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DFT gives the ground electronic state of the system. I am confused how does DFT predict the excited states? In other words, why can we obtain a whole range of density of states, including the electronic states above fermi level? Thanks.

because the diagonalization of the Hamiltonian gives all eigenvalues of the matrix, and the number of basis functions has to be larger than the absolutely required minimum in order to give some variational degrees of freedom

Dear Admin:

Would you assign much physical meaning to the states found beyond the Fermi level?

Camilo,
Good Question. I didn't know the answer so I did some research. "VASP computes an approximate solution to the many-body Schrodinger equation, within density functional theory (DFT), solving the Kohn-Sham equations," see http://cmp.univie.ac.at/vasp/. As the Admin alluded to even unoccupied orbitals are necessary to construct the total density. Are the unoccupied states meaningful? The answer to your question would depend on who you ask! It has been stated that there is no physical meaning associated with the KS orbitals.[1] However, if you ask Baerends et. al, they state that the physical meaning of the KS orbitals are to split "the exchange-correlation part of the KS potential into a part that is directly related to the total energy and a so-called response part that is related to response of the exchange-correlation hole to density change." [2,3] I'd also read "What Do the Kohn-Sham Orbitals and Eigenvalues Mean?" written by Ralf Stowasser and Roald Hoffmann.[4] Hope this helps. I found it quite interesting.

[1] K. Burke. The ABC of DFT. http://dft.uci.edu, 2009.
[2] Baerends, E. J.; Gritsenko, O. V.; van Leeuwen, R. In Chemical
Application of Density-Functional Theory; Laird, B. B., R. B., Eds.;
[3] Baerends, E. J.; Gritsenko, O. V. J. Phys. Chem. 1997, 101, 5383.
[4] J. Am. Chem. Soc. 1999, 121, 3414-3420







<span class='smallblacktext'>[ Edited Thu Jul 12 2012, 05:15PM ]</span>

jlbettis, thank you very much for this nice collection of references!