Signature of multiradical character in second hyperpolarizabilities of rectangular graphene nanoflakes

Using spin-unrestricted density functional theory methods, the second hyperpolarizabilities, γ, of rectangular graphene nanoflakes of different sizes have been investigated for their singlet ground state in conjunction with their open-shell character. It is shown that their multiradical nature leads to a unique dependence of the γ component along the armchair edges and that this behavior can be rationalized not only in terms of the diradical character (y₀) derived from the HOMO and LUMO occupation numbers, but also in terms of the one (y₁) derived from the HOMO-1 and LUMO+1 ones: the γ components are enhanced when the systems take intermediate y₁ values in addition to intermediate y₀ values.