It can be derived by L'Hopital's rule that θ → 0 + and fH(θ) → 3 when n → ∞, i.e., HMO method and the particle in a ring model have the same chemical image for an infinite ring. For reliability, the eigenvalues of Fock operator obtained by DMRG calculations are adopted as natural orbital energy for evaluation purpose instead of DFT results. The error of two models in predicting energy level gaps of cyclic conjugated systems in cyclo-[2n]-carbon is summarized in Table . For comparison, corresponding DFT results is listed in Table . It should also be noted that C6 and C8 are excluded based on previous discussion.