The hardness (η) and chemical potential (μ) of a number of open shell systems have been calculated by ab initio SCF, MP2 and MP4 methods. Both vertical and adiabatic values of ionisation potential (I) and electron affinity (A) have been used to evaluate η and μ. The effect of spin contamination on various calculated quantities has been examined by performing UHF as well as ROHF calculations in appropriate cases. It has been observed that in the case of closely related species the hardness values obtained by almost all the methods of calculation employed here are capable of predicting the empirical hardness sequence of the corresponding anions. However, overall best agreement between theory and experiment is achieved only at the MP4 level. Barring minor exceptions the corresponding calculated values follow the experimental order for both η and μ.