As shown in Table , the HOMO energy of both OLU -and pHBDI -are reasonably accurate from eo-DFT calculations, with an error of 2.0-5.0 × 10 -7 eV for the anions in a representative solvent configuration. The LUMO energy, on the other hand, are off by 0.0415 and 0.187 eV, respectively, from eo-DFT(P 0 ) based on a standard ground-state density matrix. As shown in the 3rd and 5th columns of Table , these errors fall to the order of 10 -6 or 10 -7 eV once one or more virtual orbitals of the chromophore-solvent com-plex is added to the computation of the density matrix. LUMO+1, which contributes substantially to the S 1 excitation of pHBDI -, requires the density matrix to be augmented by contributions from at least two virtual orbitals as one would expect.