A Fundamental Invariant-Neural Network Representation Of Quasi-Diabatic Hamiltonians For The Two Lowest States Of H-3

The fundamental invariant neural network (FI-NN) approach is developed to represent coupled potential energy surfaces in quasidiabatic representations with two-dimensional irreducible representations of the complete nuclear permutation and inversion (CNPI) group. The particular symmetry properties of the diabatic potential energy matrix of H-3 for the 1A ' and (2)A ' electronic states were resolved arising from the E symmetry in the D-3h point group. This FI-NN framework with symmetry adaption is used to construct a new quasidiabatic representation of H-3, which reproduces accurately the ab initio energies and derivative information with perfect symmetry behaviors and extremely small fitting errors. The quantum dynamics results on the new FI-NN diabatic PESs give rise to accurate oscillation patterns in the product state-resolved differential cross sections. These results strongly support the accuracy and efficiency of the FI-NN approach to construct reliable diabatic representations with complicated symmetry problems.