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

Abstract

In a previous paper, we have demonstrated that artificial neural networks (NNs) can be used to generate quasidiabatic Hamiltonians (Hd) 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, 21A states of NH3 is used as an example. The NN fitting results are compared to that of a previous fitting with symmetry adapted polynomials.