e reference excitation energy, obtained at the CC3/ANO-L-VQZP level is 7.18 eV 124 (see also Ref. 45). Note that this particular transition is fairly insensitive to the basis set as long as at least one set of di use functions is included. For example, we have obtained 7.14 and 7.13 eV at the CC3/aug-cc-pVDZ and CC3/aug-cc-pVTZ levels, respectively. In Fig. , we plot the energy convergence of the ground state (GS) and the excited state (ES) as a function of the number of determinants N det , with and without the second-order perturbative contribution. From the data gathered in Table , one can see that, although E is still large (roughly 0.02 a.u.), the sCI+PT2 and sCI+rPT2 excitation energies converge to a value of 7.20 eV compatible with the reference energy obtained in a larger basis set. We have also plo ed the sCI+rPT2 energy given by E (0) + ZE (see Sec. II D 2) and we clearly see that this quantity converges much faster than the usual sCI+PT2 energy. Even for very small reference wave function, the energy gap between GS and ES is qualitatively correct. e graph of Fig. , which shows the zeroth-order energy E (0) as a function of the second-order energy E (do ed lines) or its renormalization variant Z E (solid lines), also indicates that it is practically much easier to extrapolate to the FCI limit using the rPT2 correction.