Constructing Diabatic Potential Energy Matrices with Quantum Dynamic Accuracy: A Neural Network Based Δ-Machine Learning Approach

A neural network (NN) based Δ-machine learning (Δ-ML) approach, which is based on inexpensive low-level energy data and a small number of high-level energies, for constructing the global diabatic potential energy matrices (PEMs) of the coupled states in molecular systems is proposed. Particularly in this so-called NN-based Δ-ML approach, two schemes, namely, training the low-level and high-level adiabatic energy data simultaneously (scheme A) or separately (scheme B), are introduced to construct the final high-level diabatic PEMs. Taking the nonadiabatic reaction Na(3p) + H₂ → NaH(Σ⁺) + H and photodissociation reaction NH₃ + hv → H + NH₂(A~/X~) for example, this NN-based Δ-ML approach with both schemes A and B is demonstrated to represent the global diabatic PEMs effectively and accurately, as evidenced by not only ∼87% of the high-level calculation costs saved for both two systems, but also by the reproduction of the nonadiabatic reaction probability for the former and absorption spectra and product branching ratios for the latter in further quantum dynamical calculations. Furthermore, it is found that the training efficiency of the schemes A and B is quite similar in the triatomic NaH₂ system, while in the NH₃ system the scheme B behaves much better than scheme A due to its higher degrees of freedom.