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

The search for new models rapidly delivering accurate excited-state energies and properties is one of the most active research lines of theoretical chemistry. Along with these developments, the performance of known methods is constantly reassessed on the basis of new benchmark values. In this Letter, we show that 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. This is demonstrated by extensive comparisons with several hundred high-quality vertical transition energies obtained with FCI, CCSDTQ, and CCSDT. Direct comparisons with experimental 0-0 energies of small- and medium-size molecules support the same conclusion, which holds for both valence and Rydberg transitions. Considering these results, we introduce a composite approach, ADC(2.5), which consists of 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.