Machine-Learning-Assisted Tuning of Exchange–Correlation Functional Parameters for the eXact-Integral Simplified Tamm-Dancoff Approximation Method

Abstract

Here, we improve the accuracy of eXact-integral simplified Tamm–Dancoff approximation (XsTDA) excitation energies through reference-guided and machine-learning-assisted molecule-specific tuning of exchange–correlation functional parameters in the XsTDA response calculation. Using DLPNO-STEOM-CCSD excitation energies for 55,624 organic molecules, we systematically tune one exchange–correlation functional parameter for four hybrid functionals: the exact-exchange fraction ax for PBE0 and M06–2X, and the range-separation parameter ω for CAM-B3LYP and ωB97X-D. Two objectives are considered, targeting either the first 10 singlet excited states or only S1. With the standard functional parameters, XsTDA yields 10-state MAEs of 0.61–0.97 eV relative to DLPNO-STEOM-CCSD, whereas molecule-specific tuning reduces these errors to 0.19–0.28 eV. The two objectives reveal a clear one-parameter trade-off: S1-specific tuning provides the highest S1 accuracy but compromises higher excited states, whereas 10-state tuning gives more balanced multistate performance. To enable practical application to new molecules, five machine-learning architectures are trained to predict the tuned parameters directly from molecular structure, yielding held-out-test MAEs of 0.21–0.30 eV for the 10-state objective and 0.13–0.16 eV for the S1-only objective. Among the models, a directed message-passing neural network shows the strongest overall transferability; combined with ωB97X-D, it yields MAEs of 0.23 and 0.24 eV for the 10-state and S1-only objectives on the 32-molecule subset derived from the original XsTDA benchmark. These results establish ML-assisted molecule-specific parameter tuning as a practical route to improve XsTDA excitation energies while retaining its computational efficiency.