Accurate excitation energy prediction of BODIPY dyes through stacking-ensemble Δ-learning

Accurate prediction of excitation energies is critical for the rational design of boron-dipyrromethene (BODIPY) dyes, but conventional time-dependent density functional theory (TD-DFT) often suffers from pronounced functional-dependent errors for this class of chromophores. To improve TD-DFT predictions toward DLPNO-STEOM-CCSD level accuracy at a much lower computational cost, we developed a stacking ensemble Δ-learning framework that combines computationally affordable ωB97X-D3 calculations with DLPNO-STEOM-CCSD reference data to achieve accurate and transferable predictions of vertical S1 excitation energies for BODIPY derivatives. Using a dataset of 866 BODIPY derivatives containing up to 42 atoms, we first benchmarked 21 exchange-correlation functionals against DLPNO-STEOM-CCSD. ωB97X-D3 was used as a representative TD-DFT baseline for demonstrating the Δ-learning workflow. Among the 13 regression models, the stacking ensemble model achieved the best overall performance on the test set according to various metrics. This model generalized well to a size-extrapolation set of 134 BODIPY derivatives containing 43 atoms. It was further validated on an external experimental benchmark set of 15 larger BODIPYs previously reported in the literature and demonstrated transferability to nine structurally distinct near-infrared aza-BODIPYs. These results demonstrate that the proposed stacking ensemble Δ-learning framework provides an accurate, efficient, and transferable approximation to DLPNO-STEOM-CCSD level excitation energies, enabling large-scale screening and rational design of BODIPY chromophores at substantially reduced computational cost.