Difference between chemical potential, ionization energy, band gap energy, and Fermi level?

[new_986]

Kohn-Sham Eigen values?

Hi everybody...
I have read about Density functional theory and Kohn-Sham theorem, I have found in many references that the Kohn-Sham Eigen values have no physically meaning, except the highest Eigen value has been proved by the Sham and Kohn as the Chemical potential and by perdew,Parr,Levy and Balduz as the negative of the ionization energy
my question is, what is the different between chemical potential, ionization energy, band gap energy and Fermi level?
I really wanted understand this but I couldn't..
thanks with best regards

 

[TeethWhitener]

Kohn-Sham Eigen values?

Hi everybody...
I have read about Density functional theory and Kohn-Sham theorem, I have found in many references that the Kohn-Sham Eigen values have no physically meaning, except the highest Eigen value has been proved by the Sham and Kohn as the Chemical potential and by perdew,Parr,Levy and Balduz as the negative of the ionization energy
my question is, what is the different between chemical potential, ionization energy, band gap energy and Fermi level?
I really wanted understand this but I couldn't..
thanks with best regards

It's kind of difficult to understand what all this means. The lowest eigenenergy of the Hamiltonian in DFT corresponds to the ground state energy. The derivative of energy with respect to particle number at constant potential $V$ in DFT corresponds to chemical potential (which corresponds to the Fermi level):
$$\mu=\left(\frac{\partial E}{\partial N}\right)_V$$
The second derivative corresponds to chemical hardness:
$$\eta=\left(\frac{\partial^2 E}{\partial N^2}\right)_V$$
They are related to ionization potential $I$ and electron affinity $A$ via:
$$\mu\approx\frac{1}{2}(-I-A)$$
$$\eta\approx\frac{1}{2}(I-A)$$
So that $\eta-\mu\approx I$.