Advertisement

CT-MQC – a coupled-trajectory mixed quantum/classical method including nonadiabatic quantum coherence effects

  • Basile F. E. Curchod
  • Federica Agostini
  • Ivano Tavernelli
Regular Article
Part of the following topical collections:
  1. Topical issue: Special issue in honor of Hardy Gross

Abstract

Upon photoexcitation by a short light pulse, molecules can reach regions of the configuration space characterized by strong nonadiabaticity, where the motion of the nuclei is strongly coupled to the motion of the electrons. The subtle interplay between the nuclear and electronic degrees of freedom in such situations is rather challenging to capture by state-of-the-art nonadiabatic dynamics approaches, limiting therefore their predictive power. The Exact Factorization of the molecular wavefunction, though, offers new perspectives in the solution of this longstanding issue. Here, we investigate the performance of a mixed quantum/classical (MQC) limit of this theory, named Coupled Trajectory-MQC, which was shown to reproduce the excited-state dynamics of small systems accurately. The method is applied to the study of the photoinduced ring opening of oxirane and the results are compared with two other nonadiabatic approaches based on different Ansätze for the molecular wavefunction, namely Ehrenfest dynamics and Ab Initio Multiple Spawning (AIMS). All simulations were performed using linear-response time-dependent density functional theory. We show that the CT-MQC method can capture the (de)coherence effects resulting from the dynamics through conical intersections, in good agreement with the results obtained with AIMS and in contrast with ensemble Ehrenfest dynamics.

