The European Physical Journal B

, Volume 77, Issue 3, pp 305–329 | Cite as

Modelling non-adiabatic processes using correlated electron-ion dynamics

  • E. J. McEniry
  • Y. Wang
  • D. Dundas
  • T. N. Todorov
  • L. Stella
  • R. P. Miranda
  • A. J. Fisher
  • A. P. Horsfield
  • C. P. Race
  • D. R. Mason
  • W. M.C. Foulkes
  • A. P. Sutton
Colloquium

Abstract.

Here we survey the theory and applications of a family of methods (correlated electron-ion dynamics, or CEID) that can be applied to a diverse range of problems involving the non-adiabatic exchange of energy between electrons and nuclei. The simplest method, which is a paradigm for the others, is Ehrenfest Dynamics. This is applied to radiation damage in metals and the evolution of excited states in conjugated polymers. It is unable to reproduce the correct heating of nuclei by current carrying electrons, so we introduce a moment expansion that allows us to restore the spontaneous emission of phonons. Because of the widespread use of Non-Equilibrium Green's Functions for computing electric currents in nanoscale systems, we present a comparison of this formalism with that of CEID with open boundaries. When there is strong coupling between electrons and nuclei, the moment expansion does not converge. We thus conclude with a reworking of the CEID formalism that converges systematically and in a stable manner.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R.S. Sorbello, Solid State Phys. 51, 159 (1997) Google Scholar
  2. 2.
    E.J. McEniry, D.R. Bowler, D. Dundas, A.P. Horsfield, C.G. Sánchez, T.N. Todorov, J. Phys.: Condens. Matter 19, 196201 (2007) CrossRefADSGoogle Scholar
  3. 3.
    E.J. McEniry, T. Frederiksen, T.N. Todorov, D. Dundas, A.P. Horsfield, Phys. Rev. B 78, 035446 (2008) CrossRefADSGoogle Scholar
  4. 4.
    D. Dundas, E.J. McEniry, T.N. Todorov, Nature Nano. 4, 99 (2009) CrossRefADSGoogle Scholar
  5. 5.
    M. Born, R. Oppenheimer, Annalen der Physik 84, 457 (1927) CrossRefADSGoogle Scholar
  6. 6.
    R.M. Martin, Electronic Structure: Basic Theory and Practical Methods (Cambridge University Press, Cambridge, 2004) Google Scholar
  7. 7.
    R.P. Feynman, Phys. Rev. 56, 340 (1939) MATHCrossRefADSGoogle Scholar
  8. 8.
    J.B. Delos, W.R. Thorson, S.K. Knudson, Phys. Rev. A 6, 709 (1972) CrossRefADSGoogle Scholar
  9. 9.
    E. Runge, E.K.U. Gross, Phys. Rev. Lett. 52, 997 (1984) CrossRefADSGoogle Scholar
  10. 10.
    M.A.L. Marques, C.A. Ullrich, F. Nogueira, A. Rubio, K. Burke, Time-Dependent Density Functional Theory, Lecture Notes in Physics, 706 (Springer, Berlin/Heidelberg, 2006) Google Scholar
  11. 11.
    J.B. Delos, W.R. Thorson, Phys. Rev. A 6, 720 (1972) CrossRefADSGoogle Scholar
  12. 12.
    J.C. Tully, J. Chem. Phys. 93, 1061 (1990) CrossRefADSGoogle Scholar
  13. 13.
    A.P. Horsfield, D.R. Bowler, A.J. Fisher, T.N. Todorov, C.G. Sánchez, J. Phys.: Condens. Matter 17, 4793 (2005) CrossRefADSGoogle Scholar
  14. 14.
    E.J. Heller, Acc. Chem. Res. 39, 127 (2006) CrossRefMathSciNetGoogle Scholar
  15. 15.
    J. le Page, D.R. Mason, W.M.C. Foulkes, J. Phys.: Condens. Matter 20, 125212 (2008) CrossRefADSGoogle Scholar
  16. 16.
    J.M. Pruneda, D. Sanchez-Portal, A. Arnau, J.I. Juaristi, E. Artacho, Phys. Rev. Lett. 99, 235501 (2007) CrossRefADSGoogle Scholar
  17. 17.
    D.R. Mason, J. le Page, C.P. Race, W.M.C. Foulkes, M.W. Finnis, A.P. Sutton, J. Phys.: Condens. Matter 19, 436209 (2007) CrossRefGoogle Scholar
  18. 18.
    A.P. Sutton, T.N. Todorov, M.J. Cawkwell, J. Hoekstra, Philosophical Magazine A 81, 1833 (2001) CrossRefADSGoogle Scholar
  19. 19.
    T.N. Todorov, J. Phys.: Condens. Matter 13, 10125 (2001) CrossRefADSGoogle Scholar
  20. 20.
