Approximate spin-projected spin-unrestricted density functional theory method: Application to the diradical character dependences of the (hyper)polarizabilities in p-quinodimethane models

To demonstrate the performance of a novel approximate spin-projected (ASP) spin-unrestricted density functional theory (UDFT) method, we examine the diradical character dependences of the static polarizability (α) and second hyperpolarizability (γ) of a model open-shell singlet molecule, p-quinodimethane (PQM), using several hybrid and long-range corrected (LC) exchange-correlation functionals. The ASP-LC-UBLYP method with a range-separating parameter μ = 0.47 is found to reproduce semi-quantitatively the diradical character dependences of α and γ of the PQM model calculated using the strongly-correlated UCCSD(T) method.