Fig. 7: Validation of the machine-learning force field (ML-FF).

a Correlation between predicted energies by ML-FF and density functional theory (DFT) results. b The root mean squared error (RMSE) is given for both energies and forces, calculated from n = 700 and n = 23,850 points, respectively. The ML error is the ML-FF predicted value subtracted from the DFT result. c Metadynamics simulation for the diffusion of \({[{{{\rm{Cu}}}}{({{{{\rm{NH}}}}}_{3})}_{2}]}^{+}\) in a 2 × 1 × 1 unit cell as a function of the collective variable (CV). d Structure used for metadynamic simulation in (c), with an arrow indicating diffusion path. Atomic color codes: H (white), N (blue), O (red), Al (purple), Si (yellow), and Cu (bronze). Source data are provided as a Source Data file.