    J. le Page, D.R. Mason, C.P. Race, W.M.C. Foulkes, New Journal of Physics 11, 013004 (2009) CrossRefADSGoogle Scholar
  21. 21.
    C.P. Race, D.R. Mason, A.P. Sutton, J. Phys.: Condens. Matter 21, 115702 (2009) CrossRefADSGoogle Scholar
  22. 22.
    C.P. Race, D.R. Mason, J. le Page, M.W. Finnis, W.M.C. Foulkes, A.P. Sutton, in Multiphysics Modeling in Materials Design (Mater. Res. Soc. Symp. Proc), edited by M. Asta, A. Umantsev, J. Neugebauer, Vol. 1229E, Warrendale, PA, 2010, USA, 2009. Mater. Res. Soc. Google Scholar
  23. 23.
    M.W. Finnis, P. Agnew, A.J.E. Foreman, Phys. Rev. B 44, 567 (1991) CrossRefADSGoogle Scholar
  24. 24.
    A. Caro, M. Victoria, Phys. Rev. A 40, 2287 (1989) CrossRefADSGoogle Scholar
  25. 25.
    D.M. Duffy, A.M. Rutherford, J. Phys.: Condens. Matter 19, 016207 (2007) CrossRefADSGoogle Scholar
  26. 26.
    F. Gao, D.J. Bacon, P.E.J. Flewitt, T.A. Lewis, Modelling and Simulation in Materials Science and Engineering 6, 543 (1998) CrossRefADSGoogle Scholar
  27. 27.
    K. Nordlund, L. Wei, Y. Zhong, R.S. Averback, Phys. Rev. B 57, R13965 (1998) CrossRefADSGoogle Scholar
  28. 28.
    O.B. Firsov, Sov. Phys. JETP 36, 1076 (1959) Google Scholar
  29. 29.
    J. Lindhard, M. Scharff, Phys. Rev. 124, 128 (1961) CrossRefADSGoogle Scholar
  30. 30.
    J. Lindhard, Matematisk Fysiske Meddelelser–Kongelige Danske Videnskabernes Selskab 28 (1954) Google Scholar
  31. 31.
    S. Khakshouri, D. Alfè, D.M. Duffy, Phys. Rev. B (Condens. Matter Mater. Phys.) 78, 224304 (2008) ADSGoogle Scholar
  32. 32.
    Z. Lin, R.E. Allen, J. Phys.: Condens. Matter 21, 485503 (2009) CrossRefGoogle Scholar
  33. 33.
    S. Günes, H. Neugebauer, N.S. Sariciftci, Chem. Rev. 107, 1324 (2007) CrossRefGoogle Scholar
  34. 34.
    A.J. Heeger, S. Kivelson, J.R. Schrieffer, W.P. Su. Rev. Mod. Phys. 60, 781 (1988) CrossRefADSGoogle Scholar
  35. 35.
    W. Barford, Electronic and Optical Properties of Conjugated Polymers (Clarendon Press, Oxford, 2005) Google Scholar
  36. 36.
    W.P. Su, J.R. Schrieffer, Proc. Natl. Acad. Sci. USA 77, 5626 (1980) CrossRefADSGoogle Scholar
  37. 37.
    E.J. Mele, Phys. Rev. B 26, 6901 (1982) CrossRefADSGoogle Scholar
  38. 38.
    S.R. Phillpot, A.R. Bishop, B. Horovitz, Phys. Rev. B 40, 1839 (1989) CrossRefADSGoogle Scholar
  39. 39.
    H.W. Streitwolf, Phys. Rev. B 58, 14356 (1998) CrossRefADSGoogle Scholar
  40. 40.
    Z. An, C.Q. Wu, X. Sun, Phys. Rev. Lett. 93, 216407 (2004) CrossRefADSGoogle Scholar
  41. 41.
    P.H. de Oliveira Neto, W.F. da Cunha, R. Gargano, G.M. e Silva, Int. J. Quantum Chem. 108, 2442 (2008) CrossRefADSGoogle Scholar
  42. 42.
    C.L. Wang, F. Martino, Phys. Rev. B 34, 5540 (1986) CrossRefADSGoogle Scholar
  43. 43.
    W. Förner, W. Utz, J. Mol. Model. 4, 12 (1998) CrossRefGoogle Scholar
  44. 44.
    A. Yamashiro, A. Takahashi, J. Phys. Soc. Jpn 67, 2938 (1998) CrossRefADSGoogle Scholar
  45. 45.
    S. Tretiak, A. Saxena, R.L. Martin, A.R. Bishop, Proc. Natl. Acad. Sci. USA 100, 2185 (2003) CrossRefADSGoogle Scholar
  46. 46.
