Accurate and Efficient Schemes for Mapping Out Two Isolated Seams of Conical Intersections with Neural Networks Solely Based on Adiabatic Energies: A Case Study of H⁺ + NO(<i>X</i>²Π) → H + NO⁺(<i>X</i>¹Σ<s

A new scheme in the neural network (NN) diabatization approach that solely utilizes the adiabatic energies for constructing the global diabatic potential energy matrices (PEMs) of the molecular systems with two isolated seams of conical intersections (CIs) is proposed. Taking a prototype charge transfer reaction H⁺ + NO(<i>X</i>²Π) → H + NO⁺(<i>X</i>¹Σ⁺), where two seams of CIs are located at the different linear geometries N-O-H and O-N-H, for example, the diabatization with the new scheme including a diabatic state constraint is shown to map out the topographies of both two linear CIs with 100% of the success rate in 10 different trainings, while the diabatization without such constraint hardly represents CIs, in which the avoided crossings appear instead. Simultaneously, we propose a scheme to separate the whole reactive space into three different regions and define the minimal Euclidean distances for each region to efficiently sample the energy points for the NN trainings. Through adjusting the minimal Euclidean distances, the number of the adiabatic energy data needed in the construction of diabatic PEM can be heavily decreased, lowered from ∼2000 to ∼280 energy points, which is much less than the number (>22 000) of <i>ab initio</i> energy points used in earlier spline diabatic PEM. Further quantum dynamic calculations show that the reaction probabilities, vibrational state distributions, and vibrational state resolved differential cross sections are well reproduced on the new NN diabatic PEM, validating these schemes for constructing the diabatic PEM.