Reported in this paper are simplified models for the hardness kernel eta(r,r') and theoretical values of the global hardness for the first 54 neutral atoms calculated using these models. It is found that a particularly simple model for the hardness kernel, eta(r,r')=1/\r-r'\ + C, where C is a constant, generates good results for the global hardness eta. Both main-group elements and transition metal elements are considered, as are various conventional models, in approximating energy components.