The fundamental of diradical-character-based molecular design for singlet fission is clarified through the correlation between the diradical character, the first singlet (S 1 ) and triplet (T 1 ) excitation energies, the frontier orbital energy gap, and the energy level matching condition (2E(T 1 ) − E(S 1 ) ≈ 0 or < 0) for singlet fission by using the analytical solution of the electronic structure for a model system with two electrons in two orbitals. Moreover, the S 1 −T 1 gap is found to be a key factor for governing the amplitude of E(T 1 ) for 2E(T 1 ) − E(S 1 ) ≈ 0. These findings are indeed justified by the spin-flip time-dependent density functional theory calculations for a series of typical alternant/ nonalternant hydrocarbons, that is, phenacenes, acenes, and isobenzofulvene. The present results demonstrate that a weak diradical character is the underlying concept for efficient singlet fission molecules.

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Using the time-dependent tuned long-range corrected density functional theory method, the feasibility for singlet fission in oligorylenes has been investigated within the scope of the diradical character based guideline and of the energy level matching conditions for the isolated monomers. It is found that the relatively small-size oligorylenes, that is, terrylene and quaterrylene, which present intermediate diradical character without significant tetraradical character, are possible candidates for energetically efficient singlet fission. In relation to this result, we also raise the possibility that the unsettled ultrafast dynamics previously observed on quaterrylene is evidence for singlet fission.

By applying the diradical character based molecular design guideline for singlet fission (SF), we investigate the feasibility of efficient SF in condensed-ring π-conjugated molecules with 4nπ electrons (n = 4, 5, ...), i.e., antiaromatic polycyclic hydrocarbons composed of fiveand sixmembered rings. The multiple diradical character (y i ), which takes a value between 0 (closed shell) and 1 (pure open shell), is defined as the occupation number of the lowest unoccupied natural orbital (LUNO) + i (i = 0, 1, ...) calculated using the approximately spin-projected spinunrestricted Hartree−Fock method. The excitation energies are also evaluated using the tuned long-range corrected time-dependent density functional theory method with the Tamm−Dancoff approximation to examine the energy level matching conditions for SF: (i) 2E(T 1 ) − E(S 1 ) ∼ 0 or ≤ 0 and (ii) 2E(T 1 ) − E(T 2 ) < 0, where S 1 , T 1 and T 2 represent singlet first, triplet first, and triplet second excited states, respectively. It turns out that the energy level matching conditions are satisfied in relatively small-size antiaromatic condensed-ring molecules with y 0 ∼ 0.4 and y 1 /y 0 < 0.2, i.e., intermediate diradical character without significant tetraradical character. This finding also demonstrates the reliability of our design guidelines presented in our previous study.