in place of l A→B . When collected into a matrix ξ the diagonal and anti-diagonal axes measure electronhole separation (intracule coordinate) and overall exciton size (extracule coordinate), respectively. This is analogous to the way that the Ω matrix is analyzed; see Fig. . Heat maps of ξ are depicted in Fig. for a 20-unit PPV oligomer, where indices A and B in ξ AB refer to PPV units. In these examples, the length PR adiag in the anti-diagonal direction (extracule coordinate r elec + r hole ) signifies that the excitation is delocalized over essentially the entire oligomer, regardless of the exchange-correlation functional that is employed. On the other hand, the coherence length (in the diagonal direction), which indicates charge separation, is rather sensitive to the fraction of Hartree-Fock exchange, as it was for (pentacene) 4 . For functionals with a large fraction of exact exchange, including Hartree-Fock theory itself, L coh approaches a limiting value of ≈ 2 monomer units, but for semilocal functionals such as BLYP and PBE, the coherence length approaches the length of the entire polymer. This is observed in other conjugated polymers as well. (5.4) and (5.5) but is essentially the matrix Ω defined in Section 4.2. Equivalently, this information is a spatial representation of the transition density T (r hole , r elec ), with both axes measured in units of PPV monomers. The horizontal axis represents the hole coordinate (amplitude represents a hole located on the site in question) and the vertical axis presents the complementary information for the excited electron. Equivalently, the heat map represents the probability of transferring charge from the site indicated on the horizontal axis to the site indicated on the vertical axis. Adapted from Ref. 318; copyright 2007 American Institute of Physics.