This set includes all irreducible 118 diagrams consisting of at least two circles, and now uses ρ-circles that contribute factors ρ α (i) and black 'f -bonds', which are related to e-bonds by e α,γ (i, j) = f α,γ (i, j) + 1. We note that the summation over species index α is implied by each ρ α -circle, and that only one f -bond is permitted between two ρ-circles. As an example, the second term on the right side is given as: