Quote by saray1360
Now, according to the formula of chemical potential you have kindly mentioned and the information we have from the pseudopotential of the fictitious "H", is there a way to calculate the derivative of "F" and then calculate the chmical potential of the "H"

Well, that'd be the usual methods for determining a
functional derivative (the WP article conveniently includes some exact values of [tex]\frac{\delta E[\rho]}{\delta\rho}[/tex] for some of the simpler approximate densityfunctionals.) The exact density functional is not known, though.
Also, if we calculated the chemical potential, could it be used for calculating the formation energy? Or in the formation energy real atoms are considered?

Well, no, not really. And using the formula given requires that you already know the energy (E[rho]). But no quantumchemical method I know of requires Z to be an integer.