# How to use Hartree-Fock for helium?

I am thinking of using Hartree-Fock approximation to calculate the ground state energy of helium. The ground state wave function must have a symmetric orbital wave function. But in HF we need a Slater determinant wave function. So how to handle the problem?

• Just follow the variational idea. The energy depends on the orbital part of the wave function only, which is either symmetric or antisymmetric. Then write down the equation for the single particle orbitals by the stationary condition. Apr 12, 2015 at 18:46

The ground state wave function must have a symmetric orbital wave function.

Wrong (or not even wrong). The total wave-function (spin and space) must be anti-symmetric under particle interchange.

But in HF we need a Slater determinant wave function. So how to handle the problem?

Use a Slater determinant. There is no problem with this approach.

There is no problem. In the framework of Hartree Fock approximation you will treat the nuclei as a potential focus (not really like a particle). The particles involved are just electrons, so the wavefunction is antisymmetric under a permutation of their coordinates.