Constructing Diabatic Potential Energy Matrices with Neural Networks Based on Adiabatic Energies and Physical Considerations: Toward Quantum Dynamic Accuracy.

A permutation invariant polynomial-neural network (PIP-NN) approach for constructing the global diabatic potential energy matrices (PEMs) of the coupled states of molecules is proposed. Specifically, the diabatization scheme is based merely on the adiabatic energy data of the system, which is ideally a most convenient way due to not requiring additional calculations for the data of the derivative coupling or any other physical properties of the molecule. Considering the permutation and coupling characteristics of the system, particularly in the presence of conical intersections, some vital treatments for the off-diagonal terms in diabatic PEM are essentially needed. Taking the photodissociation of HO()/NH() and nonadiabatic reaction Na(3) + H → NaH(Σ) + H for example, this PIP-NN method is shown to build up the global diabatic PEMs effectively and accurately. The root-mean-square errors of the adiabatic potential energies in the fitting for three different systems are all small (<10 meV). Further quantum dynamic calculations show that the absorption spectra and product branching ratios in both HO() and NH() nonadiabatic photodissociation are well reproduced on the new diabatic PEMs, and the nonadiabatic reaction probability of Na(3) + H → NaH(Σ) + H obtained on the new diabatic PEMs of the 1A and 1B states is in reasonably good agreement with previous theoretical result as well, validating this new PIP-NN method.