Three-dimensional diabatic potential energy surfaces of thiophenol with neural networks ^†

Three-dimensional (3D) diabatic potential energy surfaces (PESs) of thiophenol involving the S0, and coupled ¹ππ^* and ¹πσ* states were constructed by a neural network approach. Specifically, the diabatization of the PESs for the ¹ππ^* and ¹πσ^* states was achieved by the fitting approach with neural networks, which was merely based on adiabatic energies but with the correct symmetry constraint on the off-diagonal term in the diabatic potential energy matrix. The root mean square errors (RMSEs) of the neural network fitting for all three states were found to be quite small (<4 meV), which suggests the high accuracy of the neural network method. The computed low-lying energy levels of the S₀ state and lifetime of the 0° state of S₁ on the neural network PESs are found to be in good agreement with those from the earlier diabatic PESs, which validates the accuracy and reliability of the PESs fitted by the neural network approach.