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  • Open Access

Role of Anisotropic Electronic Friction in Laser-Driven Hydrogen Recombination on Copper

Alexander Spears1,2, Wojciech G. Stark1,3, and Reinhard J. Maurer1,2,4,*

  • *Contact author: reinhard.maurer@univie.ac.at
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Phys. Rev. Lett. 137, 178001 – Published 22 October, 2026

DOI: https://doi.org/10.1103/sply-f2km

Abstract

Ultrafast light-driven chemical dynamics at surfaces are governed by energy transfer from excited electrons to vibrational degrees of freedom. When this nonadiabatic energy transfer is anisotropic, it can lead to dynamical steering effects that affect reaction probabilities or nonthermal final energy distributions in molecules. Here, enabled by a machine-learning-based simulation framework, we compare isotropic and anisotropic models of electronic friction during laser-driven hydrogen evolution on the (111) facet of copper. While anisotropic electronic friction determines the rate of energy transfer into the adsorbate and the fluence dependence of desorption probabilities, final translational, vibrational, and rotational energy distributions are mainly governed by the potential energy landscape at the barrier and insensitive to nonadiabatic effects.

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References (59)

  1. I. Langmuir, A chemically active modification of hydrogen, J. Am. Chem. Soc. 34, 1310 (1912).
  2. S. W. Lee, Hot electron-driven chemical reactions: A review, Appl. Surf. Sci. Adv. 16, 100428 (2023).
  3. H. Petek, A. Li, X. Li, S. Tan, and M. Reutzel, Plasmonic decay into hot electrons in silver, Prog. Surf. Sci. 98, 100707 (2023).
  4. I. Campillo, V. M. Silkin, J. M. Pitarke, E. V. Chulkov, A. Rubio, and P. M. Echenique, First-principles calculations of hot-electron lifetimes in metals, Phys. Rev. B 61, 13484 (2000).
  5. C. Frischkorn and M. Wolf, Femtochemistry at metal surfaces: Nonadiabatic reaction dynamics, Chem. Rev. 106, 4207 (2006).
  6. B. Rethfeld, K. Sokolowski-Tinten, D. von der Linde, and S. Anisimov, Timescales in the response of materials to femtosecond laser excitation, Appl. Phys. A 79, 767 (2004).
  7. C. Frischkorn, Ultrafast reaction dynamics of the associative hydrogen desorption from Ru(001), J. Phys. Condens. Matter 20, 313002 (2008).
  8. K.-I. Inoue, K. Watanabe, T. Sugimoto, Y. Matsumoto, and T. Yasuike, Disentangling multidimensional nonequilibrium dynamics of adsorbates: CO desorption from Cu(100), Phys. Rev. Lett. 117, 186101 (2016).
  9. N. Hertl, C. L. Box, and R. J. Maurer, Mode selectivity in electron-promoted vibrational relaxation of chemisorbed hydrogen on molybdenum and tungsten surfaces, Faraday Discuss 265, 250 (2026).
  10. M. Morin, N. J. Levinos, and A. L. Harris, Vibrational energy transfer of CO/Cu(100): Nonadiabatic vibration/electron coupling, J. Chem. Phys. 96, 3950 (1992).
  11. J. Gadzuk and A. Luntz, On vibrational lineshapes of adsorbed molecules, Surf. Sci. 144, 429 (1984).
  12. C. L. Box, N. Hertl, W. G. Stark, and R. J. Maurer, Room temperature hydrogen atom scattering experiments are not a sufficient benchmark to validate electronic friction theory, J. Phys. Chem. Lett. 15, 12520 (2024).
  13. R. J. Maurer, B. Jiang, H. Guo, and J. C. Tully, Mode specific electronic friction in dissociative chemisorption on metal surfaces: H2 on Ag(111), Phys. Rev. Lett. 118, 256001 (2017).
  14. W. G. Stark, C. L. Box, M. Sachs, N. Hertl, and R. J. Maurer, Nonadiabatic reactive scattering of hydrogen on different surface facets of copper, Phys. Rev. B 112, 035422 (2025).
  15. S. Lindner, I. Lončarić, L. Vrček, M. Alducin, J. I. Juaristi, and P. Saalfrank, Femtosecond laser-induced desorption of hydrogen molecules from Ru(0001): A systematic study based on machine-learned potentials, J. Phys. Chem. C 127, 14756 (2023).
  16. B. Mladineo, J. I. Juaristi, M. Alducin, P. Saalfrank, and I. Lončarić, Photoinduced dynamics of CO on Ru (0001): Understanding experiments by simulations with all degrees of freedom, J. Chem. Phys. 163, 044103 (2025).
  17. F. J. Gonzalez, A. S. Muzas, J. I. Juaristi, M. Alducin, and H. F. Busnengo, Femtosecond laser-induced diffusion and desorption of CO adsorbed on a weak electron-phonon coupling surface: Cu(110), J. Chem. Phys. 162, 174701 (2025).
