- Open Access
Nonadiabatic reactive scattering of hydrogen on different surface facets of copper
Phys. Rev. B 112, 035422 – Published 21 July, 2025
DOI: https://doi.org/10.1103/h7vd-94pk
Abstract
Dissociative chemisorption is a key process in hydrogen-metal surface chemistry, where nonadiabatic effects caused by low-lying electron-hole-pair excitations may affect reaction outcomes. Molecular dynamics with electronic friction simulations can capture weak nonadiabatic effects at metal surfaces, but require energy landscapes and electronic friction tensors as input. Here, we present full-dimensional machine learning surrogate models of the electronic friction tensor to study reactive hydrogen chemistry at the low-index surface facets Cu(100), Cu(110), Cu(111), and Cu(211). We combine these surrogate models with machine learning interatomic potentials to simulate quantum-state-resolved reactive scattering on pristine copper surfaces. The predicted sticking coefficient and survival probabilities are in excellent agreement with experiments. Comparison between adiabatic and nonadiabatic simulations reveals that the influence of electron-hole pair excitations on the scattering dynamics is weak, and that the probability for dissociative adsorption is dominated by the shape of the underlying potential energy surface and the initial vibrational quantum state. Nonadiabatic effects only lead to subtle changes in rovibrationally inelastic state-to-state scattering probabilities. The differences between jellium-based isotropic local density friction and full ab initio response-theory-based orbital-dependent friction are even more subtle. The presented machine learning models represent the most accurate publicly available, full-dimensional models for on copper to date.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (97)
- M. P. Andersson, F. Abild-Pedersen, I. N. Remediakis, T. Bligaard, G. Jones, J. Engbæk, O. Lytken, S. Horch, J. H. Nielsen, J. Sehested et al., Structure sensitivity of the methanation reaction: -induced CO dissociation on nickel surfaces, J. Catal. 255, 6 (2008).
- D. Hollenbach and E. E. Salpeter, Surface recombination of hydrogen molecules, Astrophys. J. 163, 155 (1971).
- M. Wilde, K. Fukutani, W. Ludwig, B. Brandt, J.-H. Fischer, S. Schauermann, and H.-J. Freund, Influence of carbon deposition on the hydrogen distribution in Pd nanoparticles and their reactivity in olefin hydrogenation, Angew. Chem. Int. Ed. 47, 9289 (2008).
- S. M. Lee, K. S. Park, Y. C. Choi, Y. S. Park, J. M. Bok, D. J. Bae, K. S. Nahm, Y. G. Choi, S. C. Yu, N.-G. Kim et al., Hydrogen adsorption and storage in carbon nanotubes, Synth. Met. 113, 209 (2000).
- R. Kirchheim, Hydrogen solubility and diffusivity in defective and amorphous metals, Prog. Mater. Sci. 32, 261 (1988).
- G. S. Higashi, Y. J. Chabal, G. W. Trucks, and K. Raghavachari, Ideal hydrogen termination of the Si(111) surface, Appl. Phys. Lett. 56, 656 (1990).
- D. Haberer, D. V. Vyalikh, S. Taioli, B. Dora, M. Farjam, J. Fink, D. Marchenko, T. Pichler, K. Ziegler, S. Simonucci et al., Tunable band gap in hydrogenated quasi-free-standing graphene, Nano Lett. 10, 3360 (2010).
- N. Liu, L. Wu, Z. Qin, and D. W. Shoesmith, Roles of radiolytic and externally generated in the corrosion of fractured spent nuclear fuel, Environ. Sci. Technol. 50, 12348 (2016).
- G. Ertl, Reactions at surfaces: From atoms to complexity (Nobel lecture), Angew. Chem. Int. Ed. 47, 3524 (2008).
- D. J. Auerbach, J. C. Tully, and A. M. Wodtke, Chemical dynamics from the gas-phase to surfaces, Nat. Sci. 1, e10005 (2021).
- D. Farías and R. Miranda, Diffraction of molecular hydrogen from metal surfaces, Prog. Surf. Sci. 86, 222 (2011).
- L. Zhang, F. Nitz, D. Borodin, A. M. Wodtke, and H. Guo, Ring polymer molecular dynamics rates for hydrogen recombinative desorption on Pt(111), Precis. Chem. 3, 319 (2025).
- R. J. Maurer, B. Jiang, H. Guo, and J. C. Tully, Mode specific electronic friction in dissociative chemisorption on metal surfaces: on Ag(111), Phys. Rev. Lett. 118, 256001 (2017).
- R. J. Maurer, Y. Zhang, H. Guo, and B. Jiang, Hot electron effects during reactive scattering of from Ag(111): assessing the sensitivity to initial conditions, coupling magnitude, and electronic temperature, Faraday Discuss. 214, 105 (2019).