    Y. Meng, B. Di, X.J. Liu, Z. An, C.Q. Wu, J. Chem. Phys. 128, 184903 (2008) CrossRefADSGoogle Scholar
  47. 47.
    R.P. Miranda, A.J. Fisher, L. Stella, A.P. Horsfield, A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states, submitted to Chem. Phys. (2010) Google Scholar
  48. 48.
    R.P. Miranda, A.J. Fisher, L. Stella, A.P. Horsfield, A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. II. Coulomb interaction effects in single conjugated polymer chains, submitted to J. Chem. Phys. (2010) Google Scholar
  49. 49.
    S.T. Epstein, The Variation Method in Quantum Chemistry (Academic Press, New York, 1974) Google Scholar
  50. 50.
    R. McWeeny, Methods of Molecular Quantum Mechanics (Academic Press, London, 1989) Google Scholar
  51. 51.
    F.W. Bobrowicz, W.A. Goddard III, in Methods of Electronic Structure Theory, edited by H.F. Schaefer III (Plenum Press, New York, 1977), pp. 79–127 Google Scholar
  52. 52.
    W.D. Edwards, M.C. Zerner, Theor. Chim. Acta 72, 347 (1987) CrossRefGoogle Scholar
  53. 53.
    C. Kollmar, Int. J. Quantum Chem. 62, 617 (1997) CrossRefGoogle Scholar
  54. 54.
    E. Hairer, S.P. Nørsett, G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems (Springer, Berlin, 1987) Google Scholar
  55. 55.
    Y. Tanabe, in Macromolecular Science and Engineering: New Aspects, edited by Y. Tanabe (Berlin, Springer, 1999), pp. 319–344 Google Scholar
  56. 56.
    J.S. Wilson, A.S. Dhoot, A.J.A.B. Seeley, M.S. Khan, A. Köhler, R.H. Friend, Nature 413, 828 (2001) CrossRefADSGoogle Scholar
  57. 57.
    W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, Cambridge, 1992) Google Scholar
  58. 58.
    J. Nocedal, Math. Comput. 35, 773 (1980) MATHMathSciNetGoogle Scholar
  59. 59.
    P.B. Miranda, D. Moses, A.J. Heeger, Phys. Rev. B 70, 085212 (2004) CrossRefADSGoogle Scholar
  60. 60.
    C.-X. Sheng, M. Tong, S. Singh, Z.V. Vardeny, Phys. Rev. B 75, 085206 (2007) CrossRefADSGoogle Scholar
  61. 61.
    B.C. Stipe, M.A. Rezaei, W. Ho, Phys. Rev. Lett. 82, 1724 (1999) CrossRefADSGoogle Scholar
  62. 62.
    N. Agraït, A.L. Yeyati, J.M. van Ruitenbeek, Phys. Rep. 377, 81 (2003) CrossRefADSGoogle Scholar
  63. 63.
    N. Agraït, C. Untiedt, G. Rubio-Bollinger, S. Vieira, Phys. Rev. Lett. 88, 216803 (2002) CrossRefADSGoogle Scholar
  64. 64.
    R.H.M. Smit, Y. Noat, C. Untiedt, N.D. Lang, M.C.V. Hemert, J.M. van Ruitenbeek, Nature 419, 906 (2002) CrossRefADSGoogle Scholar
  65. 65.
    M.J. Montgomery, T.N. Todorov, J. Phys.: Condens. Matter 15, 8781 (2003) CrossRefADSGoogle Scholar
  66. 66.
    H. Haug, A.P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer, Berlin, 1996) Google Scholar
  67. 67.
    G.D. Mahan, Many-Particle Physics (Plenum Press, New York, 1990) Google Scholar
  68. 68.
    M. Galperin, M.A. Ratner, A. Nitzan, J. Chem. Phys. 121, 11965 (2004) CrossRefADSGoogle Scholar
  69. 69.
    D.A. Ryndyk, M. Hartung, G. Cuniberti, Phys. Rev. B 73, 045420 (2006) CrossRefADSGoogle Scholar
  70. 70.
    T. Frederiksen, M. Brandbyge, N. Lorente, A.P. Jauho, Phys. Rev. Lett. 93, 256601 (2004) CrossRefADSGoogle Scholar
  71. 71.
    M. Paulsson, T. Frederiksen, M. Brandbyge, Phys. Rev. B 72, 201101(R) (2005) CrossRefADSGoogle Scholar
  72. 72.
    T. Frederiksen, M. Paulsson, M. Brandbyge, A.P. Jauho, Phys. Rev. B 75, 205413 (2007) Ã CrossRefADSGoogle Scholar
  73. 73.
    A.P. Jauho, N.S. Wingreen, Y. Meir, Phys. Rev. B 50, 5528 (1994) CrossRefADSGoogle Scholar
  74. 74.
