. hi everyone here , i have a problem about the exhange energy . IN quantum mechanics, there is a example how to solve eigenvalue and eigenfunction of helium within the framework of perturbation theory . when two electrons are in different eigenstates,the first order correction of energy is :E(1)=k+(-)J K:coulomb energy and J is exhcange energy when + : spin anti-parallel and -: spin parallel and recently i have read about hartree-fock theory ,and found the exchange-energy exists only spin-parallel. Exchange integrals additionally arise if the electrons are of the same spin so my problen is why there is inconsistency between them ?