Previous theoretical studies demonstrated that only exchange-correlation functionals with more than 25% Hartree-Fock (HF) exchange can reliably optimize ground-state geometry of the C18 molecule , and the ωB97XD 44 /def2-TZVP level has been proved to robustly reproduce the high-precision computational result and experimental observation. In addition, in our recent series of theoretical works on C18 ring and related systems , ωB97XD was also shown to be reliable in studying various properties of them, including electronic structure, photophysical property, and optical nonlinearity. Hence in the present work, the geometric structure and excitation characteristic of the studied C18 derivatives were respectively calculated by DFT and TD-DFT methods at the ωB97XD/def2-TZVP level in the gas phase. The molecular first hyperpolarizability was calculated by both analytic derivatives of the system energy, namely coupled-perturbed Kohn-Sham (CPKS) , and finite field (FF) methods at the ωB97XD/aug-cc-pVTZ(-f,-d) level, where aug-cc-pVTZ(-f,-d) is a reduced version of the aug-cc-pVTZ basis set with the removal of f-type polarization functions of non-hydrogen atoms and d-type polarization functions of hydrogen atoms.