Boys localization is most commonly applied to the occupied MOs but the algorithm is perfectly well-defined for the virtual space and we have used it to localize both the occupied and (separately) the virtual MOs. In the latter case, the unbound and spatially diffuse nature of the canonical virtual orbitals leads to Boys orbitals that are extremely diffuse in a few cases. For example, the Rydberg state S 3 primarily involves a pair of excitations (with opposite phase) into a single ultradiffuse virtual orbital, such that R ia (Boys) ≈ 366 Å and σ ia (Boys) ≈ 462 Å for both of these amplitudes. In contrast, the relatively compact S 0 → S 1 excitation (Fig. ) involves amplitudes for which σ ia (Boys) 5 Å, which is actually smaller than the corresponding values for S 0 → S 1 in the CMO basis. The latter range σ ia (CMO) = 7.4 Å to σ ia (CMO) = 13.5 Å.