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Quantum chemical calculations. All calculations were performed using the
Gaussian 09 program package. The geometries in the ground state were optimized
via DFT calculations at the B3LYP/6-31G* level. Vertical absorption energies (EVA)
were calculated based on TD-DFT with the B3LYP, PBE0, MPW1B95, BMK, M06-
2X and M06-HF functionals using 6-31G* basis sets. The calculated EVA(S1)
corresponding to LE or CT transitions were distinguished by orbital transition
analyses. Based on the relationship between q and the optimal HF% (OHF), that is,
OHF ¼ 42q, EVA(1CT, OHF) was read from the fitted straight line of the EVA(1CT)¨C
HF% points plotted on a log¨Clog scale (Supplementary Fig. 2), and E0¨C0(1CT) was
obtained using a common gap of 0.24 eV between E0¨C0(1CT) and EVA(1CT, OHF).
Furthermore, by looking at the change in EVA(S1)¨CEVA(T1) with HF%, we
distinguished the EVA(T1) points corresponding to the 3CT or 3LE transitions and
calculate E0¨C0(3CT) and E0¨C0(3LE) from them, respectively (Supplementary Fig. 2
and Table 1). For more details on the calculations of CT amount (q), optimal HF%,
E0¨C0(1CT), E0¨C0(3CT) and E0¨C0(3LE), see our previous report30.
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