- P. Spiering and J. Meyer, Testing electronic friction models: vibrational de-excitation in scattering of and from Cu(111), J. Phys. Chem. Lett. 9, 1803 (2018).
- G.-J. Kroes, Computational approaches to dissociative chemisorption on metals: towards chemical accuracy, Phys. Chem. Chem. Phys. 23, 8962 (2021).
- H. A. Michelsen, C. T. Rettner, and D. J. Auerbach, State-specific dynamics of desorption from Cu(111): The role of molecular rotational motion in activated adsorption-desorption dynamics, Phys. Rev. Lett. 69, 2678 (1992).
- C. T. Rettner, Dynamics of the direct reaction of hydrogen atoms adsorbed on Cu(111) with hydrogen atoms incident from the gas phase, Phys. Rev. Lett. 69, 383 (1992).
- C. T. Rettner, H. A. Michelsen, and D. J. Auerbach, Determination of quantum state-specific gas-surface energy transfer and adsorption probabilities as a function of kinetic energy, Chem. Phys. 175, 157 (1993).
- E. Watts and G. O. Sitz, State-to-state scattering in a reactive system: from Cu(100), J. Chem. Phys. 114, 4171 (2001).
- L. C. Shackman and G. O. Sitz, State-to-state scattering of from Cu(100) and Pd(111), J. Chem. Phys. 123, 064712 (2005).
- A. Hodgson, J. Moryl, and H. Zhao, Scattering of vibrationally excited from Cu(111), Chem. Phys. Lett. 182, 152 (1991).
- M. J. Murphy and A. Hodgson, Adsorption and desorption dynamics of and on Cu(111): The role of surface temperature and evidence for corrugation of the dissociation barrier, J. Chem. Phys. 108, 4199 (1998).
- K. Cao, G. Füchsel, A. W. Kleyn, and L. B. F. Juurlink, Hydrogen adsorption and desorption from Cu(111) and Cu(211), Phys. Chem. Chem. Phys. 20, 22477 (2018).
- G. Anger, A. Winkler, and K. D. Rendulic, Adsorption and desorption kinetics in the systems , and , Surf. Sci. 220, 1 (1989).
- P. Rasmussen, P. Holmblad, H. Christoffersen, P. Taylor, and I. Chorkendorff, Dissociative adsorption of hydrogen on Cu(100) at low temperatures, Surf. Sci. 287–288, 79 (1993).
- J. Campbell and C. T. Campbell, The dissociative adsorption of and on Cu(110): activation barriers and dynamics, Surf. Sci. 259, 1 (1991).
- F. Nitz, L. Zhang, N. Hertl, I. Rahinov, O. Galparsoro, A. Kandratsenka, T. N. Kitsopoulos, D. J. Auerbach, H. Guo, A. M. Wodtke, and D. Borodin, Thermal rates and high-temperature tunneling from surface reaction dynamics and first-principles, J. Am. Chem. Soc. 146, 31538 (2024).
- H. A. Michelsen and D. J. Auerbach, A critical examination of data on the dissociative adsorption and associative desorption of hydrogen at copper surfaces, J. Chem. Phys. 94, 7502 (1991).
- H. Michelsen, C. Rettner, and D. Auerbach, On the influence of surface temperature on adsorption and desorption in the /Cu(111) system, Surf. Sci. 272, 65 (1992).
- H. A. Michelsen, C. T. Rettner, D. J. Auerbach, and R. N. Zare, Effect of rotation on the translational and vibrational energy dependence of the dissociative adsorption of on Cu(111), J. Chem. Phys. 98, 8294 (1993).
- C. T. Rettner, H. A. Michelsen, and D. J. Auerbach, Quantum-state-specific dynamics of the dissociative adsorption and associative desorption of at a Cu(111) surface, J. Chem. Phys. 102, 4625 (1995).
- S. Kaufmann, Q. Shuai, D. J. Auerbach, D. Schwarzer, and A. M. Wodtke, Associative desorption of hydrogen isotopologues from copper surfaces: Characterization of two reaction mechanisms, J. Chem. Phys. 148, 194703 (2018).
- M. J. Murphy, J. F. Skelly, A. Hodgson, and B. Hammer, Inverted vibrational distributions from recombination at Ru(001): Evidence for a metastable molecular chemisorption well, J. Chem. Phys. 110, 6954 (1999).
- C. Díaz and R. A. Olsen, A note on the vibrational efficacy in molecule-surface reactions, J. Chem. Phys. 130, 094706 (2009).
- J. C. Polanyi, Concepts in reaction dynamics, Acc. Chem. Res. 5, 161 (1972).
- Y. Huang, C. T. Rettner, D. J. Auerbach, and A. M. Wodtke, Vibrational promotion of electron transfer, Science 290, 111 (2000).
