# Band structure from DFT

1. Nov 30, 2015

### aaaa202

I'm teaching myself how to do DFT for my master's project, where I want to use it for calculating band structures for different heterostructures. Now to learn DFT I am on one hand reading a book on the basic theory, on the other hand using different freeware packages to try and calculate the band structure for some simple systems like bulk silicon.
One thing that bothers me however, is how to connect the theory I learn in the book, with how the program works. As far as I can understand the idea of DFT is to map a many body problem to a non-interacting problem, using some exchange correlation function, which will produce the same ground state density. To do so a range of methods like the LDA and different choices for the xc-potential is avaiable.
However, I don't understand how to basically go from a theory that allows you to calculate the ground state density to the band structure. Band structure is basically the dispersion of the energy of your system, i.e. E(k), which, for a noninteracting electron gas for example, is a parabola. But how can I get this from the ground state density?
I think the Kohn-sham eigenvalues are not the true eigenvalues of the system and neither are the kohn-sham orbitals.

2. Dec 1, 2015

### vino

It is commonly believed that DFT is a theory to predict ground state properties of a system only (e.g. the total energy, atomic structure, etc.), and that excited state properties cannot be determined by DFT. This is a misconception. In principle, DFT can determine any property (ground state or excited state) of a system given a functional that maps the ground state density to that property. This is the essence of the Hohenburg–Kohn theorem. In practice, however, no known functional exists that maps the ground state density to excitation energies of electrons within a material. Thus, what in the literature is quoted as a DFT band plot is a representation of the DFT Kohn–Sham energies, i.e., the energies of a fictive non-interacting system, the Kohn–Sham system, which has no physical interpretation at all. The Kohn–Sham electronic structure must not be confused with the real, quasiparticle electronic structure of a system, and there is no Koopman's theorem holding for Kohn–Sham energies, as there is for Hartree–Fock energies, which can be truly considered as an approximation for https://en.wikipedia.org/w/index.php?title=Quasiparticle_energies&action=edit&redlink=1 [Broken]. Hence, in principle, Kohn–Sham based DFT is not a band theory, i.e., not a theory suitable for calculating bands and band-plots. In principle time-dependent DFT can be used to calculate the true band structure although in practice this is often difficult. A popular approach is the use of hybrid functionals, which incorporate a portion of Hartree–Fock exact exchange; this produces a substantial improvement in predicted bandgaps of semiconductors, but is less reliable for metals and wide-bandgap materials.
(SOURCE: WIKIPEDIA)

Last edited by a moderator: May 7, 2017
3. Dec 1, 2015

### DrDu

There is no such thing as a band structure on a fundamental level for an interacting electron system. Hence it can not be calculated neither with DFT nor with other methods. What you can calculate is the dependence of the Fermi energy on the number of particles for the ground state. From this you can infer the band gap.
However, most exchange correlation functionals don't perform well in this respect.
What one usually does is to use DFT Kohn Sham orbitals as an input for other methods like the GW method if one is interested in excited state properties.