Thirdly, for in-plane system in smaller rings (n = 5 and 6), both models fail to describe the relative energy level. Considering the discussed two models are both single-particle approximation, when ring size reaches C10 and C12, the electron correlation effect still plays an important role in the electronic structure of in-plane π-conjugated system. Nevertheless, for ring size larger than C14, the electron correlation effect decreases obviously since single-particle models can also give reasonable results. Therefore, we suggest that DFT calculations could be reasonable in studying cyclo-[2n]-carbon molecules larger than C14 (included), however, DFT results of C8, C10 and C12 should be carefully checked, and is especially unreliable when discussing C6.