Long-range-corrected UDFT study on second hyperpolarizabilities of open-shell singlet systems

The long-range correction (LC) scheme for the electron exchange in spin-unrestricted density functional theory (DFT), combined with the Becke-Lee-Yang-Parr exchange-correlation functional, i.e., LC-UBLYP, is applied to the calculation of the static second hyperpolarizabilities (γ) of p-quinodimethane, o-dimethylenepyrrole, and o-dimethylenefuran, which have different diradical characters. The spin-unrestricted HF (UHF) and post-UHF electron correlation methods, e.g., spin-unrestricted Møller-Plesset nth-order perturbation theory [UMPn (n = 2, 4)], spinunrestricted coupled cluster singles and doubles (UCCSD) and that with perturbative triples correction [UCCSD(T)] methods as well as the conventional DFT and the spin-flip CI (SF-CI) methods, are applied to the model systems in order to compare the results with that obtained by the LC-UBLYP method. It is found that for the systems having intermediate and large diradical characters, the γ values obtained by the LC-UBLYP method are in good agreement with those obtained by the UCCSD(T) method though it fails to reproduce the UCCSD(T) result for the system with small diradical character.