Data-driven approach for benchmarking DFTB-approximate excited state methods

In this work we propose a chemically-informed data-driven approach to benchmark the approximate density-functional tight-binding (DFTB) excited state (ES) methods that are currently available within the DFTB+ suite. By taking advantage of the large volume of low-detail ES-data in the machine learning (ML) dataset, QM8, we were able to extract valuable insights regarding the limitations of the benchmarked methods in terms of the approximations made to the parent formalism, density-functional theory (DFT), while providing recommendations on how to overcome them. For this benchmark, we compared the first singlet-singlet vertical excitation energies ($E_1$) predicted by the DFTB-approximate methods with predictions of less approximate methods from the reference ML-dataset. For the nearly 21,800 organic molecules in the GDB-8 chemical space, we were able to identify clear trends in the $E_1$ prediction error distributions, with respect to second-order approximate coupled cluster (CC2), showing a strong dependence on chemical identity.