Using spin-unrestricted density functional theory methods, the second hyperpolarizabilities, gamma, of square nanographenes presenting different diradical characters are investigated from the viewpoint of open-shell singlet nonlinear optical systems. For nanographenes with intermediate diradical character, the gamma component along the armchair edges is enhanced and amounts to about four times the gamma component along the zigzag edges, whereas these gamma components are of similar amplitudes when the system displays nearly pure diradical character. These observations are in conformity with the diradical character dependence of gamma predicted in our previous studies. (C) 2008 Elsevier B.V. All rights reserved.