where E B is the energy of the broken-symmetry state. This equation is commonly referred to as the non-projected (NP) approach as it does not involve spin projection. The deficiency of the NP method is that the LS energy typically involves a spin contaminated KS determinant. Addressing this issue, Noodleman proposed a spin-projected (SP) approach that was latter extended and generalized by Dai and Whangbo. The SP scheme maps broken-symmetry and HS states onto the Heisenberg Hamiltonian to give the following expression for J,