- B. C. Krüger, S. Meyer, A. Kandratsenka, A. M. Wodtke, and T. Schäfer, Vibrational inelasticity of highly vibrationally excited NO on Ag(111), J. Phys. Chem. Lett. 7, 441 (2016).
- N. Shenvi, S. Roy, and J. C. Tully, Nonadiabatic dynamics at metal surfaces: Independent-electron surface hopping, J. Chem. Phys. 130, 174107 (2009).
- G. Meng, J. Gardner, N. Hertl, W. Dou, R. J. Maurer, and B. Jiang, First-principles nonadiabatic dynamics of molecules at metal surfaces with vibrationally coupled electron transfer, Phys. Rev. Lett. 133, 036203 (2024).
- M. Head-Gordon and J. C. Tully, Molecular dynamics with electronic frictions, J. Chem. Phys. 103, 10137 (1995).
- Y. Li and G. Wahnström, Nonadiabatic effects in hydrogen diffusion in metals, Phys. Rev. Lett. 68, 3444 (1992).
- J. I. Juaristi, M. Alducin, R. Diez Muiño, 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).
- A. S. Muzas, J. I. Juaristi, M. Alducin, R. D. Muiño, G. J. Kroes, and C. Díaz, Vibrational deexcitation and rotational excitation of and scattered from Cu(111): Adiabatic versus non-adiabatic dynamics, J. Chem. Phys. 137, 064707 (2012).
- 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).
- C. L. Box, Y. Zhang, R. Yin, B. Jiang, and R. J. Maurer, Determining the effect of hot electron dissipation on molecular scattering experiments at metal surfaces, JACS Au 1, 164 (2021).
- B. Hellsing and M. Persson, Electronic damping of atomic and molecular vibrations at metal surfaces, Phys. Scr. 29, 360 (1984).
- M. Askerka, R. J. Maurer, V. S. Batista, and J. C. Tully, Role of tensorial electronic friction in energy transfer at metal surfaces, Phys. Rev. Lett. 116, 217601 (2016).
- 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).
- 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).
- P. Spiering, K. Shakouri, J. Behler, G.-J. Kroes, and J. Meyer, Orbital-dependent electronic friction significantly affects the description of reactive scattering of from Ru(0001), J. Phys. Chem. Lett. 10, 2957 (2019).
- 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).
- J. Behler and M. Parrinello, Generalized neural-network representation of high-dimensional potential-energy surfaces, Phys. Rev. Lett. 98, 146401 (2007).
- J. Behler, Representing potential energy surfaces by high-dimensional neural network potentials, J. Phys.: Condens. Matter 26, 183001 (2014).
- V. L. Deringer, M. A. Caro, and G. Csányi, Machine learning interatomic potentials as emerging tools for materials science, Adv. Mater. 31, 1902765 (2019).
- E. Kocer, T. W. Ko, and J. Behler, Neural network potentials: A concise overview of methods, Annu. Rev. Phys. Chem. 73, 163 (2022).
- L. Zhu, Y. Zhang, L. Zhang, X. Zhou, and B. Jiang, Unified and transferable description of dynamics of dissociative adsorption on multiple copper surfaces via machine learning, Phys. Chem. Chem. Phys. 22, 13958 (2020).
- 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).
- 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).
- Y. Zhang, R. J. Maurer, and B. Jiang, Symmetry-adapted high dimensional neural network representation of electronic friction tensor of adsorbates on metals, J. Phys. Chem. C 124, 186 (2020).
- 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).
- R. Drautz, Atomic cluster expansion for accurate and transferable interatomic potentials, Phys. Rev. B 99, 014104 (2019).
- R. Drautz, Atomic cluster expansion of scalar, vectorial, and tensorial properties including magnetism and charge transfer, Phys. Rev. B 102, 024104 (2020).
- M. Wijzenbroek, D. Helstone, J. Meyer, and G.-J. Kroes, Dynamics of dissociation on the close-packed (111) surface of the noblest metal: , J. Chem. Phys. 145, 144701 (2016).
- M. Calandra and F. Mauri, Electron-phonon coupling and phonon self-energy in : Interpretation of Raman spectra, Phys. Rev. B 71, 064501 (2005).
- M. J. Puska and R. M. Nieminen, Atoms embedded in an electron gas: Phase shifts and cross sections, Phys. Rev. B 27, 6121 (1983).
- 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).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/h7vd-94pk for a description of electronic structure convergence, machine learning model parameter optimization, and additional simulation data.
- L. Zhang, B. Onat, G. Dusson, A. McSloy, G. Anand, R. J. Maurer, C. Ortner, and J. R. Kermode, Equivariant analytical mapping of first principles Hamiltonians to accurate and transferable materials models, npj Comput Mater 8, 158 (2022).
