CAS-SCF and density functional calculations of second hyperpolarizabilities for a nitronyl nitroxide radical

In this study, we investigated a multireference-based nondynamical electron correlation dependence of the second hyperpolarizability, γ. We performed complete active space self-consistent-field (CAS–SCF) calculations including the effect of π electrons. Although the sign of γ obtained by CAS–SCF calculation was found to be negative, the magnitude of γ was found to be much larger than that at the CCSD(T) level. We also applied density functional (DF) methods with different exchange–correlation functionals (BLYP and B3LYP) to the calculation of γ. Although the B3LYP method is found to provide negative γ, its magnitude is much smaller than that at the CCSD(T) level. This feature is discussed in detail by using γ density plots.