Moment-Constrained Neural Network for Attosecond–Nanosecond Carrier Dynamics and Optical Spectra in Adsorbate–Metal Clusters

Currently, to precisely control energy absorption, conversion, and dissipation in photon-electron-phonon coupling systems, adsorbate-metal complexes must exhibit narrow-band localized surface plasmon resonance, high energy efficiency, and a tunable damping coefficient. However, resolving the multiscale dynamics that involve subfemtosecond charge coherence and nanoscale geometry remains constrained by the computational scaling of real-time time-dependent density functional theory (rt-TDDFT), hindering large-scale nonequilibrium carrier simulations. The present study utilized a 13-atom adsorbed CO₂ complex as the test platform. We developed an improved hierarchical interactive particle neural network (HIP-NN) that incorporated moment propagation theory (MPT). This enabled the construction of a moment-constrained hierarchical interactive particle network, which encoded the charge, second-order moment, and distance matrix. By combining charge/dipole conservation and MPT loss, we achieved a 32 fs kinetic inference that was reduced from several hours to 20 s, with a peak error typically less than 0.3 eV. Under the same PBE/DZP rt-TDDFT setup, our model surrogate reproduces dipole trajectories and absorption features within small quantitative deviations, while providing 540 speed-ups. The analysis is consistent with metal-regulated CO₂ activation and hot-carrier mechanisms and may assist consistent evaluation across subfemtosecond-nanosecond time scales in structure-performance optimization studies.