How accurate are EOM-CC4 vertical excitation energies?.

We report the first investigation of the performance of EOM-CC4 -- an approximate equation-of-motion coupled-cluster model which includes iterative quadruple excitations -- for vertical excitation energies in molecular systems. By considering a set of 28 excited states in 10 small molecules for which we have computed CCSDTQP and FCI reference energies, we show that, in the case of excited states with a dominant contribution from the single excitations, CC4 yields excitation energies with sub-kJ~mol$^{-1}$ accuracy, in very close agreement with its more expensive CCSDTQ parent. Therefore, if one aims at high accuracy, CC4 stands as a highly competitive approximate method to model molecular excited states, with a significant improvement over both CC3 and CCSDT. Our results also evidence that, although the same qualitative conclusions hold, one cannot reach the same level of accuracy for transitions of double excitation nature.