  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.
