  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 different 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 identified by considering the most
important wave function excitation coefficients 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-defined 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, effect of spin-orbit couplings on state character, and
comparison among results obtained from different electronic structure methods.
