Densities reveal how overall charge is moved about upon excitation but they sacrifice the phase (sign) information that is contained in the orbitals, which might have been helpful for understanding the character of an excited state. If the number of significant amplitudes x ia is small, then the canonical Kohn-Sham MOs are a good way to visualize the state in question but often this is not the case, especially when hybrid functionals are employed. A quantity that does contain phase information is the transition density T (r, r ′ ) that is defined in Eqs. (2.5) and (2.8), which can be plotted in three-dimensional space by setting r = r ′ . This quantity, however, cannot be interpreted directly in terms of the movement of charge in the same way that the particle, hole, and difference densities can be. For example, consider the transition density T (r) ≡ T (r, r) for the fluorenone-terminated polyfluorene oligomer that was considered above (Fig. ). Although its nodal structure contains elements of the nodal structures of both ∆ρ elec and ∆ρ hole , T (r) is clearly distinct from the difference density. What can be gleaned from T (r) is the nature of the transition moment for the excitation in question, which must lie along the long axis of the molecule because the negative and positive lobes of T (r) approximately cancel along the short axis. Clearly, the result of the fluorenone defect is that this particular excited state is a property of the terminal monomer (fluorenone), not a property of the whole polymer. This fact is not obvious from the canonical MOs that participate in the transition, which are shown in Fig. . The natural transition orbitals (NTOs), which are introduced below, will help to recover an electron/hole picture within a representation that contains phase information.