Analytical use of local density approximation in density functional theory

[new_986]

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

 

[alxm]

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.

 

[new_986]

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.

thank you and I am sorry because I am late in replying