References

  1. 1.
    R. Kapral, G. Ciccotti, J. Chem. Phys. 110, 8916 (1999) ADSCrossRefGoogle Scholar
  2. 2.
    F. Agostini, S. Caprara, G. Ciccotti, Europhys. Lett. 78, 30001 (2007) ADSCrossRefGoogle Scholar
  3. 3.
    T. Yonehara, K. Hanasaki, K. Takatsuka, Chem. Rev. 112, 499 (2012) CrossRefGoogle Scholar
  4. 4.
    J.C. Tully, J. Chem. Phys. 137, 22A301 (2012) CrossRefGoogle Scholar
  5. 5.
    M. Vacher, M.J. Bearpark, M.A. Robb, J.P. Malhado, Phys. Rev. Lett. 118, 083001 (2017) ADSCrossRefGoogle Scholar
  6. 6.
    M. Born, R.J. Oppenheimer, Ann. Phys. 389, 457 (1927) CrossRefGoogle Scholar
  7. 7.
    C. Xie, C.L. Malbon, D.R. Yarkony, D. Xie, H. Guo, J. Am. Chem. Soc. 140, 1986 (2018) CrossRefGoogle Scholar
  8. 8.
    A. Scherrer, F. Agostini, D. Sebastiani, E.K.U. Gross, R. Vuilleumier, Phys. Rev. X 7, 031035 (2017) Google Scholar
  9. 9.
    A. Schild, F. Agostini, E.K.U. Gross, J. Phys. Chem. A 120, 3316 (2016) CrossRefGoogle Scholar
  10. 10.
    A. Scherrer, F. Agostini, D. Sebastiani, E.K.U. Gross, R. Vuilleumier, J. Chem. Phys. 143, 074106 (2015) ADSCrossRefGoogle Scholar
  11. 11.
    L. Wang, A. Akimov, O.V. Prezhdo, J. Phys. Chem. Lett. 7, 2100 (2016) CrossRefGoogle Scholar
  12. 12.
    B.F.E. Curchod, U. Rothlisberger, I. Tavernelli, ChemPhysChem 14, 1314 (2013) CrossRefGoogle Scholar
  13. 13.
    I. Tavernelli, Acc. Chem. Res. 48, 792 (2015) CrossRefGoogle Scholar
  14. 14.
    J.E. Subotnik, A. Jain, B. Landry, A. Petit, W. Ouyang, N. Bellonzi, Ann. Rev. Phys. Chem. 67, 387 (2016) ADSCrossRefGoogle Scholar
  15. 15.
    J.C. Tully, J. Chem. Phys. 93, 1061 (1990) ADSCrossRefGoogle Scholar
  16. 16.
    J.C. Tully, Faraday Discuss. 110, 407 (1998) ADSCrossRefGoogle Scholar
  17. 17.
    J.C. Tully, Faraday Discuss. 110, 407 (1998) ADSCrossRefGoogle Scholar
  18. 18.
    F. Agostini, S.K. Min, A. Abedi, E.K.U. Gross, J. Chem. Theory Comput. 12, 2127 (2016) CrossRefGoogle Scholar
  19. 19.
    M. Ben-Nun, J. Quenneville, T.J. Martínez, J. Phys. Chem. A 104, 5161 (2000) CrossRefGoogle Scholar
  20. 20.
    E. Tapavicza, I. Tavernelli, U. Rothlisberger, Phys. Rev. Lett. 98, 023001 (2007) ADSCrossRefGoogle Scholar
  21. 21.
    B.F.E. Curchod, T.J. Penfold, U. Rothlisberger, I. Tavernelli, Phys. Rev. A 84, 042507 (2011) ADSCrossRefGoogle Scholar
  22. 22.
    A. Abedi, F. Agostini, E.K.U. Gross, Europhys. Lett. 106, 33001 (2014) ADSCrossRefGoogle Scholar
  23. 23.
    F. Agostini, A. Abedi, E.K.U. Gross, J. Chem. Phys. 141, 214101 (2014) ADSCrossRefGoogle Scholar
  24. 24.
    N.L. Doltsinis, D. Marx, Phys. Rev. Lett. 88, 166402 (2002) ADSCrossRefGoogle Scholar
  25. 25.
    A.W. Jasper, S. Nangia, C. Zhu, D.G. Truhlar, Acc. Chem. Res. 39, 101 (2006) CrossRefGoogle Scholar
  26. 26.
    B.F.E. Curchod, I. Tavernelli, U. Rothlisberger, Phys. Chem. Chem. Phys. 13, 3231 (2011) CrossRefGoogle Scholar
  27. 27.
    P. Huo, D.F. Coker, J. Chem. Phys. 137, 22A535 (2012) CrossRefGoogle Scholar
  28. 28.
    R. Mitrić, J. Petersen, V. Bonačić-Koutecký, Phys. Rev. A 79, 053416 (2009) ADSCrossRefGoogle Scholar
  29. 29.
    M. Richter, P. Marquetand, J. González-Vázquez, I. Sola, L. González, J. Chem. Theory Comput. 7, 1253 (2011) CrossRefGoogle Scholar
  30. 30.
    R. Kapral, Annu. Rev. Phys. Chem. 57, 129 (2006) ADSCrossRefGoogle Scholar
  31. 31.
    E.R. Dunkel, S. Bonella, D.F. Coker, J. Chem. Phys. 129, 114106 (2008) ADSCrossRefGoogle Scholar
  32. 32.
    T.J. Martínez, M. Ben-Nun, R.D. Levine, J. Phys. Chem. 100, 7884 (1996) CrossRefGoogle Scholar
  33. 33.
    T.J. Martínez, R.D. Levine, J. Chem. Soc. Faraday Trans. 93, 941 (1997) CrossRefGoogle Scholar
  34. 34.
    M. Ben-Nun, T.J. Martínez, J. Chem. Phys. 108, 7244 (1998) ADSCrossRefGoogle Scholar
  35. 35.
