Static third-order hyperpolarizabilities(gamma) for neutral, ion radical and ion states of centrosymmetric systems are calculated by the use of the ab initio method. The dependences of basis sets and electron correlation effects on the gamma values for allyl systems are examined. It is found that the extended basis set with diffuse p and d functions and Moller-Plesset second-order perturbation (MP2) method are necessary for reasonable descriptions of at least relative tendencies for these charged states of allyl. We also show that triafulvalene (alternant conjugated system) exhibits positive gamma value, while the anion radical state of pentalene (condensed-ring conjugated system) does negative one by the ab initio MP2 calculations using 6-31G+pd(zeta(p,d)=0.05).