Is ADC(3) as Accurate as CC3 for Valence and Rydberg Transition Energies?

The search for new ab initio models rapidly delivering accurate excited state energies and properties is one of the most active research lines of theoretical chemistry. Along with these methodological developments, the performances of known methods are constantly reassessed thanks to the emergence of new benchmark values. In this Letter, we show that, in contrast to previous claims, the third-order algebraic diagrammatic construction, ADC(3), does not yield transition energies of the same quality as the third-order coupled cluster method, CC3. There is indeed a significant difference in terms of accuracy between the two approaches, as we clearly and unambiguously demonstrate here thanks to extensive comparisons with several hundreds high-quality vertical transition energies obtained with FCI, CCSDTQ, and CCSDT. Direct comparisons with experimental 0-0 energies of small- and medium-size organic molecules support the same conclusion, which holds for both valence and Rydberg transitions, as well as singlet and triplet states. In regards of these results, we introduce a composite method that we named ADC(2.5) which consists in averaging the ADC(2) and ADC(3) excitation energies. Although ADC(2.5) does not match the CC3 accuracy, it significantly improves the ADC(3) results, especially for vertical energies. We hope that the present contribution will stimulate further developments and, in particular, improvements of the ADC-type methods which have the indisputable advantage of being computationally lighter than their equivalent-order CC variants.