Skip to main content
SpringerLink
Log in

Quantum molecular dynamics simulations of the effect of secondary modes on the photoisomerization of a retinal chromophore model

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

In this paper, we report on the performance of various quantum molecular dynamics simulation methods in describing the photo-induced nonadiabatic dynamics underlying the isomerization process of the retinal chromophore in rhodopsin. We focus on purely quantum vibronic wavepacket techniques and on various trajectory-based schemes, discussing their capability of accurately capture the isomerization process using a two-dimensional two-state model system coupled to an environment of secondary harmonic modes. Numerical results of various algorithms and time-independent grid schemes for the purely quantum approaches are presented, which also serve as benchmark for the trajectory-based calculations. Independent-trajectory and coupled-trajectory methods are compared as well, devoting particular attention to the scaling of their computational cost when increasing the number of degrees of freedom.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data availability

The datasets generated during and analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. A. Abedi, N.T. Maitra, E.K.U. Gross, Exact factorization of the time-dependent electron-nuclear wave function. Phys. Rev. Lett. 105(12), 123002 (2010)

    ADS  Google Scholar 

  2. A. Abedi, N.T. Maitra, E.K.U. Gross, Correlated electron-nuclear dynamics: exact factorization of the molecular wave-function. J. Chem. Phys. 137(22), 22A530 (2012)

    Google Scholar 

  3. F. Agostini, B.F.E. Curchod, Different flavors of nonadiabatic molecular dynamics. WIREs Comput. Mol. Sci. 9, e1417 (2019)

    Google Scholar 

  4. F. Agostini, E.K.U. Gross, Exact factorization of the electron-nuclear wavefunction: theory and applications, in Quantum Chemistry and Dynamics of Excited States, Methods and Applications. ed. by L. González, R. Lindh (Wiley, New Jersey, 2020), pp.531–562

    Google Scholar 

  5. F. Agostini, E.K.U. Gross, Ultrafast dynamics with the exact factorization. Eur. Phys. J. B 94, 179 (2021)

    ADS  Google Scholar 

  6. F. Agostini, S.K. Min, A. Abedi et al., Quantum-classical non-adiabatic dynamics: coupled- vs. independent-trajectory methods. J. Chem. Theory Comput. 12(5), 2127–2143 (2016)

    Google Scholar 

  7. F. Agostini, B.F.E. Curchod, R. Vuilleumier et al., TDDFT and quantum-classical dynamics: a universal tool describing the dynamics of matter, in Handbook of Materials Modeling. ed. by W. Andreoni, S. Yip (Springer, Netherlands, 2018), pp.1–47

    Google Scholar 

  8. F. Agostini, E. Marsili, F. Talotta, G-CTMQC. https://gitlab.com/agostini.work/g-ctmqc. Accessed July 2022

  9. E.V. Arribas, F. Agostini, N.T. Maitra, Exact factorization adventures: a promising approach for non-bound states. Molecules 27, 4002 (2022)

    Google Scholar 

  10. G. Avila, T. Carrington, Nonproduct quadrature grids for solving the vibrational Schrödinger equation. J. Chem. Phys. 131(17), 174103 (2009). https://doi.org/10.1063/1.3246593

    Article  ADS  Google Scholar 

  11. G. Avila, T. Carrington, Using a pruned basis, a non-product quadrature grid, and the exact Watson normal-coordinate kinetic energy operator to solve the vibrational Schrödinger equation for C\(_{2}\)H\(_{4}\). J Chem Phys 135(6), 064101 (2011). https://doi.org/10.1063/1.3617249

    Article  ADS  Google Scholar 

  12. G. Avila, T. Carrington, Using nonproduct quadrature grids to solve the vibrational Schrödinger equation in 12D. J. Chem. Phys. 134(5), 054126 (2011). https://doi.org/10.1063/1.3549817

    Article  ADS  Google Scholar 

  13. G. Avila, E. Matyus, Full-dimensional (12D) variational vibrational states of CH\(_4\)F: interplay of anharmonicity and tunneling. J. Chem. Phys. 151(15), 154301 (2019). https://doi.org/10.1063/1.5124532. arXiv:1908.00809

