Why is the exchange interaction isotropic in a simple system of 2 electrons?

[Davide86]

Considered a simple system composed by 2 electrons, like the H2 molecule, the exchange interaction is isotropic: there's no preferential direction of the spins in physical space. What is the reason? Maybe the fact that the exchange interaction deals with only with the Pauli exclusion prinicple, so relative orientation of the 2 spins, and with no spatial degrees of freedom?
Thanks

 

[cgk]

There is no fundamental "exchange interaction". There is just something that can be interpreted as an effective interaction in an mean field sense, which originates from the combination of the antisymmetry of the wave functiona and the Coulomb interaction. And that something is certainly not isotropic, except for closed-shell atoms (e.g., noble gases).

This becomes more clear when you read up on Hartree-Fock theory. Basically, the "exchange interaction" is a term in the Fock operator (i.e., the approximated mean field interaction) which accounts for electrons not being able to share the same occupied spin-orbital in an energetic sense.