Abstract
Capturing nuclear dynamics through conical intersections is pivotal to understand the fate of photoexcited molecules. The concept of a conical intersection, however, belongs to a specific definition of the electronic states, within a Born–Huang representation of the molecular wavefunction. How would these ultrafast funneling processes be translated if an exact factorization of the molecular wavefunction were to be used? In this article, we build upon our recent analysis [B.F.E. Curchod, F. Agostini, J. Phys. Chem. Lett. 8, 831 (2017)] and address this question in a broader perspective by studying the dynamics of a nuclear wavepacket through two types of conical intersections, differing by the strength of their underlying diabatic coupling. Our results generalize our previous findings by (i) showing that the time-dependent potential energy surface smoothly varies, both in time and in position, between the corresponding diabatic and adiabatic potentials, with sometimes more complex features if interferences are observed, (ii) highlighting the non-trivial behavior of the time-dependent vector potential and the fact that it cannot be gauged away in general, and (iii) justifying some approximations employed in the derivation of a mixed quantum/classical scheme based on the exact factorization.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Köppel, W. Domcke, L.S. Cederbaum, Adv. Chem. Phys. 57, 59 (1984)
D.R. Yarkony, Rev. Mod. Phys. 68, 985 (1996)
D.R. Yarkony, J. Phys. Chem. 105, 6277 (2001)
W. Domcke, D. Yarkony, H. Köppel (Eds.), in Conical intersections: electronic structure, dynamics & spectroscopy (World Scientific Pub Co Inc., Singapore, 2004), Vol. 15
G.A. Worth, L.S. Cederbaum, Annu. Rev. Phys. Chem. 55, 127 (2004)
B.G. Levine, T.J. Martínez, Annu. Rev. Phys. Chem. 58, 613 (2007)
W. Domcke, D. Yarkony, H. Köppel (Eds.), in Conical intersections: theory, computation and experiment (World Scientific Pub Co Inc., Singapore, 2012), Vol. 17
W. Domcke, D.R. Yarkony, Annu. Rev. Phys. Chem. 63, 325 (2012)
J. Michl, V. Bonačić-Koutecký, Electronic aspects of organic photochemistry (John Wiley and Sons, New York, 1990)
J. Michl, Mol. Photochem. 4, 243 (1972)
C.A. Mead, D.G. Truhlar, J. Chem. Phys. 70, 2284 (1979)
M.V. Berry, M. Wilkinson, Proc. R. Soc. Lond. Ser. A 392, 15 (1984)
M.V. Berry, Proc. R. Soc. Lond. Ser. A 392, 45 (1984)
F. Bernardi, M. Olivucci, M.A. Robb, Chem. Soc. Rev. 25, 321 (1996)
M. Baer, Beyond born-oppenheimer: electronic nonadiabatic coupling terms and conical intersections (John Wiley & Sons, Inc., 2006)
T.J. Martinez, Nature 467, 412 (2010)
S. Matsika, P. Krause, Annu. Rev. Phys. Chem. 62, 621 (2011)
J.P. Malhado, M.J. Bearpark, J.T. Hynes, Front. Chem. 2, 97 (2014)
X. Zhu, D.R. Yarkony, Mol. Phys. 114, 1983 (2016)
C. Xie, C.L. Malbon, D.R. Yarkony, D. Xie, H. Guo, J. Am. Chem. Soc. 140, 1986 (2018)
C.A. Mead, D.G. Truhlar, J. Chem. Phys. 77, 6090 (1982)
T. Pacher, L. Cederbaum, H. Köppel, J. Chem. Phys. 89, 7367 (1988)
T. Pacher, L. Cederbaum, H. Köppel, Adv. Chem. Phys. 84, 293 (2007)
F. Plasser, G. Granucci, J. Pittner, M. Barbatti, M. Persico, H. Lischka, J. Chem. Phys. 137, 22A514 (2012)