  14. G. Avila, E. Mátyus, Toward breaking the curse of dimensionality in (ro)vibrational computations of molecular systems with multiple large-amplitude motions. J. Chem. Phys. 150(17), 174107 (2019). https://doi.org/10.1063/1.5090846. arXiv:1904.04588

  15. G. Avila, D. Papp, G. Czakó et al., Exact quantum dynamics background of dispersion interactions: case study for CH\(_4\)Ar in full (12) dimensions. Phys. Chem. Chem. Phys. 22(5), 2792–2802 (2020). https://doi.org/10.1039/C9CP04426D. arXiv:1908.05432

  16. B. Balzer, G. Stock, Transient spectral features of a cis–trans photoreaction in the condensed phase: a model study. J. Phys. Chem. A 108, 6464–6473 (2004)

    Google Scholar 

  17. B. Balzer, S. Dilthey, S. Hahn et al., Quasiperiodic orbit analysis of nonadiabatic cis–trans photoisomerization dynamics. J. Chem. Phys. 119, 4204 (2003)

    ADS  Google Scholar 

  18. B. Balzer, S. Hahn, G. Stock, Mechanism of a photochemical funnel: a dissipative wave-packet dynamics study. Chem. Phys. Lett. 379, 351–358 (2003)

    ADS  Google Scholar 

  19. M. Barbatti, Nonadiabatic dynamics with trajectory surface hopping method. WIREs Comput. Mol. Sci. 1, 620–633 (2011)

    Google Scholar 

  20. D.M. Benoit, D. Lauvergnat, Y. Scribano, Does cage quantum delocalisation influence the translation-rotational bound states of molecular hydrogen in clathrate hydrate? Faraday Discuss. 212, 533–546 (2018). https://doi.org/10.1039/C8FD00087E

    Article  ADS  Google Scholar 

  21. M. Bonfanti, G.A. Worth, I. Burghardt, Multi-configuration time-dependent hartree methods: from quantum to semiclassical and quantum-classical, in Quantum Chemistry and Dynamics of Excited States: Methods and Applications. ed. by L. González, R. Lindh (John Wiley & Sons, Chichester, 2021)

    Google Scholar 

  22. A. Chen, D.M. Benoit, Y. Scribano et al., Smolyak algorithm adapted to a system-bath separation: application to an encapsulated molecule with large-amplitude motions. J. Chem. Theory Comput. 18, 4366–4372 (2022)

    Google Scholar 

  23. R. Crespo-Otero, M. Barbatti, Recent advances and perspectives on nonadiabatic mixed quantum-classical dynamics. Chem. Rev. 118, 7026–7068 (2018)

    Google Scholar 

  24. B.F.E. Curchod, Full and ab initio multiple spawning, in Quantum Chemistry and Dynamics of Excited States: Methods and Applications. ed. by L. González, R. Lindh (John Wiley & Sons, Chichester, 2021)

    Google Scholar 

  25. B.F.E. Curchod, F. Agostini, On the dynamics through a conical intersection. J. Phys. Chem. Lett. 8, 831–837 (2017)

    Google Scholar 

  26. B.F.E. Curchod, T.J. Martínez, Ab initio nonadiabatic quantum molecular dynamics. Chem. Rev. 118, 3305–3336 (2018)

    Google Scholar 

  27. R. Dawes, T. Carrington, How to choose one-dimensional basis functions so that a very efficient multidimensional basis may be extracted from a direct product of the one-dimensional functions: energy levels of coupled systems with as many as 16 coordinates. J. Chem. Phys. 122(13), 134101 (2005). https://doi.org/10.1063/1.1863935

    Article  ADS  Google Scholar 

  28. D. Dey, N.E. Henriksen, On weak-field (one-photon) coherent control of photoisomerization. J. Phys. Chem. Lett. 11, 8470–8476 (2020)

    Google Scholar 

  29. L. Dupuy, D. Lauvergnat, Y. Scribano, Smolyak representations with absorbing boundary conditions for reaction path Hamiltonian model of reactive scattering. Chem. Phys. Lett. 787(2021), 139241 (2022). https://doi.org/10.1016/j.cplett.2021.139241

    Article  Google Scholar 

  30. L. Dupuy, F. Talotta, F. Agostini et al., Adiabatic and nonadiabatic dynamics with interacting quantum trajectories. J. Chem. Theory Comput. 18, 6447–6462 (2022)