  18. L. González and R. Lindh, Quantum Chemistry and Dynamics of Excited States: Methods and Applications, edited by L. González and R. Lindh (John Wiley & Sons, Hoboken, NJ, 2021), p. 52, 10.1002/9781119417774.
  19. C. Schäfer and G. Johansson, Shortcut to self-consistent light-matter interaction and realistic spectra from first principles, Phys. Rev. Lett. 128, 156402 (2022).
  20. L. Shi, M. Schröder, H.-D. Meyer, D. Peláez, A. M. Wodtke, K. Golibrzuch, A.-M. Schönemann, A. Kandratsenka, and F. Gatti, Full quantum dynamics study for H atom scattering from graphene, J. Phys. Chem. A 129, 1896 (2025).
  21. M. Head-Gordon and J. C. Tully, Molecular dynamics with electronic frictions, J. Chem. Phys. 103, 10137 (1995).
  22. G. Füchsel, T. Klamroth, S. Monturet, and P. Saalfrank, Dissipative dynamics within the electronic friction approach: The femtosecond laser desorption of H2/D2 from Ru(0001), Phys. Chem. Chem. Phys. 13, 8659 (2011).
  23. A. C. Luntz, M. Persson, S. Wagner, C. Frischkorn, and M. Wolf, Femtosecond laser induced associative desorption of H2 from Ru(0001): Comparison of “first principles” theory with experiment, J. Chem. Phys. 124, 244702 (2006).
  24. M. Alducin, N. Camillone, S.-Y. Hong, and J. I. Juaristi, Electrons and phonons cooperate in the laser-induced desorption of CO from Pd(111), Phys. Rev. Lett. 123, 246802 (2019).
  25. S. I. Anisimov, Emission of electrons from the surface of metals induced by ultrashort laser pulses, Zh. Eksp. Teor. Fiz. 66, 776 (1974) [Sov. Phys.-JETP 39 (1974)].
  26. A. C. Luntz and M. Persson, How adiabatic is activated adsorption/associative desorption?, J. Chem. Phys. 123, 074704 (2005).
  27. R. Scholz, G. Floß, P. Saalfrank, G. Füchsel, I. Lončarić, and J. I. Juaristi, Femtosecond-laser induced dynamics of CO on Ru(0001): Deep insights from a hot-electron friction model including surface motion, Phys. Rev. B 94, 165447 (2016).
  28. X. Wang, J. Wang, P. Spiering, L. Liu, J. Meyer, J. L. LaRue, and H. Xin, Unveiling the interplay of electronic and phononic excitations in laser-induced oxygen activation on Ru(0001), J. Chem. Phys. 163, 114109 (2025).
  29. J. I. Juaristi, M. Alducin, R.Diezmuiño, H. F. Busnengo, and A. Salin, Role of electron-hole pair excitations in the dissociative adsorption of diatomic molecules on metal surfaces, Phys. Rev. Lett. 100, 116102 (2008).
  30. B. Hellsing and M. Persson, Electronic damping of atomic and molecular vibrations at metal surfaces, Phys. Scr. 29, 360 (1984).
  31. M. Persson and B. Hellsing, Electronic damping of adsorbate vibrations on metal surfaces, Phys. Rev. Lett. 49, 662 (1982).
  32. R. J. Maurer, M. Askerka, V. S. Batista, and J. C. Tully, Ab initio tensorial electronic friction for molecules on metal surfaces: Nonadiabatic vibrational relaxation, Phys. Rev. B 94, 115432 (2016).
  33. C. L. Box, W. G. Stark, and R. J. Maurer, Ab initio calculation of electron-phonon linewidths and molecular dynamics with electronic friction at metal surfaces with numeric atom-centred orbitals, Electron. Struct. 5, 035005 (2023).
  34. K. Shakouri, J. Behler, J. Meyer, and G.-J. Kroes, Accurate neural network description of surface phonons in reactive gas-surface dynamics: N2+Ru(0001), J. Phys. Chem. Lett. 8, 2131 (2017).
  35. A. C. Luntz, I. Makkonen, M. Persson, S. Holloway, D. M. Bird, and M. S. Mizielinski, Comment on “Role of electron-hole pair excitations in the dissociative adsorption of diatomic molecules on metal surfaces”, Phys. Rev. Lett. 102, 109601 (2009).
  36. W. G. Stark, C. van der Oord, I. Batatia, Y. Zhang, B. Jiang, G. Csányi, and R. J. Maurer, Benchmarking of machine learning interatomic potentials for reactive hydrogen dynamics at metal surfaces, Mach. Learn. Sci. Technol. 5, 030501 (2024).
  37. W. G. Stark, J. Westermayr, O. A. Douglas-Gallardo, J. Gardner, S. Habershon, and R. J. Maurer, Machine learning interatomic potentials for reactive hydrogen dynamics at metal surfaces based on iterative refinement of reaction probabilities, J. Phys. Chem. C 127, 24168 (2023).
  38. F. Nattino, C. Díaz, B. Jackson, and G.-J. Kroes, Effect of surface motion on the rotational quadrupole alignment parameter of D2 reacting on Cu(111), Phys. Rev. Lett. 108, 236104 (2012).
