga, J. Phys. Chem. A 102, 9464 (1998)CrossRefGoogle Scholar
  46. 46.
    R. Zavin, I. Vorobeichik, N. Moiseyev, Chem. Phys. Lett. 288, 413 (1998)Google Scholar
  47. 47.
    A. Vibok, G.G. Balint-Kurti, J. Phys. Chem. 96, 8712 (1992)CrossRefGoogle Scholar
  48. 48.
    U.V. Riss, H.D. Meyer, J. Chem. Phys. 105, 1409 (1996)CrossRefADSGoogle Scholar
  49. 49.
    M.A.L. Marques, A. Castro, G. Bertsch, A. Rubio, Comput. Phys. Commun. 151, 60 (2003)CrossRefADSGoogle Scholar
  50. 50.
    X. Andrade, A. Castro, H. Appel, M. Oliveira, C.A. Rozzi, F. Lorenzen, M.A.L. Marques, E.K.U. Gross, A. Rubio, Phys. Stat. Sol. B 243, 2465 (2006)CrossRefADSGoogle Scholar
  51. 51.
    X. Andrade et al., J. Phys.: Condens. Matter 24, 233202 (2012)ADSMathSciNetGoogle Scholar
  52. 52.
    A.H. Larsen, U. De Giovannini, A. Rubio, Density-functional methods for excited states (Springer Berlin, Heidelberg, 2015), Topics in Current ChemistryGoogle Scholar
  53. 53.
    C. Jhala, M. Lein, I. Dreissigacker, Phys. Rev. A 82, 063415 (2010)Google Scholar
  54. 54.
    M.A.L. Marques, N.T. Maitra, F. Nogueira, E.K.U. Gross, A. Rubio, Fundamentals of Time-Dependent Density Functional Theory (Springer-Verlag, Berlin, 2011)Google Scholar
  55. 55.
    R. Kosloff, D. Kosloff, J. Comput. Phys. 63, 363 (1986)CrossRefADSMATHMathSciNetGoogle Scholar
  56. 56.
    W. Magnus, Commun. Pure Appl. Math. 7, 649 (1954)CrossRefMATHMathSciNetGoogle Scholar
  57. 57.
    N. Moiseyev, J.O. Hirschfelder, J. Chem. Phys. 88, 1063 (1988)CrossRefADSMathSciNetGoogle Scholar
  58. 58.
    N. Moiseyev, Non-Hermitian Quantum Mechanics (Cambridge University Press, 2011)Google Scholar
  59. 59.
    U.V. Riss, H. Meyer, J. Phys. B 26, 4503 (1993)CrossRefADSMathSciNetGoogle Scholar
  60. 60.
    R. Santra, Phys. Rev. A 74, 034701 (2006)CrossRefADSGoogle Scholar
  61. 61.
    Y. Sajeev, M. Sindelka, N. Moiseyev, Chem. Phys. 329, 307 (2006)Google Scholar
  62. 62.
    D.J. Kalita, A.K. Gupta, J. Chem. Phys. 134, 094301 (2011)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Umberto De Giovannini
    • 1
  • Ask Hjorth Larsen
    • 1
  • Angel Rubio
    • 1
    • 2
  1. 1.Nano-Bio Spectroscopy Group and ETSF Scientific Development Centre, Departamento de Física de MaterialesUniversidad del País Vasco, CSIC-UPV/EHU-MPC and DIPCSan SebastiánSpain
  2. 2.Max Planck Institute for the Structure and Dynamics of MatterHamburgGermany

Personalised recommendations