The left side of Figure shows the absolute error of the tPBE0 calculations of the excitation energies with active spaces generated by the nine values of λ. The figure shows that no single value of λ yields accurate results for all 30 cases. For each value of λ, several excitations have an error greater than 1 eV. Although the mean absolute error is lowest for λ = 1 (0.56 eV), this is much larger than the mean absolute error of our previous benchmark results (0.19 eV) when we excluded poor active spaces. However, for all 30 excitations, the new scheme produces at least one value of λ that give an absolute error less than 0.55 eV. This motivated the use of a variational scheme to find the best value of λ for each case. As mentioned above, the criterion we use in the λAPC-tPBE selection scheme is to choose the active space that gives the lowest average tPBE absolute energy between the ground state and the excited state under investigation. Next we compare using the tPBE energy for variational selection to using the wave function energy, which can be called λAPC-CASCI.