Assessing Excited State Methods by Adiabatic Excitation Energies.

We compile a 109-membered benchmark set of adiabatic excitation energies (AEEs) from high-resolution gas-phase experiments. Our data set includes a variety of organic chromophores with up to 46 atoms, radicals, and inorganic transition metal compounds. Many of the 91 molecules in our set are relevant to atmospheric chemistry, photovoltaics, photochemistry, and biology. The set samples valence, Rydberg, and ionic states of various spin multiplicities. As opposed to vertical excitation energies, AEEs are rigorously defined by energy differences of vibronic states, directly observable, and insensitive to errors in equilibrium structures. We supply optimized ground state and excited state structures, which allows fast and convenient evaluation of AEEs with two single-point energy calculations per system. We apply our benchmark set to assess the performance of time-dependent density functional theory using common semilocal functionals and the configuration interaction singles method. Hybrid functionals such as B3LYP and PBE0 yield the best results, with mean absolute errors around 0.3 eV. We also investigate basis set convergence and correlations between different methods and between the magnitude of the excited state relaxation energy and the AEE error. A smaller, 15-membered subset of AEEs is introduced and used to assess the correlated wave function methods CC2 and ADC(2). These methods improve upon hybrid TDDFT for systems with single-reference ground states but perform less well for radicals and small-gap transition metal compounds. None of the investigated methods reaches "chemical accuracy" of 0.05 eV in AEEs.