Accurate and Robust Prediction of Vertical Excitation Energies with XYG3-Type Doubly Hybrid Density Functionals

The XYG3-type doubly hybrid density functionals (xDHs) have demonstrated remarkable success in predicting ground-state energies and properties. However, until now, no method has been available to compute excited states with xDHs. In this work, we propose a method that combines the second order constricted variational density functional theory [CV(2)-DFT] within the Tamm-Dancoff approximation (TDA) and the configuration interaction singles with perturbative doubles correction [CIS(D)] method to predict vertical excitation energies using xDHs. This new black-box method, dubbed TDA-xDH, has been benchmarked against a collective dataset of 410 excitation energies. The results demonstrate the high accuracy and robustness of xDHs. For local valence and Rydberg excitations represented by 352 benchmark data points, XYGJ-OS achieves a mean absolute deviation (MAD) of 0.08 eV, outperforming the more expensive coupled cluster singles and doubles (CCSD) method (MAD = 0.11 eV). For 30 intramolecular charge-transfer (CT) excitations, XYGJ-OS also emerges as the best performer among tested functionals, with an MAD of 0.14 eV. Furthermore, XYGJ-OS exhibits excellent performance in predicting the 1La-1Lb gap for six linear polycyclic aromatic hydrocarbons (PAHs), achieving an MAD of merely 0.01 eV. A case study on HAP-3MF further reveals that xDHs are able to correctly predict the inverted singlet-triplet gap. These results highlight the great promise of xDHs for accurately predicting a wide range of molecular excitation energies.