The character of an electronically excited state is one of the most important descriptors employed to discuss the photophysics and photochemistry of transition metal complexes. In transition metal complexes, the interaction between the metal and the di erent ligands gives rise to a rich variety of excited states, including metal-centered, intra-ligand, metal-to-ligand charge transfer, ligand-to-metal charge transfer, and ligand-to-ligand charge transfer states. Most often, these excited states are identi ed by considering the most important wave function excitation coe cients and inspecting visually the involved orbitals. This procedure is tedious, subjective, and imprecise. Instead, automatic and quantitative techniques for excited-state characterization are desirable. In this contribution we review the concept of charge transfer numbers-as implemented in the TheoDORE package-and show its wide applicability to characterize the excited states of transition metal complexes. Charge transfer numbers are a formal way to analyze an excited state in terms of electron transitions between groups of atoms based only on the well-de ned transition density matrix. Its advantages are many: it can be fully automatized for many excited states, is objective and reproducible, and provides quantitative data useful for the discussion of trends or patterns. We also introduce a formalism for spin-orbit-mixed states and a method for statistical analysis of charge transfer numbers. The potential of this technique is demonstrated for a number of prototypical transition metal complexes containing Ir, Ru, and Re. Topics discussed include orbital delocalization between metal and carbonyl ligands, nonradiative decay through metal-centered states, e ect of spin-orbit couplings on state character, and comparison among results obtained from di erent electronic structure methods.

The ultrafast luminescent decay of [Re(CO)(phen)(im)], representative of Re(I) carbonyl α-diimine photosensitizers, is investigated by means of wavepacket propagations based on the multiconfiguration time-dependent Hartree (MCTDH) method. On the basis of electronic structure data obtained at the time-dependent density functional theory (TD-DFT) level, the luminescence decay is simulated by solving a 14 electronic states multimode problem including both vibronic and spin-orbit coupling (SOC) up to 15 vibrational modes. A careful analysis of the results provides the key features of the mechanism of the intersystem crossing (ISC) in this complex. The intermediate state, detected by means of fs - ps time-resolved spectroscopies, is assigned to the T state corresponding to the triplet intraligand (IL) transition localized on the phen ligand. By switching off/on SOC and vibronic coupling in the model it is shown that efficient population transfer occurs from the optically active metal-to-ligand-charge-transfer1,3MLCT states to T and to the lowest long-lived phosphorescent MLCT (T) state. The early ultrafast SOC-driven decay followed by a T/T equilibration controlled by vibronic coupling underlies the photoluminescent properties of [Re(CO)(phen)(im)]. The impact of the axial and N,N ligands on the photophysics of this class of Re(I) complexes is further rationalized on the basis of their calculated optical properties. The relative position of the IL and upperMLCT states with respect to the optically active singlet state is influenced by the N,N ligand and affects the relaxation dynamics.