Six-Dimensional State-to-State Scattering of CO and NO from Au(111): A Comparison of Quantum and Quasi-Classical Dynamics

Inelastic scattering processes of NO and CO from metal surfaces have served as benchmarks in revealing vibrational energy transfer dynamics at gas–surface interfaces. While the quasi-classical trajectory (QCT) method has been widely employed for modeling such processes because of its superior efficiency, considering the discrete nature of vibrational transitions, its accuracy has seldom been verified against the accurate quantum dynamical (QD) method. This is mainly due to the difficulty of high-dimensional state-to-state QD scattering calculations for heavy molecules on the surfaces. In this work, we report the first six-dimensional state-to-state quantum dynamics of NO and CO from a rigid Au(111) surface, allowing us to compare them with corresponding QCT dynamics in the same conditions based on first-principles neural network-fit potential energy surfaces. It is found that for rare vibrational transition events, QCT substantially underestimates vibrationally inelastic scattering probabilities. While for processes with more apparent vibrational inelasticity, for example, NO (vi = 3 → vf ≠ 3), QCT and QD results align with each other reasonably well. In addition, both methods predict similar rotational state distributions with consistent energy-dependent patterns. This validates the appropriateness of QCT in describing translational-to-rotational energy transfer. These findings highlight the necessity of using the QD method for accurately predicting low-probability vibrationally inelastic scattering channels. Meanwhile, they also suggest the validity of QCT for studying highly vibrationally and rotationally inelastic molecule–surface state-to-state scattering processes, where high-dimensional QD simulations remain intractable.