Notably, the HONOs are highly degenerate in C6. HONOs in each system with degeneracy of two are very close in energy resulting in higher degeneracy of four. The numerical values can be found in supporting information, section 2. In such case, the electron correlation effect is highly enhanced and DFT could not predict a correct electronic structure. The frontier molecule orbitals energy levels obtained by DFT calculations do not possess such a degeneracy of four. Whereas, for a larger ring of C8, DFT calculations predict correct qualitative results, due to 1). energy level splits for stabilization arisen from anti-aromaticity and 2). comparatively weaker 1,3-σ-and 1,4-σ-interactions. When the ring size continues to increase, the weakening of in σ, π-mixing result in a decrease in inner-system electron correlation effect. Thus, for common aromaticity systems, the orbital degeneracy is ideal which is composed of shoulder-to-shoulder bonding p orbitals. Therefore, the in-plane aromaticity system of C6 can be regarded as a special case among all cyclo-[2n]-carbon molecules. Inspired from the wisdom of Armstrong's centric model of benzene , it is better to describe the structure of C6 as Figure shows, which is composed of one benzene structure with hydrogens removed and a centric structure. This description method can better emphasize the special bonding feature of in-plane π-system. This special description for C6 is entirely different from the average-bonding form, or single-triplet bonds alternating, which is commonly adopted to describe the Lewis structure of cyclo-[2n]-carbon molecules in previous studies. For cyclo-[2n]-carbon with larger ring size (n ≥ 5), where 1,3-σ-and 1,4-σ-interactions can be ignored, a similar chemical image is pictured based on both of DFT and DMRG calculations. When studying Hückel aromaticity in cyclic conjugated system, apart from ab initio calculation, Hückel molecular orbital (HMO) theory is a convenient but also important tool for quick predicting properties such as energy level, orbital occupation and (anti-)aromaticity, etc. There is a mnemonic device based on Hückel molecular orbital (HMO) theory, which is often used in predicting energy levels of cyclic aromatic systems, known as Frost circle. For a planar, cyclic conjugated system constructed by n p-angular orbitals: 1). draw a circle, the radius of which represents twice of exchange integral (β) of two neighboring p-angular orbitals; 2). draw a regular n-gon inscribed in a circle, with one of its vertexes being located at the bottom of the circle. The ground state energy level is α -2β, where α is Coulomb integral; 3). The energy level is then expressed as eq. 1, which can be simply calculated from the geometric distribution of vertexes in the circle.