  Striving to define very accurate vertical transition energies, we perform
both high-level coupled cluster (CC) calculations (up to CCSDTQP) and selected
configuration interaction (sCI) calculations (up to several millions of
determinants) for 18 small compounds. By systematically increasing the order of
the CC expansion, the number of determinants in the CI expansion as well as the
size of the one-electron basis set, we have been able to reach near full CI
(FCI) quality transition energies. These calculations are carried out on
CC3/aug-cc-pVTZ geometries, using a series of increasingly large atomic basis
sets systematically including diffuse functions. In this way, we define a list
of 110 transition energies for states of various characters to be used as
references for further calculations. Benchmark transition energies are provided
at the aug-pVTZ level as well as with additional basis set corrections, in
order to obtain results close to the complete basis set limit. These reference
data are used to benchmark a series of twelve excited-state wave function
methods accounting for double and triple contributions, namely ADC(2), ADC(3),
CIS(D), CIS(D$_\infty$), CC2, STEOM-CCSD, CCSD, CCSDR(3), CCSDT-3, CC3, CCSDT
and CCSDTQ. It turns out that CCSDTQ yields a negligible difference with the
extrapolated CI values with a mean absolute error as small as $0.01$ eV,
whereas the coupled cluster approaches including iterative triples are also
very accurate (mean absolute error of $0.03$ eV). Consequently, CCSDT-3 and CC3
can be used to define reliable benchmarks. This observation does not hold for
ADC(3) that delivers quite large errors for this set of small compounds, with a
clear tendency to overcorrect its second-order version, ADC(2). Finally, we
discuss the possibility to use basis set extrapolation approaches so as to
tackle more easily larger compounds.
