Density functional theory

1. Nov 4, 2004

RedX

I'm trying to learn density functional theory by myself, but I'm a bit confused as to how to use it. Is the following methodology correct (I think it'd take forever to use LaTex to write the equations, so I have a link to small webpage that already has the equations laid out and numbered)?

http://docserver.ub.rug.nl/eldoc/dis/science/f.kootstra/c2.pdf [Broken]

Once you have an expression for the exchange correlation energy as a functional of the density:

1) Guess at a density to plug into 2.31
2) Solve 2.3.1
3) Using the energy eigenfunctions obtained from 2), calculate 2.22 and 2.33
4) Plug 3) into 2.24 to get the energy

Now using the density obtained in 3), go through the whole process again, until you get no change in 4). Then you're at the ground state energy?

I understand that if you want to find the ground state energy of any problem, you can pick arbitrary wave functions and evaluate:

<Energy>=<wave function | Hamiltonian | wave function>

until you find the wave function which minimizes <energy>.

Now

<wave function | Hamiltonian | wave function>
=<wave function | T | wave function>
+<wave function | Vexternal | wave function>
+<wave function | Vinternal | wave function>

Now the last two terms, once given the density, is an electrostatics problem. The problem is calculating the average value of the kinetic energy given the density. Using the auxilliary non-interacting system with the Kohn-Sham equations allows you to calculate a wavefunction which is a function of just 4 variables (including spin), and you can get a kinetic energy from the wavefunctions. Am I correct in this assesment?

Last edited by a moderator: May 1, 2017
2. Nov 19, 2004

santoshroy

Yes your interpretation is correct. This way of getting a minimised energy eigen value is actually variational principle where variation in E should be a extremum w.r.t the assumed density functional.