While for HMO method in addressing the in-plane π-conjugated system in cyclo-[2n]-carbon, the cyclic boundary condition is considered using secular determinant, where atoms separated on the ring is explicitly displayed to form a discrete periodic condition. Therefore, the description based on HMO is strongly limited by the symmetry of geometric structure. Moreover, HMO method assumes a cyclic, shoulder-to-shoulder interaction chain of p-angular orbitals. However, for medium size of cyclo-[2n]-carbon molecules, e.g. n = 8 and 9, the in-plane interaction still has strong tension due to strained geometric structures, thus boundary conditions could not be treated properly by HMO method. Yet the geometric structures have already close to a circle at medium size, which is exactly the advantage of the particle in a ring model.