The static second hyperpolarizabilities (gamma) of polycyclic hydrocarbons involving phenalenyl radical units, IDPL and PDPL, are calculated by the hybrid density functional theory (DIFT), BHandHLYP, method. These molecules exhibit intermediate and somewhat large diradical characters and turn out to provide about one-order larger gamma values than similar size closed-shell polycyclic hydrocarbons, in which diradical character disappears. This is in agreement with our previous prediction that the diradical molecules with intermediate diradical charcaters tend to enhance gamma values as compared to the closed-shell molecules. (c) 2005 Elsevier B.V. All rights reserved.