which has both positive and negative regions in space, ∆ρ elec (r) ≥ 0 everywhere, and ∆ρ hole (r) ≤ 0. Sometimes it is more informative to visualize these two quantities separately. It is therefore suggested that ∆ρ elec (r) should be called the particle density and ∆ρ hole (r) the hole density. (These terms are sometimes used differently, 14 but our usage is consistent with the idea of ∆P hole as the density matrix for the hole. ) An example is depicted in Fig. , where the particle and hole densities can be visually superimposed by the reader to suggest the difference density, which is also shown. The Z-vector contribution is omitted in this example, making these unrelaxed densities. The molecule in Fig. is a polyfluorene oligomer with a single keto defect (fluorenone) as one of the terminal monomer units. It provides an example of how particle and hole densities are useful for interpreting excited states that are strongly mixed in the canonical MO basis, meaning there are numerous amplitudes x ia that are similar in magnitude. In this particular example, each of the valence MOs is completely delocalized along the length of the oligomer, which is not atypical for π-conjugated chromophores. Nevertheless, it is obvious from the densities in Fig. that the excited state in question is localized as a result of the defect. This is not obvious within the canonical MO basis, however, wherein the transition density consists of a roughly equal mixture of four different ψ i → ψ a excitations as shown in Fig. . Localization arises from phase interference in a coherent superposition of four terms, but this would be essentially impossible to discern by inspecting the relevant MOs alone.