Speed-Up of the Excited-State Benchmarking: Double-Hybrid Density Functionals as Test Cases

The EX6-0, EX7-0, and EX7-1 representative benchmark sets are developed for the fast evaluation of the performance of a density functional, or more generally of a computational protocol, in modeling low-lying valence singlet-singlet excitation energies of organic dyes within the range of 1.5 to 4.5 eV. All sets share the advantage of being small (a maximum of 7 molecules) but providing statistical errors representative of larger and extended databases. To that extent, the EX7-1 benchmark set goes a step further and is composed of systems as small as possible in order to alleviate the associated computational cost. The reliability of all the sets is assessed through the benchmarking of 15 modern double-hybrid density functionals. The investigation shows not only that the 3 benchmark sets provide close error metrics for each density functional but also that when taking advantage of the Resolution-of-the-Identity and a balanced triple-ζ basis set (e.g., def2-TZVP), double hybrids overperform the "popular" hybrids in modeling vertical absorption, emission, and adiabatic energies.