“…In the benchmark calculations, the composite high-level ab initio methods, including Gaussian-n (Gn) series (G3, G3B3, , G4, and G4MP2) and complete-basis-set (CBS) series (CBS-QB3, , ROCBS-QB3, CBS-Q, and CBS-APNO , ), which are suitable for systems of less than eight non-hydrogen atoms as well as the 25 kinds of DFT methods including B3LYP, B3LYP-D3, CAM-B3LYP, BP86, B3P86, B3PW91, B97D, B97D3, M05-2X, M06-2X, M06-HF, MPW1B95, MPW1KCIS, TPSS1KCIS, TPSSLYP1W, M11, N12, MN12-L, MN12-SX, PBE1W, PBE1PBE, SOGGA11, SOGGA11-X, WB97, and WB97-X were selected. For all of the DFT calculations, the geometry optimization and the frequency calculation of molecules and the corresponding radicals were conducted at the B3LYP/6-31+G(d) level due to its high accuracy and lower computational cost; − at the same time the correct nature of the stationary points was confirmed and the zero-point vibrational energies (ZPEs) were extracted. The basis set of single-point energy calculation by 25 DFT methods is 6-311++G(2df,2p).…”