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The excited states of fac-tris(phenylpyridinato)iridium[Ir(ppy)3] and the smaller model complex Ir(C3H4N)3are computed using a number of high-levelab initio methods, including the recently implemented algebraic diagrammaticconstruction method to third-order ADC(3). A detailed descriptionof the states is provided through advanced analysis methods, whichallow a quantification of different charge transfer and orbital relaxationeffects and give extended insight into the many-body wave functions.Compared to the ADC(3) benchmark an unexpected striking differenceof ADC(2) is found for Ir(C3H4N)3, which derives from an overstabilization of charge transfer effects.Time-dependent density functional theory (TDDFT) using the B3LYP functionalshows an analogous but less severe error for charge transfer states,whereas the ωB97 results are in good agreement with ADC(3).Multireference configuration interaction computations, which are inreasonable agreement with ADC(3), reveal that static correlation doesnot play a significant role. In the case of the larger Ir(ppy)3complex, results at the TDDFT/B3LYP and TDDFT/ωB97levels of theory are presented. Strong discrepancies between the twofunctionals, which are found with respect to the energies, characters,as well as the density of the low lying states, are discussed in detailand compared to experiment. [ABSTRACT FROM AUTHOR]