Hartree-Fock Questions Answers

[skipito]

Hello,

I have posted my questions and my thoughts on this image, to make it more clear:

[PLAIN]http://img529.imageshack.us/img529/3486/naeng.jpg
http://img529.imageshack.us/img529/3486/naeng.jpg

Thank you!

 

[alxm]

In the Hartree-Fock approximation, you're always using the ordinary electronic Hamiltonian.

The approximation, or ansatz, is that you assume the wave function takes a specific form, namely a (single) Slater determinant; an antisymmetrized product of single-particle wave functions. By plugging that into the full electronic Hamiltonian and using the orthonormality properties of the orbitals, you get (and it's a rather tedious derivation) the Hartree-Fock equations, which is the Hamitonian for these single-particle wave functions. These are still interdependent, but the dependency is reduced to having the wave functions of the other particles in the exchange and coulomb integrals, where you're integrating over all coordinates.

So one orbital depends on the other orbitals, but not on the coordinates of the other electrons. Since you assumed single-particle wave functions (of single coordinates) it can't depend on more than one coordinate. Which is why you don't have correlation.