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Molecular dynamics with electronic friction (MDEF) at the level of the local density friction approximation (LDFA) has been applied to describe electronically non-adiabatic energy transfer accompanying H atom collisions with many solid metal surfaces. When implemented with full dimensional potential energy and electron density functions, excellent agreement with experiment is found. Here, we compare the performance of a reduced dimensional MDEF approach involving a simplified description of H atom coupling to phonons to that of full dimensional MDEF calculations known to yield accurate results. Both approaches give remarkably similar results for H atom energy loss distributions with a 300 K W(110) surface. At low surface temperature differences are seen; but, quantities like average energy loss are still accurately reproduced. Both models predict similar conditions under which H atoms that have penetrated into the subsurface regions could be observed in scattering experiments. The authors acknowledge the support of the French Embassy in Cuba, the University of Bordeaux, the CNRS, the Erasmus Mundus programme for funding and ISM and University of Bordeaux for providing computing resources. This work was conducted in the scope of the transborder joint Laboratory QuantumChemPhys: Theoretical Chemistry and Physics at the Quantum Scale (ANR-10-IDEX-03-02). This work was partly performed in the framework of the Elementary Dynamical Processes at Model Catalytic Surfaces (EDPMCS) Experiment, a part of the Molecular Physics at Interfaces Initiative at the Dalian Coherent Light Source. NH, AK and AMW acknowledge support for this project from the Max Planck Society Central Funds, the international partnership program of the Chinese Academy of Science (No. 121421KYSB20170012) as well as the Max Planck Institute for Multidisciplinary Sciences and the Georg-August University of Goettingen. We further acknowledge support from the Deutsche Forschungsgemeinschaft under Grant number 217133147, which is part of the Collaborative research Center 1073 operating Project A04. AK acknowledges European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 833404). OG acknowledges financial support by the Spanish Ministerio de Ciencia e Innovacion [Grant No. PID2019-107396GB-I00/AEI/10.13039/501100011033].

Originally conceived to describe thermal diffusion, the Langevin equation includes both a frictional drag and a random force, the latter representing thermal fluctuations first seen as Brownian motion. The random force is crucial for the diffusion problem as it explains why friction does not simply bring the system to a standstill. When using the Langevin equation to describe ballistic motion, the importance of the random force is less obvious and it is often omitted, for example, in theoretical treatments of hot ions and atoms interacting with metals. Here, friction results from electronic nonadiabaticity (electronic friction), and the random force arises from thermal electron-hole pairs. We show the consequences of omitting the random force in the dynamics of H-atom scattering from metals. We compare molecular dynamics simulations based on the Langevin equation to experimentally derived energy loss distributions. Despite the fact that the incidence energy is much larger than the thermal energy and the scattering time is only about 25 fs, the energy loss distribution fails to reproduce the experiment if the random force is neglected. Neglecting the random force is an even more severe approximation than freezing the positions of the metal atoms or modelling the lattice vibrations as a generalized Langevin oscillator. This behavior can be understood by considering analytic solutions to the Ornstein-Uhlenbeck process, where a ballistic particle experiencing friction decelerates under the influence of thermal fluctuations.

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