The following simple form is considered for the electronic energy as a function of the number of electrons: E(N) = {1-exp(-(N-)}2 - where , , and are adjustable parameters. First and second-order derivatives of this equation with respect to N, which are related to chemical potential and hardness, respectively are: [E/N]= =2 exp(-(N0-)) {1- e-(N0-)} and 1/2 [2E/N2] = = 2 exp(-(N0-)) {2 exp(- (N0-)-1} where N0 is the number of electrons in the neutral system. The values obtained for the hardnesses from above equation and the corresponding experimental hardnesses are then compared to each other.