    Google Scholar 

  31. M.H. Farag, T.L.C. Jansen, J. Knoester, Probing the interstate coupling near a conical intersection by optical spectroscopy. J. Phys. Chem. Lett. 7, 3328–3334 (2016)

    Google Scholar 

  32. V.M. Freixas, A.J. White, T. Nelson et al., Nonadiabatic excited-state molecular dynamics methodologies: comparison and convergence. J. Phys. Chem. Lett. 12, 2970–2982 (2021)

    Google Scholar 

  33. L. González, R. Lindh, Quantum Chemistry and Dynamics of Excited States: Methods and Applications (John Wiley & Sons, Chichester, 2020)

    MATH  Google Scholar 

  34. G. Granucci, M. Persico, Critical appraisal of the fewest switches algorithm for surface hopping. J. Chem. Phys. 126(134), 114 (2007)

    Google Scholar 

  35. Y. Guo, F.E. Wolff, I. Schapiro et al., Different hydrogen bonding environments of the retinal protonated Schiff base control the photoisomerization in channelrhodopsin-2. Phys. Chem. Chem. Phys. 20, 27501–27509 (2018)

    Google Scholar 

  36. S. Hahn, G. Stock, Femtosecond secondary emission arising from the nonadiabatic photoisomerization in rhodopsin. Chem. Phys. 259, 297–312 (2000)

    Google Scholar 

  37. S. Hahn, G. Stock, Quantum-mechanical modeling of the femtosecond isomerization in rhodopsin. J. Phys. Chem. B 104(6), 1146–1149 (2000)

    Google Scholar 

  38. S. Hahn, G. Stock, Ultrafast cis-trans photoswitching: a model study. J. Chem. Phys. 116, 1085 (2002)

    ADS  Google Scholar 

  39. A. Kirrander, M. Vacher, Ehrenfest methods for electron and nuclear dynamics, in Quantum Chemistry and Dynamics of Excited States: Methods and Applications. ed. by L. González, R. Lindh (John Wiley & Sons, Chichester, 2021)

    Google Scholar 

  40. D. Lauvergnat, ElVibRot-TnumTana Quantum Dynamics Code. https://github.com/lauvergn/ElVibRot-TnumTan. Accessed July 2022

  41. D. Lauvergnat, QuantumModelLib. https://github.com/lauvergn/QuantumModelLib/tree/OOP_branch. Accessed July 2022

  42. D. Lauvergnat, A. Nauts, Torsional energy levels of nitric acid in reduced and full dimensionality with ElVibRot and Tnum. Phys. Chem. Chem. Phys. 12, 8405 (2010)

    Google Scholar 

  43. D. Lauvergnat, A. Nauts, Quantum dynamics with sparse grids: a combination of Smolyak scheme and cubature. Application to methanol in full dimensionality. Spectrochim. Acta A Mol. Biomol. Spectrosc. 119, 18–25 (2014)

    Google Scholar 

  44. D. Lauvergnat, P. Felker, Y. Scribano et al., H\(_{2}\), HD, and D\(_{2}\) in the small cage of structure II clathrate hydrate: Vibrational frequency shifts from fully coupled quantum six-dimensional calculations of the vibration-translation-rotation eigenstates. J. Chem. Phys. 150(15), 154303 (2019). https://doi.org/10.1063/1.5090573

    Article  ADS  Google Scholar 

  45. C. Leforestier, R.H. Bisseling, C. Cerjan et al., A comparison of different propagation schemes for the time dependent Schrödinger equation. J. Comput. Phys. 94(1), 59–80 (1991). https://doi.org/10.1016/0021-9991(91)90137-A

    Article  ADS  MathSciNet  MATH  Google Scholar 

  46. Y. Liu, J. Li, P.M. Felker et al., HCl-H 2 O dimer: an accurate full-dimensional potential energy surface and fully coupled quantum calculations of intra- and intermolecular vibrational states and frequency shifts. Phys. Chem. Chem. Phys. 23(12), 7101–7114 (2021). https://doi.org/10.1039/D1CP00865J

    Article  Google Scholar 

  47. S. Mai, P. Marquetand, L. González, Nonadiabatic dynamics: the SHARC approach. WIREs Comput. Mol. Sci. 8, e1370 (2018)