A. Abedi, N.T. Maitra, E.K.U. Gross, Phys. Rev. Lett. 105, 123002 (2010)
A. Abedi, N.T. Maitra, E.K.U. Gross, J. Chem. Phys. 137, 22A530 (2012)
B.F.E.Curchod, F. Agostini, J. Phys. Chem. Lett. 8, 831 (2017)
G. Hunter, Int. J. Quantum Chem. 9, 237 (1975)
T. Jeck, B.T. Sutcliffe, R.G. Woolley, J. Phys. A: Math. Theor. 48, 445201 (2015)
L.S. Cederbaum, J. Chem. Phys. 138, 224110 (2013)
N.I. Gidopoulos, E.K.U. Gross, Phil. Trans. R. Soc. A 372, 20130059 (2014)
L.S. Cederbaum, Chem. Phys. 457, 129 (2015)
S. Parashar, Y. Sajeev, S.K. Ghosh, Mol. Phys. 113, 3067 (2015)
R. Lefebvre, J. Chem. Phys. 142, 074106 (2015)
R. Lefebvre, J. Chem. Phys. 142, 214105 (2015)
S.K. Min, A. Abedi, K.S. Kim, E.K.U. Gross, Phys. Rev. Lett. 113, 263004 (2014)
Y.C. Chiang, S. Klaiman, F. Otto, L.S. Cederbaum, J. Chem. Phys. 140, 054104 (2014)
R. Requist, F. Tandetzky, E.K.U. Gross, Phys. Rev. A 93, 042108 (2016)
R. Requist, C.R. Proetto, E.K.U. Gross, Phys. Rev. A 96, 062503 (2017)
A. Scherrer, F. Agostini, D. Sebastiani, E.K.U. Gross, R. Vuilleumier, J. Chem. Phys. 143, 074106 (2015)
F.G. Eich, F. Agostini, J. Chem. Phys. 145, 054110 (2016)
A. Scherrer, F. Agostini, D. Sebastiani, E.K.U. Gross, R. Vuilleumier, Phys. Rev. X 7, 031035 (2017)
J. Frenkel, Wave mechanics (Clarendon, Oxford, 1934)
J.L. Alonso, J. Clemente-Gallardo, P. Echeniche-Robba, J.A. Jover-Galtier, J. Chem. Phys. 139, 087101 (2013)
A. Abedi, N.T. Maitra, E.K.U. Gross, J. Chem. Phys. 139, 087102 (2013)
F. Agostini, S.K. Min, E.K.U. Gross, Ann. Phys. 527, 546 (2015)
A. Abedi, F. Agostini, Y. Suzuki, E.K.U. Gross, Phys. Rev. Lett. 110, 263001 (2013)
F. Agostini, A. Abedi, Y. Suzuki, E.K.U. Gross, Mol. Phys. 111, 3625 (2013)
Y. Suzuki, A. Abedi, N.T. Maitra, E.K.U. Gross, Phys. Chem. Chem. Phys. 17, 29271 (2015)
F. Agostini, A. Abedi, Y. Suzuki, S.K. Min, N.T. Maitra, E.K.U. Gross, J. Chem. Phys. 142, 084303 (2015)
B.F.E. Curchod, F. Agostini, E.K.U. Gross, J. Chem. Phys. 145, 034103 (2016)
Y. Suzuki, K. Watanabe, Phys. Rev. A 94, 032517 (2016)
A. Ferretti, G. Granucci, A. Lami, M. Persico, G. Villani, J. Chem. Phys. 104, 5517 (1996)
A. Humeniuk, R. Mitrić, J. Chem. Phys. 144, 234108 (2016)
M.D. Feit, J.A. Fleck, A. Steiger, J. Comput. Phys. 47, 412 (1982)
K. Hader, J. Albert, E.K.U. Gross, V. Engel, J. Chem. Phys. 146, 074304 (2017)
S.K. Min, F. Agostini, E.K.U. Gross, Phys. Rev. Lett. 115, 073001 (2015)
F. Agostini, S.K. Min, A. Abedi, E.K.U. Gross, J. Chem. Theory Comput. 12, 2127 (2016)
S.K. Min, F. Agostini, I. Tavernelli, E.K.U. Gross, J. Phys. Chem. Lett. 8, 3048 (2017)
J.K. Ha, I.S. Lee, S.K. Min, J. Phys. Chem. Lett. 9, 1097 (2018)
R. Requist, E.K.U. Gross, Phys. Rev. Lett. 117, 193001 (2016)
Author information
Authors and Affiliations
Corresponding author
Additional information
Contribution to the Topical Issue “Special issue in honor of Hardy Gross”, edited by C.A. Ullrich, F.M.S. Nogueira, A. Rubio, and M.A.L. Marques.
Rights and permissions
Open Access This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Agostini, F., Curchod, B.F.E. When the exact factorization meets conical intersections.... Eur. Phys. J. B 91, 141 (2018). https://doi.org/10.1140/epjb/e2018-90117-6
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2018-90117-6