Accurate Neural Network Representation of the Ab Initio Determined Spin-Orbit Interaction in the Diabatic...

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.