    Google Scholar 

  48. D.V. Makhov, W.J. Glover, T.J. Martinez et al., Ab initio multiple cloning algorithm for quantum nonadiabatic molecular dynamics. J. Chem. Phys. 141(054), 110 (2014)

    Google Scholar 

  49. U. Manthe, A multilayer multiconfigurational time-dependent Hartree approach for quantum dynamics on general potential energy surfaces. J. Chem. Phys. 128(164), 116 (2008)

    Google Scholar 

  50. E. Marsili, M.H. Farag, X. Yang et al., Two-state, three-mode parametrization of the force field of a retinal chromophore model. J. Phys. Chem. A 123, 1710–1719 (2019)

    Google Scholar 

  51. E. Marsili, M. Olivucci, D. Lauvergnat et al., Quantum and quantum-classical studies of the photoisomerization of a retinal chromophore model. J. Chem. Theory Comput. 16, 6032–6048 (2020)

    Google Scholar 

  52. H.D. Meyer, Studying molecular quantum dynamics with the multiconfiguration time-dependent hartree method. WIREs Comput. Mol. Sci. 2, 351–374 (2012)

    Google Scholar 

  53. H.D. Meyer, F. Gatti, G. Worth, Multidimensional Quantum Dynamics: MCTDH Theory and Applications (Wiley-VCH, Weinheim, 2009)

    Google Scholar 

  54. S.K. Min, F. Agostini, E.K.U. Gross, Coupled-trajectory quantum-classical approach to electronic decoherence in nonadiabatic processes. Phys. Rev. Lett. 115(7), 073001 (2015)

    ADS  Google Scholar 

  55. S.K. Min, F. Agostini, I. Tavernelli et al., Ab initio nonadiabatic dynamics with coupled trajectories: a rigorous approach to quantum (de)coherence. J. Phys. Chem. Lett. 8, 3048–3055 (2017)

    Google Scholar 

  56. A. Nauts, D. Lauvergnat, Numerical on-the-fly implementation of the action of the kinetic energy operator on a vibrational wave function: application to methanol. Mol. Phys. 116(23–24), 3701–3709 (2018). https://doi.org/10.1080/00268976.2018.1473652

    Article  ADS  Google Scholar 

  57. M. Ndong, L. Bomble, D. Sugny et al., NOT gate in a cis-trans photoisomerization model. Phys. Rev. A 76(043), 424 (2007)

    Google Scholar 

  58. T.J. Park, J.C. Light, Unitary quantum time evolution by iterative Lanczos reduction. J. Chem. Phys. 85(10), 5870–5876 (1986). https://doi.org/10.1063/1.451548

    Article  ADS  Google Scholar 

  59. C. Pieroni, F. Agostini, Nonadiabatic dynamics with coupled trajectories. J. Chem. Theory Comput. 17, 5969 (2021)

    Google Scholar 

  60. A. Powers, Y. Scribano, D. Lauvergnat et al., The effect of the condensed-phase environment on the vibrational frequency shift of a hydrogen molecule inside clathrate hydrates. J. Chem. Phys. 148(14), 144304 (2018). https://doi.org/10.1063/1.5024884

    Article  ADS  Google Scholar 

  61. G.W. Richings, I. Polyak, K.E. Spinlove et al., Quantum dynamics simulations using Gaussian wavepackets: the vMCG method. Int. Rev. Phys. Chem. 34, 269–308 (2015)

    Google Scholar 

  62. M. Sala, D. Egorova, Quantum dynamics of multi-dimensional rhodopsin photoisomerization models: approximate versus accurate treatment of the secondary modes. Chem. Phys. 515, 164–176 (2018)

    Google Scholar 

  63. J. Sarka, D. Lauvergnat, V. Brites et al., Rovibrational energy levels of the F-(H\(_2\)O) and F-(D\(_2\)O) complexes. Phys. Chem. Chem. Phys. (Incorp. Faraday Trans.) 18(26), 17678–17690 (2016). https://doi.org/10.1039/C6CP02874H

    Article  ADS  Google Scholar 

  64. L. Seidner, W. Domcke, Microscopic modelling of the photoisomerization and internal-conversion dynamics. Chem. Phys. 186, 27–40 (1994)

