  A set of density functionals coming from different rungs on Jacob's ladder
are employed to evaluate the electronic excited states of three Ru(II)
complexes. While most studies on the performance of density functionals compare
the vertical excitation energies, in this work we focus on the energy gaps
between the electronic excited states, of the same and different multiplicity.
Excited state energy gaps are important for example to determine radiationless
transition probabilities. Besides energies, a functional should deliver the
correct state character and state ordering. Therefore, wavefunction overlaps
are introduced to systematically evaluate the effect of different functionals
on the character of the excited states. As a reference, the energies and state
characters from multi-state second-order perturbation theory complete active
space (MS-CASPT2) are used. In comparison to MS-CASPT2, it is found that while
hybrid functionals provide better vertical excitation energies, pure
functionals typically give more accurate excited state energy gaps. Pure
functionals are also found to reproduce the state character and ordering in
closer agreement to MS-CASPT2 than the hybrid functionals.
