Charge resonance states Interaction between various types of states that are illustrated in Fig. may lead to some mixing, such that the real picture is more muddled. An important case where both types of states are in play are π-stacked nucleobase dimers, leading to interplay between optically-allowed FE states and optically-dark CT states in single-stranded DNA. Low-lying excited states of tetracene and pentacene also exhibit this type of mixing which is relevant to the singlet fission process. In the perylene diimide dimer, which is a common singlet fission (SF) chromophore, there has been much discussion of solventinduced symmetry breaking that can convert CR states into localized CT states. Within a quantum chemistry calculation, even low-polarity dielectric boundary conditions (ǫ = 3, as in organic thin films) can provide sufficient polarization to break the electronic symmetry and localize the CT states. In cases where mixing is significant, it can be challenging to develop a conceptual picture based on detailed calculations. Because each of the four wave functions |Ψ FE ± and |Ψ CR ± is delocalized over both chromophores, FE states cannot be distinguished from CR states on the basis of particle/hole (or attachment/detachment) densities. The key to differentiating them is to recognize that the CT numbers Ω A→B or l A→B contain information about correlations between particle and hole that are averaged away in the densities ∆ρ elec and ∆ρ hole . This has been analyzed in terms of the cumulant of the two-particle density matrix, but a more straightforward analysis is to use a 2×2 matrix (Ω or l) comprised of the quantities Ω A→B or l A→B , in which the fragments A and B represent monomers. This matrix is presented in Table for the delocalized states |Ψ FE ± and |Ψ CR ± that appear Fig. , along with the four basis states that contribute to them. By means of the matrix Ω, these states become easily distinguishable: diagonal character is associated with chargeneutral excitations (FE states, where only Ω A→A is significant), whereas off-diagonal character indicates charge separation. The metric N CT [Eq. (4.13)] differentiates charge-neutral excitations (both localized and delocalized) from charge-separated ones. Note that the full matrix Ω is necessary in order to make these distinctions; the GLI in Eq. (4.11) is insufficient.