    Google Scholar 

  65. A. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions. Dokl. Akad. Nauk SSSR 148(5), 1042–1045 (1963)

    MathSciNet  MATH  Google Scholar 

  66. H. Tal-Ezer, R. Kosloff, An accurate and efficient scheme for propagating the time dependent Schrödinger equation. J. Chem. Phys. 81, 3967–3971 (1984)

    ADS  Google Scholar 

  67. F. Talotta, D. Lauvergnat, F. Agostini, Describing the photo-isomerization of a retinal chromophore model with coupled and quantum trajectories. J. Chem. Phys. 156(184), 104 (2022)

    Google Scholar 

  68. T.V. Tscherbul, P. Brumer, Quantum coherence effects in natural light-induced processes: cis-trans photoisomerization of model retinal under incoherent excitation. Phys. Chem. Chem. Phys. 17, 30904–30913 (2015)

    Google Scholar 

  69. J.C. Tully, Molecular dynamics with electronic transitions. J. Chem. Phys. 93, 1061 (1990)

    ADS  Google Scholar 

  70. I. Uspenskiy, B. Strodel, G. Stock, Classical description of the dynamics and time-resolved spectroscopy of nonadiabatic cis-trans photoisomerization. Chem. Phys. 329, 109–117 (2006)

    Google Scholar 

  71. M. Vacher, M.J. Bearpark, M.A. Robb, Direct methods for non-adiabatic dynamics: connecting the single-set variational multi-configuration Gaussian (vMCG) and Ehrenfest perspectives. Theor. Chem. Acc. 135, 187 (2016)

    Google Scholar 

  72. O. Vendrell, H.D. Meyer, Multilayer multiconfiguration time-dependent Hartree method: implementation and applications to a Henon-Heiles Hamiltonian and to pyrazine. J. Chem. Phys. 134(044), 135 (2011)

    Google Scholar 

  73. P.E. Videla, A. Markmann, V.S. Batista, Floquet study of quantum control of the cis-trans photoisomerization of rhodopsin. J. Chem. Theory Comput. 14, 1198–1205 (2018)

    Google Scholar 

  74. H. Wang, Multilayer multiconfiguration time-dependent Hartree theory. J. Phys. Chem. A 119, 7951–7965 (2015)

    Google Scholar 

  75. H. Wang, M. Thoss, Multilayer formulation of the multiconfiguration time-dependent Hartree theory. J. Chem. Phys. 119, 1289 (2003)

    ADS  Google Scholar 

  76. X.G. Wang, T. Carrington, Vibrational energy levels of CH5(+). J. Chem. Phys. 129(23), 234102 (2008). https://doi.org/10.1063/1.3027825

    Article  ADS  Google Scholar 

  77. G.A. Worth, B. Lasorne, Gaussian wave packets and the dd-vmcg approach, in Quantum Chemistry and Dynamics of Excited States: Methods and Applications. ed. by L. González, R. Lindh (John Wiley and Sons, Chichester, 2021)

    Google Scholar 

Download references

Acknowledgements

This work was supported by the ANR Q-DeLight project, Grant No. ANR-20-CE29-0014 of the French Agence Nationale de la Recherche.

Author information

Author notes

  1. Ari Pereira and Joachim Knapik contributed equally to this work.

Authors and Affiliations

  1. Université Paris-Saclay, CNRS, Institut de Chimie Physique, UMR-CNRS 8000, 91405, Orsay, France

    Ari Pereira, Joachim Knapik, David Lauvergnat & Federica Agostini

  2. Department of Chemistry, Birla Institute of Technology and Science Pilani, K K Birla Goa Campus, Goa, 403726, India

    Ari Pereira

  3. Center for Transformative Science, ShanghaiTech University, 201210, Shanghai, China

    Ahai Chen

Authors
  1. Ari Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joachim Knapik
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ahai Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. David Lauvergnat
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Federica Agostini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to David Lauvergnat or Federica Agostini.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pereira, A., Knapik, J., Chen, A. et al. Quantum molecular dynamics simulations of the effect of secondary modes on the photoisomerization of a retinal chromophore model. Eur. Phys. J. Spec. Top. 232, 1917–1933 (2023). https://doi.org/10.1140/epjs/s11734-023-00923-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-023-00923-4

Search

Navigation