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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 H3 for the 1A' and 2A' electronic states were resolved arising from the E symmetry in the D3h point group. This FI-NN framework with symmetry adaption is used to construct a new quasidiabatic representation of H3, which r
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