Computational Design of the Molecules Exhibiting Non-Overlapping HOMO and LUMO in a Same Molecular Plane

The negative energy difference between singlet and triplet excited states (ΔEST) is currently attracting significant attention; however, molecular designs remain largely confined to azaphenalene structures, as reported by Leupin and Wirz in 1980. To show a negative ΔEST, a non-overlapping HOMO and LUMO arrangement is crucial to minimize the exchange interaction in the excited state. We revisited the electronic structure of cyclazine, consisting of cyclododecahexaene ([12]annulene) and a central nitrogen atom. The 12 π-electrons of the peripheral cyclic oligoene play an important role in achieving the non-overlapping HOMO and LUMO arrangement, and the bridging by the nitrogen atom inside produces the energy difference between HOMO and LUMO while maintaining a stable planar structure. Based on these insights, we designed a set of 10 molecules in which the number of π-electrons (N) in the peripheral cyclic oligoene is 16, 20, and 24, satisfying N = 4·n (n = 4, 5, 6), and a further set of 11 molecules in which N in the peripheral cyclic oligoene is extended to 14, 18, 22, and 26, satisfying N = 4·n + 2 (n = 3, 4, 5, 6). HOMO, LUMO, and ΔEST were calculated using CIS, TD-DFT, and EOM-CCSD with the structure optimized without any symmetry constraint. Among the molecular structures with N = 4·n, only the molecules without bond alternation exhibit a non-overlapping HOMO and LUMO and a small ΔEST. In contrast, among the molecular structures with N = 4·n + 2, none of the molecules exhibit a non-overlapping HOMO and LUMO arrangement. The molecules with both N = 4·n and no bond alternation show negative ΔEST in the EOM-CCSD calculation. The findings of this study will pave the way for broader molecular designs of molecules exhibiting negative ΔEST, where the non-overlap of HOMO and LUMO is essential.