Using the spin-unrestricted density functional theory method, the relationship between the diradical characters (y) and the longitudinal second hyperpolarizabilities (c) has been investigated for several cyclic thiazyl compounds (TZs) and polyacenes (PAs) involving up to six fused rings (N = 6). It turns out that y strongly depends on the substitution position of the nitrogen and sulfur atoms in the five-membered rings of TZs and that its increase with N depends on the substitution positions. The c values of TZs show an enhancement for intermediate y values and are significantly larger than those of PAs of similar size. (C) 2013 Elsevier B.V. All rights reserved.