Table : Mean absolute errors (MAEs) and root mean squared errors (RMSEs) of SpaiNN models for the alkenes ethene, propene, and butene, as well as the methylenimmonium cation, employing either PaiNN (highlighted in gray) or SchNet representations, respectively. The models were trained on energies (E j in eV), forces (F j in eV•Å -1 ), and non-adiabatic coupling vectors (C ij ) involving the three lowest singlet states (S 0 , S 1 , and S 2 ). A weight factor of 1.0 was used for energies, forces, and non-adiabatic couplings to ensure a balanced consideration of the target attributes and their trade-offs. ). This efficiency trend could potentially be attributed to the increased data complexity in C 4 H 8 relative to the other three molecules, given that the database comprises 13 k molecules, while the other databases contain half or less than half of this size (4-6 k data points).