30-Excitation Tests. We first show the robustness of the new λAPC-tPBE active space selection scheme by carrying out calculations for the 30 excitations for which our previous approach with the aug-cc-pVTZ basis had a tPBE0 error greater than 0.55 eV; these 30 excitations involve a set of 17 molecules. We generated nine active spaces for each excitation (i.e., N trial = 9) by the method explained in section 2.2. In particular we used λ equal to 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, and 2.0. converges to the lower-energy singly excited Rydberg state (Supporting Information). We next examine excitation energies calculated by tPBE0. To prevent confusion, we stress that although the λAPC-tPBE selection scheme employs the tPBE functional, our calculations of excitation energies are based on tPBE0. These choices simply reflect that tPBE performs better in the selection scheme (as discussed below), whereas tPBE0 gives more accurate excitation energies (as shown in previous work and as also discussed below.).