On the Sanibel coefficients in the expansion of spin-projected slater determinants

Every Slater determinant D may be uniquely analyzed in terms of spin components D_l = O_lD which are pure spin eigenfunctions, so that S²D_l = l(l+1)D. Every component D_l = O_lD may in turn be written as a sum of symmetric combinations of Slater determinants, T_k = α^μ?kβ^k‖α^kβ^ν?k], and the coefficients c in the expansion O_lD = ∑_k c T_k are known as the “Sanibel coefficients.” By using the relation S²D_l = l(l+1)D, a recursion formula for the coefficients c is derived, which is then explicitly solved in the special case when S_z has the pure quantum number m = 0.