We require the overlap between the singly excited determinants Φ ā i Φ (replacing j ′ ) to the beta block. The rearrangement requires (N α -i + N α -j ′ ) (86) permutations which will change the sign of the determinant by (-1) Nα-i+Nα-j ′ = (-1) i+j ′ , a fact we will require soon.