Energy transfer plays a prominent role in many dynamical processes at surfaces, with important implications in heterogeneous catalysis, corrosion, energy storage, electromobility, and artificial photosynthesis. In close contact with a surface, the internal degrees of freedom (DOFs) of adsorbates typically couple to the substrate phonons. On metals, non-adiabatic coupling to electron-hole pairs (EHP) enhances the energy transfer rate between molecule and environment. These combined effects have been shown to drastically affect the rates and mechanisms of chemical reactions, also when the molecule-metal contact time is only of a few femtoseconds. The presence of dense sets of energy states and the huge number of DOFs renders theoretical treatment of energy transfer in the condensed phase much more challenging than in the gas phase. Fortunately, such complex reactions can usually be separated into a number of elementary steps. Despite significant advances in theoretical modelling of such elementary steps, their reaction mechanism often remains elusive, hindering further experimental progress. Understanding the role of energy transfer in these fundamental reactions is thus of prime importance.

In recent years, improved state-to-state molecular beam surface scattering experiments have demonstrated the importance of energy transfer upon molecule-surface collisions. Novel sources of atomic probes (e.g. hydrogen atoms) and high-power coherent light sources in free-electron laser facilities (e.g. Dalian Coherent Light Source) promise to provide even more detailed information about the mechanism of collisional inelasticity. The challenge is now to understand, from first principles, the dynamical implications of the coupling of (de-)excitations in the substrate (EHP and phonons) to the DOFs of atoms and molecules (translation, rotation, vibration, electronic) in the vicinity of surfaces. Translation is intimately related to adsorption and diffusion. Coupling to phonons and/or EHPs can dramatically alter the sticking probability and the mobility of adsorbates on surfaces, which influences the reactivity in subsequent steps. How energy flows in and out of reactive bonds influences the dissociation probability of a molecule, a process which is affected by its coupling to the surface. A freely rotating gas phase molecule becomes constrained in the surface vicinity, leading to strong intramolecular energy redistribution enhanced by coupling to the EHP and phonons. Electronic excitations, either as EHPs excitations or in an initially excited molecule, require proper treatment of nonadiabatic effects beyond the Born-Oppenheimer Approximation.

Two major issues to treat such fundamental reactions are the characterization of the underlying electronic structure and its representation in form of a potential energy surface (PES). Density functional theory is now the established choice for investigating molecule-surface interactions. Recent advances in cluster embedding theories offer the promise of treating even metallic systems systems with wave function methods (coupled cluster, multi-reference configuration interaction), that represent the gold standard for gas phase molecules. In recent years, PES representation has evolved from force fields, interpolation schemes (e.g. corrugation reduction procedure) and rational function design towards neural networks and machine learning representations. Since in most cases only reduced-dimensional PES can be constructed, it becomes important to include environmental effects (EHP, phonons, and neglected molecular DOFs) in the dynamics. To this end, classical molecular dynamics subject to environmental friction within a Langevin formalism is now the most widespread solution, while alternatives such as independent electron surface hopping are also used. Most methods rely on the Markovian approximation (i.e. the absence of memory from the environment) and the assumption of a weak coupling between the molecular DOFs and the surface. For EHP, new theories for the friction tensor in the weak coupling limit have been proposed in recent years. To assess the importance of quantization effects and of non-Markovianity, alternative methods such as Multi-Configuration Ehrenfest (MCE) dynamics, Time-Dependent Discrete Variable Representation (TDDVR), and Stochastic Schrödinger Equations (SSE), have been proposed in the general context of system-bath dynamics. These could help resolve important questions in fundamental surface science, in particular for reactions affected by EHP excitations. For phonon dominated processes, the consensus is that, despite its computational cost, ab initio molecular dynamics with electronic friction (AIMDEF) provides the most balanced description of the dynamics (explicit inclusion of phonons and friction-like EHP coupling). An important advantage of AIMDEF is that it circumvents the pre-computation of a PES. Direct dynamics using moving Gaussian bases has recently seen some great advances for non-adiabatic dynamics in the gas phase, and it could provide a quantum mechanical analogue to AIMDEF for surface processes.