Computational Design of Molecules Having Less Overlapping HOMO and LUMO in the Same Plane

The negative energy difference between singlet and triplet excited states (Δ<i>E</i>_ST) is currently attracting significant attention; however, molecular designs remain largely confined to azaphenalene structures, as reported by Leupin and Wirz in 1980. To show negative Δ<i>E</i>_ST, a maximally separated highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) arrangement is crucial to minimizing 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 less 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 (<i>N</i>) in the peripheral cyclic oligoene is 16, 20, and 24, satisfying <i>N</i> = 4·<i>n</i> (<i>n</i> = 4, 5, 6), and a further set of 11 molecules in which <i>N</i> in the peripheral cyclic oligoene is extended to 14, 18, 22, and 26, satisfying <i>N</i> = 4·<i>n</i> + 2 (<i>n</i> = 3, 4, 5, 6). HOMO, LUMO, exchange interaction (K), and Δ<i>E</i>_ST were calculated using configuration interaction singles, TD-DFT, and equation of motion coupled-cluster singles and doubles (EOM-CCSD), with the structure optimized without any symmetry constraint. Among the molecular structures with <i>N</i> = 4·<i>n</i>, only the molecules without bond alternation exhibit less overlapping HOMO and LUMO and a small K and Δ<i>E</i>_ST. In contrast, among the molecular structures with <i>N</i> = 4·<i>n</i> + 2, none of the molecules exhibit less overlapping HOMO and LUMO arrangement. The molecules with both <i>N</i> = 4·<i>n</i> and no bond alternation show negative Δ<i>E</i>_ST in the EOM-CCSD calculation. The findings of this study will pave the way for broader molecular designs of molecules exhibiting negative Δ<i>E</i>_ST, where a less overlap of HOMO and LUMO is essential.