# Can anyone tell me about how to use the local density approximation in

1. ### new_986

35
Can anyone tell me about how to use the local density approximation in density functional theory analytically if it possible?

2. ### alxm

1,864
Re: Lda

How do you mean 'use'? LDA is not a functional in itself, it's an ansatz, assuming the exchange-correlation energy for each point in the density can be described by each point in the density. Hence
$$E_{xc}[\rho] = \int \rho(r)\epsilon(\rho(r))dr$$

Typically you also assume that exchange and correlation contributions are separable, working from the homogeneous electron gas, you can get an analytical expression for the exchange energy, but not the correlation.

Parr and Yang's well-known book has the details.

If you're asking whether or not applying an LDA method can be done analytically, that'd depend on your system. You probably could for a homogeneous electronic gas, but not much else.

3. ### new_986

35
Re: Lda

thank you and im sorry because im late in replying