Machine-Learned Electronically Excited States with the MolOrbImage Generated from the Molecular Ground State

We present a general machine learning framework for probing the electronic state properties using the novel quantum descriptor MolOrbImage. Each pixel of the MolOrbImage records the quantum information generated by the integration of the physical operator with a pair of bra and ket molecular orbital (MO) states. Inspired by the success of deep convolutional neural networks (NNs) in computer vision, we have implemented the convolutional-layer-dominated MO-NN model. Using the orbital energy and electron repulsion integral MolOrbImages, the MO-NN model achieves promising prediction accuracies against the ADC(2)/cc-pVTZ reference for transition energies to both low-lying singlet [mean absolute error (MAE) < 0.16 eV] and triplet (MAE < 0.14 eV) states. An apparent improvement in the prediction of oscillator strength, which has been shown to be challenging previously, has been demonstrated in this study. Moreover, the transferability test indicates the remarkable extrapolation capacity of the MO-NN model to describe the out of data set systems.