    M.D. Hack, A.M. Wensmann, D.G. Truhlar, M. Ben-Nun, T.J. Martínez, J. Chem. Phys. 115, 1172 (2001) ADSCrossRefGoogle Scholar
  36. 36.
    M. Ben-Nun, T.J. Martínez, Adv. Chem. Phys. 121, 439 (2002) Google Scholar
  37. 37.
    B.F.E. Curchod, C. Rauer, P. Marquetand, L. González, T. Martínez, J. Chem. Phys. 144, 101102 (2016) ADSCrossRefGoogle Scholar
  38. 38.
    A.M. Virshup, C. Punwong, T.V. Pogorelov, B.A. Lindquist, C. Ko, T.J. Martínez, J. Phys. Chem. B 113, 3280 (2008) CrossRefGoogle Scholar
  39. 39.
    F.F. de Carvalho, M.E.F. Bouduban, B.F.E. Curchod, I. Tavernelli, Entropy 16, 62 (2014) ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    A. Abedi, F. Agostini, Y. Suzuki, E.K.U. Gross, Phys. Rev. Lett. 110, 263001 (2013) ADSCrossRefGoogle Scholar
  41. 41.
    F. Agostini, A. Abedi, Y. Suzuki, E.K.U. Gross, Mol. Phys. 111, 3625 (2013) ADSCrossRefGoogle Scholar
  42. 42.
    F. Agostini, A. Abedi, Y. Suzuki, S.K. Min, N.T. Maitra, E.K.U. Gross, J. Chem. Phys. 142, 084303 (2015) ADSCrossRefGoogle Scholar
  43. 43.
    A. Abedi, N.T. Maitra, E.K.U. Gross, Phys. Rev. Lett. 105, 123002 (2010) ADSCrossRefGoogle Scholar
  44. 44.
    A. Abedi, N.T. Maitra, E.K.U. Gross, J. Chem. Phys. 137, 22A530 (2012) CrossRefGoogle Scholar
  45. 45.
    S.K. Min, F. Agostini, E.K.U. Gross, Phys. Rev. Lett. 115, 073001 (2015) ADSCrossRefGoogle Scholar
  46. 46.
    S.K. Min, F. Agostini, I. Tavernelli, E.K.U. Gross, J. Phys. Chem. Lett. 8, 3048 (2017) CrossRefGoogle Scholar
  47. 47.
    G. Granucci, M. Persico, J. Chem. Phys. 126, 134114 (2007) ADSCrossRefGoogle Scholar
  48. 48.
    A.W. Jasper, S. Nangia, C. Zhu, D.G. Truhlar, Acc. Chem. Res. 39, 101 (2006) CrossRefGoogle Scholar
  49. 49.
    H.M. Jaeger, S. Fischer, O.V. Prezhdo, J. Chem. Phys. 137, 22A545 (2012) CrossRefGoogle Scholar
  50. 50.
    J.E. Subotnik, W. Ouyang, B.R. Landry, J. Chem. Phys. 139, 214107 (2013) ADSCrossRefGoogle Scholar
  51. 51.
    X. Gao, W. Thiel, Phys. Rev. E 95, 013308 (2017) ADSCrossRefGoogle Scholar
  52. 52.
    B.J. Schwartz, E.R. Bittner, O.V. Prezhdo, P.J. Rossky, J. Chem. Phys. 104, 5942 (1996) ADSCrossRefGoogle Scholar
  53. 53.
    J.Y. Fang, S. Hammes-Schiffer, J. Phys. Chem. A 103, 9399 (1999) CrossRefGoogle Scholar
  54. 54.
    N. Shenvi, J.E. Subotnik, W. Yang, J. Chem. Phys. 134, 144102 (2011) ADSCrossRefGoogle Scholar
  55. 55.
    N. Shenvi, J.E. Subotnik, W. Yang, J. Chem. Phys. 135, 024101 (2011) ADSCrossRefGoogle Scholar
  56. 56.
    N. Shenvi, W. Yang, J. Chem. Phys. 137, 22A528 (2012) CrossRefGoogle Scholar
  57. 57.
    J.E. Subotnik, N. Shenvi, J. Chem. Phys. 134, 024105 (2011) ADSCrossRefGoogle Scholar
  58. 58.
    J.E. Subotnik, N. Shenvi, J. Chem. Phys. 134, 244114 (2011) ADSCrossRefGoogle Scholar
  59. 59.
    I. Tavernelli, Phys. Rev. B 73, 094204 (2006) ADSCrossRefGoogle Scholar
  60. 60.
    J.L. Alonso, J. Clemente-Gallardo, P. Echeniche-Robba, J.A. Jover-Galtier, J. Chem. Phys. 139, 087101 (2013) ADSCrossRefGoogle Scholar
  61. 61.
    A. Abedi, N.T. Maitra, E.K.U. Gross, J. Chem. Phys. 139, 087102 (2013) ADSCrossRefGoogle Scholar
  62. 62.
    F. Agostini, S.K. Min, E.K.U. Gross, Ann. Phys. 527, 546 (2015) MathSciNetCrossRefGoogle Scholar
  63. 63.
    F.G. Eich, F. Agostini, J. Chem. Phys. 145, 054110 (2016) ADSCrossRefGoogle Scholar
  64. 64.
    B.F.E. Curchod, F. Agostini, E.K.U. Gross, J. Chem. Phys. 145, 034103 (2016) ADSCrossRefGoogle Scholar
  65. 65.
    B.F.E. Curchod, F. Agostini, J. Phys. Chem. Lett. 8, 831 (2017) CrossRefGoogle Scholar
  66. 66.
    E. Khosravi, A. Abedi, A. Rubio, N.T. Maitra, Phys. Chem. Chem. Phys. 19, 8269 (2017) CrossRefGoogle Scholar
  67. 67.
    Y. Suzuki, K. Watanabe, Phys. Rev. A 94, 032517 (2016) ADSCrossRefGoogle Scholar
  68. 68.
