High-level excitation energies and UV-VIS absorption spectra from machine learning-aided empirical Hamiltonians

Excitation energies and ultraviolet-visible (UV-Vis) absorption spectra are key properties when designing novel compounds. Accurate determination of these properties requires high-level quantum mechanical (HQM) methods, such as coupled cluster (CC2) and GW/BSE, which are computationally demanding. In this work, computationally inexpensive methods, Tight Binding (TB) and semi-empirical Hartree-Fock (SHF), are combined with machine learning (ML) to predict high-level excitation energies and spectra. An ML model based on kernel ridge regression (KRR) was employed to develop corrections to TB and SHF-based methods in order to reproduce CC2 excitations and spectra. The approach was applied to more than 21,000 organic molecules from the QM8 database. The ML model was tested with different descriptors, including the Columb matrix, Bag of Bonds, and connectivity. The ML+connectivity model performed best, achieving a mean absolute error (MAE) of less than 0.2 eV relative to CC2 excitations. This model also outperformed Cam-B3LYP-TDDFT. The predicted absorption spectra matched the CC2 results, with prominent peaks within 0.5 eV of the CC2 values. This work shows that the developed method can efficiently predict excitation energies and UV-Vis spectra for large systems, such as nanosystems, where HQM methods are computationally prohibitive.

Keywords: ML+connectivity, Semi-empirical Hartree-Fock,  high-level excitation energies