  39. See Supplemental Material at http://link.aps.org/supplemental/10.1103/sply-f2km for validation of the ML models used in this Letter, as well as example analysis for further trajectories. This includes Refs. [40–53].
  40. V. Blum, R. Gehrke, F. Hanke, P. Havu, V. Havu, X. Ren, K. Reuter, and M. Scheffler, Ab initio molecular simulations with numeric atom-centered orbitals, Comput. Phys. Commun. 180, 2175 (2009).
  41. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  42. B. Hammer, L. B. Hansen, and J. K. Nørskov, Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals, Phys. Rev. B 59, 7413 (1999).
  43. M. Sachs, W. G. Stark, R. J. Maurer, and C. Ortner, Machine learning configuration-dependent friction tensors in Langevin heatbaths, Mach. Learn. Sci. Technol. 6, 015016 (2025).
  44. MACE: Higher order equivariant message passing neural networks for fast and accurate force fields, in 36th Conference on Neural Information Processing Systems, edited by A. H. Oh, A. Agarwal, D. Belgrave, and K. Cho (Curran Associates, Inc., New York, NY, 2022), Vol. 2022, https://openreview.net/forum?id=YPpSngE-ZU.
  45. K. T. Schütt, M. Gastegger, A. Tkatchenko, K.-R. Müller, and R. J. Maurer, Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions, Nat. Commun. 10, 5024 (2019).
  46. K. T. Schütt, H. E. Sauceda, P.-J. Kindermans, A. Tkatchenko, and K.-R. Müller, SchNet—A deep learning architecture for molecules and materials, J. Chem. Phys. 148, 241722 (2018).
  47. W. C. Witt, C. v. d. Oord, E. Gelžinytė, T. Järvinen, A. Ross, J. P. Darby, C. H. Ho, W. J. Baldwin, M. Sachs, J. Kermode, N. Bernstein, G. Csányi, and C. Ortner, acepotentials.jl: A julia implementation of the atomic cluster expansion, J. Chem. Phys. 159, 164101 (2023).
  48. R. Scholz, S. Lindner, I. Lončarić, J. C. Tremblay, J. I. Juaristi, M. Alducin, and P. Saalfrank, Vibrational response and motion of carbon monoxide on Cu(100) driven by femtosecond laser pulses: Molecular dynamics with electronic friction, Phys. Rev. B 100, 245431 (2019).
  49. J. Gardner, O. A. Douglas-Gallardo, W. G. Stark, J. Westermayr, S. M. Janke, S. Habershon, and R. J. Maurer, nqcdynamics.jl: A julia package for nonadiabatic quantum classical molecular dynamics in the condensed phase, J. Chem. Phys. 156, 174801 (2022).
  50. A. H. Larsen et al., The atomic simulation environment–A python library for working with atoms, J. Phys. Condens. Matter 29, 273002 (2017).
  51. N. Gerrits, J. I. Juaristi, and J. Meyer, Electronic friction coefficients from the atom-in-jellium model for Z=1−92, Phys. Rev. B 102, 155130 (2020).
  52. A. J. Larkoski, D. G. Ellis, and L. J. Curtis, Numerical implementation of Einstein-Brillouin-Keller quantization for arbitrary potentials, Am. J. Phys. 74, 572 (2006).
  53. S. Wagner, C. Frischkorn, M. Wolf, M. Rutkowski, H. Zacharias, and A. C. Luntz, Energy partitioning in the femtosecond-laser-induced associative D2 desorption from Ru(0001), Phys. Rev. B 72, 205404 (2005).
  54. J. A. Misewich, T. Heinz, and D. M. Newns, Desorption induced by multiple electronic transitions, Phys. Rev. Lett. 68, 3737 (1992).
  55. G. Füchsel, J. C. Tremblay, T. Klamroth, and P. Saalfrank, Quantum dynamical simulations of the femtosecond-laser-induced ultrafast desorption of H2 and D2 from Ru(0001), ChemPhysChem 14, 1471 (2013).
  56. P. Spiering and J. Meyer, Testing electronic friction models: Vibrational de-excitation in scattering of H2 and D2 from Cu(111), J. Phys. Chem. Lett. 9, 1803 (2018).
  57. S. P. Rittmeyer, D. J. Ward, P. Gütlein, J. Ellis, W. Allison, and K. Reuter, Energy dissipation during diffusion at metal surfaces: Disentangling the role of phonons versus electron-hole pairs, Phys. Rev. Lett. 117, 196001 (2016).
  58. E. M. McIntosh, K. T. Wikfeldt, J. Ellis, A. Michaelides, and W. Allison, Quantum effects in the diffusion of hydrogen on Ru(0001), J. Phys. Chem. Lett. 4, 1565 (2013).
  59. A. Spears, W. Stark, and R. Maurer, Simulation results and analysis data for “Role of anisotropic electronic friction in laser-driven hydrogen recombination on copper”, Zenodo, 10.5281/zenodo.23079231 (2026).

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Phys. Rev. Lett. 137, 178001– Published 22 October, 2026
  • Received 31 March 2026
  • Accepted 29 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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