    Y. Zhu, J. Maciejko, T. Ji, H. Guo, J. Wang, Phys. Rev. B 71, 075317 (2005) CrossRefADSGoogle Scholar
  75. 75.
    A.P. Horsfield, D.R. Bowler, A.J. Fisher, T.N. Todorov, C.G. Sánchez, J. Phys.: Condens. Matter 16, 8251 (2004) CrossRefADSGoogle Scholar
  76. 76.
    S. Kurth, G.G. Stefanucci, C.-O. Almbladh, A. Rubio, E.K.U. Gross, Phys. Rev. B 72, 035308 (2005) CrossRefADSGoogle Scholar
  77. 77.
    E.J. McEniry, T.N. Todorov, D. Dundas, J. Phys.: Condens. Matter 21, 195304 (2009) CrossRefADSGoogle Scholar
  78. 78.
    E.J. McEniry, T.N. Todorov, D. Dundas, The effect of electron-phonon interactions in tunnelling systems, in preparation (2010) Google Scholar
  79. 79.
    Y. Wang, L. Kantorovich, Phys. Rev. B 76, 144304 (2007) CrossRefADSGoogle Scholar
  80. 80.
    Y. Wang, Phys. Rev. B 79, 235102 (2009) CrossRefADSGoogle Scholar
  81. 81.
    P. Hyldgaard, S. Hershfield, J.H. Davies, J.W. Wilkins, Ann. Phys. 236, 1 (1994) CrossRefADSGoogle Scholar
  82. 82.
    L. Stella, M. Meister, A.J. Fisher, A.P. Horsfield, J. Chem. Phys. 127, 214104 (2007) CrossRefADSGoogle Scholar
  83. 83.
    L. Stella, A.P. Horsfield, A.J. Fisher, Analog of rabi oscillations in resonant electron-ion systems, in preparation Google Scholar
  84. 84.
    A.P. Horsfield, D.R. Bowler, H. Ness, C.G. Sánchez, T.N. Todorov, A.J. Fisher, Rep. Prog. Phys. 69, 1195 (2006) CrossRefADSGoogle Scholar
  85. 85.
    A.A. Budini, R.L. Matos Filho, N. Zagury, Phys. Rev. A 65, 041402(R) (2002) CrossRefADSGoogle Scholar
  86. 86.
    W.P. Su, J.R. Schrieffer, A.J. Heeger, Phys. Rev. Lett. 42, 1698 (1979) CrossRefADSGoogle Scholar
  87. 87.
    W.P. Su, J.R. Schrieffer, A.J. Heeger, Phys. Rev. B 22, 2099 (1980) CrossRefADSGoogle Scholar
  88. 88.
    L. Stella, A.P. Horsfield, A.J. Fisher, Ultrafast nonradiative decay in photoexcited π-conjugated polymers, in preparation Google Scholar
  89. 89.
    C. Gadermaier, G. Cerullo, C. Manzoni, U. Scherf, E.J.W. List, G. Lanzani, Chem. Phys. Lett. 384, 251 (2004) CrossRefADSGoogle Scholar
  90. 90.
    C. Manzoni, A. Gambetta, E. Menna, M. Meneghetti, G. Lanzani, G. Cerullo, Phys. Rev. Lett. 94, 207401 (2005) CrossRefADSGoogle Scholar
  91. 91.
    E. Collini, G.D. Scholes, Science 323, 369 (2009) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • E. J. McEniry
    • 1
  • Y. Wang
    • 2
  • D. Dundas
    • 3
  • T. N. Todorov
    • 3
  • L. Stella
    • 4
  • R. P. Miranda
    • 5
    • 6
  • A. J. Fisher
    • 5
    • 6
  • A. P. Horsfield
    • 7
  • C. P. Race
    • 8
  • D. R. Mason
    • 8
  • W. M.C. Foulkes
    • 8
  • A. P. Sutton
    • 8
  1. 1.Interdisciplinary Centre for Advanced Materials Simulation, Ruhr-Universität BochumBochumGermany
  2. 2.Department of ChemistryTulane UniversityNew OrleansUSA
  3. 3.Atomistic Simulation Centre, School of Mathematics and Physics, Queen’s University of BelfastBelfastUK
  4. 4.Nano-Bio Spectroscopy Group and ETSF Scientific Development Centre, Dpto. Física de Materiales, Universidad del País VascoSan SebastiánSpain
  5. 5.Department of Physics and AstronomyUniversity College LondonLondonUK
  6. 6.London Centre for Nanotechnology, 17-19 Gordon StreetLondonUK
  7. 7.Department of MaterialsLondonUK
  8. 8.Department of PhysicsLondonUK

Personalised recommendations