The static second hyperpolarizabilities (gamma) of 1,3-dipole molecules in singlet states are investigated using various ab initio molecular orbital (MO) electron correlation methods and density functional theory (DFT) methods with extended basis sets. Substantial dependences of gamma as a function of the method of calculation are observed. At the UCCSD(T) level of theory, we observe the enhancement of gamma in the intermediate diradical character regions as compared to those of small and pure diradical character regions.