Most of current neural network models in quantum chemistry (QC) exclude the molecular symmetry, separate the well-correlated real space (R space), and momenta space (K space) into two individuals, which lack the essential physics in molecular chemistry. In this work, by endorsing the molecular symmetry and elementals of group theory, we propose a comprehensive method to apply symmetry in the graph neural network (SY-GNN), which extends the property-predicting coverage to all the orbital symmetry for both ground and excited states. SY-GNN shows excellent performance in predicting both the absolute and relative of R and K spaces quantities. Besides the numerical properties, SY-GNN also can predict the orbitals distributions in real space, providing the active regions of chemical reactions. We believe the symmetry endorsed deep learning scheme covers the significant physics inside and is essential for the application of neural networks in QC and many other research fields in the future.
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