Accurate Neural Network Representation of the Ab Initio Determined Spin–Orbit Interaction in the Diabatic Representation Including the Effects of Conical Intersections

A method for fitting ab initio determined spin–orbit coupling interactions, in the Breit–Pauli approximation, based on quasidiabatic representations using neural network fits is reported. The algorithm generalizes our recently reported neural network approach for representing the dipole interaction. The S₀, S₁, and T₁ states of formaldehyde are used as an example. First, the two singlet states S₀ and S₁ are diabatized with a modified Boys Localization diabatization method. Second, the spin–orbit coupling between singlet and triplet states is transformed to the diabatic representation. This removes the discontinuities in the adiabatic representation. The diabatized spin–orbit couplings are then fit with smooth neural network functions. The analytic representation of spin–orbit coupling interactions in a diabatic basis by neural networks will make accurate full-dimensional quantum dynamical treatment of both internal conversion and intersystem crossing possible, which will help us to gain better understanding of both processes.