    Y. Suzuki, A. Abedi, N.T. Maitra, K. Yamashita, E.K.U. Gross, Phys. Rev. A 89, 040501(R) (2014) ADSCrossRefGoogle Scholar
  69. 69.
    E. Khosravi, A. Abedi, N.T. Maitra, Phys. Rev. Lett. 115, 263002 (2015) ADSCrossRefGoogle Scholar
  70. 70.
    S.K. Min, A. Abedi, K.S. Kim, E.K.U. Gross, Phys. Rev. Lett. 113, 263004 (2014) ADSCrossRefGoogle Scholar
  71. 71.
    R. Requist, F. Tandetzky, E.K.U. Gross, Phys. Rev. A 93, 042108 (2016) ADSCrossRefGoogle Scholar
  72. 72.
    P.R. Holland, The quantum theory of motion – an account of the de Broglie–Bohm causal interpretation of quantum mechanics (Cambridge University Press, Cambridge, UK, 1993) Google Scholar
  73. 73.
    B.F.E. Curchod, T.J. Martínez, Chem. Rev. 118, 3305 (2018) CrossRefGoogle Scholar
  74. 74.
    E.J. Heller, J. Chem. Phys. 75, 2923 (1981) ADSMathSciNetCrossRefGoogle Scholar
  75. 75.
    S. Yang, J.D. Coe, B. Kaduk, T.J. Martínez, J. Chem. Phys. 130, 04B606 (2009) Google Scholar
  76. 76.
    B. Mignolet, B.F.E. Curchod, arXiv:1801.06639 (2018)
  77. 77.
    B.G. Levine, J.D. Coe, A.M. Virshup, T.J. Martinez, Chem. Phys. 347, 3 (2008) ADSCrossRefGoogle Scholar
  78. 78.
    J.W. Snyder Jr., B.F.E. Curchod, T.J. Martínez, J. Phys. Chem. Lett. 7, 2444 (2016) CrossRefGoogle Scholar
  79. 79.
    H. Tao, B.G. Levine, T.J. Martínez, J. Chem. Phys. A 113, 13656 (2009) CrossRefGoogle Scholar
  80. 80.
    S. Pijeau, D. Foster, E.G. Hohenstein, J. Phys. Chem. A 121, 4595 (2017) CrossRefGoogle Scholar
  81. 81.
    B.F.E. Curchod, A. Sisto, T.J. Martínez, J. Phys. Chem. A 121, 265 (2017) CrossRefGoogle Scholar
  82. 82.
    CPMD, Copyright IBM Corp 1990–2015, Copyright MPI für Festkörperforschung Stuttgart 1997–2001. http://www.cpmd.org/
  83. 83.
    J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996) ADSCrossRefGoogle Scholar
  84. 84.
    E. Runge, E.K.U. Gross, Phys. Rev. Lett. 52, 997 (1984) ADSCrossRefGoogle Scholar
  85. 85.
    M. Petersilka, U.J. Gossmann, E.K.U. Gross, Phys. Rev. Lett. 76, 1212 (1996) ADSCrossRefGoogle Scholar
  86. 86.
    M.E. Casida, Time-dependent density-functional response theory for molecules, in Recent advances in density functional methods, edited by D.P. Chong (World Scientific, Singapore, 1995), p. 155 Google Scholar
  87. 87.
    I. Tamm, J. Phys. 9, 449 (1945) Google Scholar
  88. 88.
    S.M. Dancoff, Phys. Rev. 78, 382 (1950) ADSCrossRefGoogle Scholar
  89. 89.
    C.A. Ullrich, Time-dependent density-functional theory (Oxford University Press, 2012) Google Scholar
  90. 90.
    B.G. Levine, C. Ko, J. Quenneville, T.J. Martinez, Mol. Phys. 104, 1039 (2006) ADSCrossRefGoogle Scholar
  91. 91.
    E. Tapavicza, I. Tavernelli, U. Rothlisberger, C. Filippi, M.E. Casida, J. Chem. Phys. 129, 124108 (2008) ADSCrossRefGoogle Scholar
  92. 92.
    L. Kleinman, D.M. Bylander, Phys. Rev. Lett. 48, 1425 (1982) ADSCrossRefGoogle Scholar
  93. 93.
    C.M. Isborn, N. Luehr, I.S. Ufimtsev, T.J. Martínez, J. Chem. Theory Comput. 7, 1814 (2011) CrossRefGoogle Scholar
  94. 94.
    I.S. Ufimtsev, T.J. Martinez, J. Chem. Theory Comput. 4, 222 (2008) CrossRefGoogle Scholar
  95. 95.
    I.S. Ufimtsev, T.J. Martinez, J. Chem. Theory Comput. 5, 1004 (2009) CrossRefGoogle Scholar
  96. 96.
    I.S. Ufimtsev, T.J. Martinez, J. Chem. Theory Comput. 5, 2619 (2009) CrossRefGoogle Scholar
  97. 97.
    R. Ditchfield, W.J. Hehre, J.A. Pople, J. Chem. Phys. 54, 724 (1971) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Basile F. E. Curchod
    • 1
  • Federica Agostini
    • 2
  • Ivano Tavernelli
    • 3
  1. 1.Department of ChemistryDurham UniversityDurhamUK
  2. 2.Laboratoire de Chimie Physique, UMR 8000 CNRS/University Paris-SudOrsayFrance
  3. 3.IBM Research GmbH, Zürich Research LaboratoryRüschlikonSwitzerland

Personalised recommendations