  Using a series of increasingly refined wavefunction methods able to tackle
electronic excited states, namely ADC(2), CC2, CCSD, CCSDR(3) and CC3, we
investigate the interplay between geometries and 0-0 energies. We show that,
due to a strong and nearly systematic error cancelation between the vertical
transition and geometrical reorganization energies, CC2 and CCSD structures can
be used to obtain chemically-accurate 0-0 energies, though the underlying
geometries are rather far from the reference ones and would deliver significant
errors for many chemical and physical properties. This indicates that obtaining
0-0 energies matching experiment does not demonstrate the quality of the
geometrical parameters. In contrast, accurate computation of vertical
excitation energies is mandatory in order to reach chemical accuracy. By
determining CC3 total energies on CCSD structures, we model a large set of
compounds (including radicals) and electronic transitions (including
singlet-triplet excitations) and successfully reach chemical accuracy in a near
systematic way. Indeed, for this particular set, our protocol delivers a mean
absolute error as small as $0.032$ eV, chemical accuracy (error smaller than
$1$ kcal.mol$^{-1}$ or $0.043$ eV) being obtained in 80\%\ of the cases. In
only three cases the error exceeds $0.15$ eV which is of the order of the
typical error provided by TD-DFT or second-order wavefunction methods for this
particular property. The present composite protocol is therefore very effective
despite the fact that the geometries may not be considered as very accurate.
