Neural network based quasi-diabatic Hamiltonians with symmetry adaptation and a correct description of conical intersections

In a previous paper, we have demonstrated that artificial neural networks (NNs) can be used to generate quasidiabatic Hamiltonians (H-d) that are capable of representing adiabatic energies, energy gradients, and derivative couplings. In this work, two additional issues are addressed. First, symmetry-adapted functions such as permutation invariant polynomials are introduced to account for complete nuclear permutation inversion symmetry. Second, a partially diagonalized representation is introduced to facilitate a better description of near degeneracy points. The diabatization of 1, 2(1)A states of NH3 is used as an example. The NN fitting results are compared to that of a previous fitting with symmetry adapted polynomials.