  Nonadiabatic effects that arise from the concerted motion of electrons and
atoms at comparable energy and time scales are omnipresent in thermal and
light-driven chemistry at metal surfaces. Excited (hot) electrons can
measurably affect molecule-metal reactions by contributing to state-dependent
reaction probabilities. Vibrational state-to-state scattering of NO on Au(111)
has been one of the most studied examples in this regard, providing a testing
ground for developing various nonadiabatic theories. This system is often cited
as the prime example for the failure of electronic friction theory, a very
efficient model accounting for dissipative forces on metal-adsorbed molecules
due to the creation of hot electrons in the metal. However, the exact failings
compared to experiment and their origin from theory are not established for any
system, because dynamic properties are affected by many compounding simulation
errors of which the quality of nonadiabatic treatment is just one. We use a
high-dimensional machine learning representation of electronic structure theory
to minimize errors that arise from quantum chemistry. This allows us to perform
a comprehensive quantitative analysis of the performance of nonadiabatic
molecular dynamics in describing vibrational state-to-state scattering of NO on
Au(111) and compare directly to adiabatic results. We find that electronic
friction theory accurately predicts elastic and single-quantum energy loss, but
underestimates multi-quantum energy loss and overestimates molecular trapping
at high vibrational excitation. Our analysis reveals that multi-quantum energy
loss can potentially be remedied within friction theory, whereas the
overestimation of trapping constitutes a genuine breakdown of electronic
friction theory. Addressing this overestimation for dynamic processes in
catalysis and surface chemistry will require more sophisticated theories.
