From the viewpoint of “diradical character,” referred to as “diradicalology,” we investigate the second hyperpolarizability γ—the molecular third‐order nonlinear optical (NLO) property—of one‐dimensional supermolecular systems composed of acetylene‐linked phenalenyl/pyrene rings using long‐range corrected spin‐unrestricted density functional theory. It turns out that the pyrene‐based superpolyenes (Py‐n) behave like closed‐shell systems, whereas phenalenyl‐based superpolyenes (Ph1‐n and Ph2‐n) have different diradical characters depending on the linked form, that is, Ph1‐n and Ph2‐n have intermediate and pure diradical characters, respectively. In comparison with Py‐n and Ph2‐n, the longitudinal γ of Ph1‐n is significantly larger, and it displays larger enhancement as a function of system size. Substitutions to the terminal rings by donor (NH2) and acceptor (NO2) groups further enhance γ in Ph1‐n, more than in Ph2‐n and Py‐n. These results are in agreement with the structure–property relationships derived for open‐shell NLO systems with symmetric and asymmetric charge distributions (Nakano et al., J. Chem. Phys. 2010, 133, 154302). © 2012 Wiley Periodicals, Inc.