Accurate Prediction of Excited-State Energies from Molecular Orbital Energies Based on Graph Neural Network with Transfer Learning

In the high-throughput screening of molecules with desired excited-state properties, machine learning offers an efficient alternative to quantum chemical calculations but suffers from limited excited-state data. Here, we introduce a transfer learning framework that leverages the ground-state energy gap between the highest occupied and the lowest unoccupied molecular orbital (HL gap) to enhance prediction of lowest singlet (S₁) and triplet (T₁) energies in low-data regimes. We train a graph neural network with a graph isomorphism network with edge features (GINE) and a set transformer pooling scheme to predict the HL gap and then evaluate three transfer strategies for excited-state energy prediction tasks. Among them, a hybrid strategy that concatenates the HL gap to the graph-level readout and transfers parameters from the GINE layers of the HL gap pretrained model consistently yields the best performance across training sets of 10k, 50k, and 100k molecules. At 10k training samples, this strategy reduces the test mean absolute error for both S₁ and T₁ by 41% relative to baseline models trained directly. These results establish the HL gap as a chemically interpretable and effective source domain for improving predictions of the lowest-lying excited-state energies.