- I. Batatia, D. P. Kovacs, G. Simm, C. Ortner, and G. Csányi, MACE: Higher order equivariant message passing neural networks for fast and accurate force fields, Advances in Neural Information Processing Systems, Vol. 33 (Curran Associates, Inc., 2022), pp. 11423–11436.
- F. Nattino, C. Díaz, B. Jackson, and G.-J. Kroes, Effect of surface motion on the rotational quadrupole alignment parameter of reacting on Cu(111), Phys. Rev. Lett. 108, 236104 (2012).
- J. P. Perdew, K. Burke, and Y. Wang, Generalized gradient approximation for the exchange-correlation hole of a many-electron system, Phys. Rev. B 54, 16533 (1996).
- 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).
- 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).
- G. Henkelman, B. P. Uberuaga, and H. Jónsson, A climbing image nudged elastic band method for finding saddle points and minimum energy paths, J. Chem. Phys. 113, 9901 (2000).
- W. C. Witt, C. van der Oord, E. Gelžinytė, T. Järvinen, A. Ross, J. P. Darby, C. H. Ho, W. J. Baldwin, M. Sachs, J. Kermode et al., ACEpotentials.jl: A Julia implementation of the atomic cluster expansion, J. Chem. Phys. 159, 164101 (2023).
- https://github.com/ACEsuit/ACEds.jl.
- https://github.com/ACEsuit/ACEpotentials.jl.
- https://github.com/ACEsuit/ACEfriction.jl.
- 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).
- https://github.com/NQCD/NQCDynamics.jl.
- 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).
- A. C. Luntz and M. Persson, How adiabatic is activated adsorption/associative desorption?, J. Chem. Phys. 123, 074704 (2005).
- G. J. Kroes, E. Pijper, and A. Salin, Dissociative chemisorption of on the Cu(110) surface: A quantum and quasiclassical dynamical study, J. Chem. Phys. 127, 164722 (2007).
- M. Gostein and G. O. Sitz, Scattering of from Cu(110): Survival probability versus incident energy, J. Vac. Sci. Technol. A: Vac. Surf. Films 14, 1562 (1996).
- M. Gostein, H. Parhikhteh, and G. O. Sitz, Survival probability of (v = 1, J = 1) scattered from Cu(110), Phys. Rev. Lett. 75, 342 (1995).
- L. Zhang, L. Zhu, and B. Jiang, Six-dimensional state-to-state quantum dynamics of scattering from Cu(100): Validity of site-averaging model, Chin. J. Chem. Phys. 35, 143 (2022).
- L. Sementa, M. Wijzenbroek, B. J. van Kolck, M. F. Somers, A. Al-Halabi, H. F. Busnengo, R. A. Olsen, G. J. Kroes, M. Rutkowski, C. Thewes, N. F. Kleimeier, and H. Zacharias, Reactive scattering of from Cu(100): Comparison of dynamics calculations based on the specific reaction parameter approach to density functional theory with experiment, J. Chem. Phys. 138, 044708 (2013).
- J. Klimeš, D. R. Bowler, and A. Michaelides, Chemical accuracy for the van der Waals density functional, J. Phys.: Condens. Matter 22, 022201 (2010).
- E. W. F. Smeets and G.-J. Kroes, Designing new SRP density functionals including non-local vdW- correlation for and their transferability to (111), Au(111) and Pt(111), Phys. Chem. Chem. Phys. 23, 7875 (2021).
- Y. Zhang, R. J. Maurer, H. Guo, and B. Jiang, Hot-electron effects during reactive scattering of from Ag(111): the interplay between mode-specific electronic friction and the potential energy landscape, Chem. Sci. 10, 1089 (2019).
- J. I. Juaristi, M. Alducin, and P. Saalfrank, Femtosecond laser induced desorption of , , and HD from Ru(0001): Dynamical promotion and suppression studied with ab initio molecular dynamics with electronic friction, Phys. Rev. B 95, 125439 (2017).
- G. Füchsel, T. Klamroth, S. Monturet, and P. Saalfrank, Dissipative dynamics within the electronic friction approach: the femtosecond laser desorption of / from Ru(0001), Phys. Chem. Chem. Phys. 13, 8659 (2011).
- Y. Litman, E. S. Pós, C. L. Box, R. Martinazzo, R. J. Maurer, and M. Rossi, Dissipative tunneling rates through the incorporation of first-principles electronic friction in instanton rate theory. II. Benchmarks and applications, J. Chem. Phys. 156, 194107 (2022).
- W. G. Stark, Machine learning models for gas-surface dynamics, Ph.D. thesis, University of Warwick, 2024.
- https://github.com/wgst/ml-gas-surface.
- W. G. Stark, “wgst/ml-gas-surface: Release v1.0”, Zenodo, https://doi.org/10.5281/zenodo.15720346.