This example underscores the fact that using ∆P rlx rather than ∆P can have a significant effect on excited-state properties, especially for states with a high degree of CT character. The relaxed dipole moment, for example, which is the correct dipole moment for the excited state according to linear response theory, is computed as µ rlx x = tr(µ x P exc ) for the x component, and its unrelaxed analog is µ unrlx x = tr(µ x P unrlx ). In Table , these two quantities are juxtaposed for the first excited state of formaldehyde ( 1 A 2 ), and for an excited state of p-nitroaniline that is characterized by excitation from the highest occupied MO (HOMO) to the lowest unoccupied MO (LUMO) that transfers charge from the amino group to the nitro group. Even for the comparatively benign case of formaldehyde, use of the relaxed density alters the total dipole moment by more than 1 D for several different density functionals, bringing it much closer to experiment. The contrast is more dramatic for p-nitroaniline, where 1 CT state exhibits a large dipole moment (µ ≈ 13 D), and one might therefore expect significant orbital relaxation effects. Unrelaxed densities overestimate this dipole moment by more than a factor of two in some cases, although the effect decreases as the fraction of exact exchange is increased. (Relaxed and unrelaxed dipole moments differ by more than a factor of two for formaldehyde as well, but the dipole moment is much smaller.)