The second version of the expression combines the densities and valencies into a single sum, which becomes zero in an electroneutral system. This is true of many diagrams in this expansion, because any odd factor of the valency z α will sum to zero. The lowest-order set of terms where this is not the case are the so-called ring diagrams. The third diagram involves both types of bonds. Its expression is the same as the second diagram, but the inter-particle separation is restricted by the f 0 -bond. Such restriction does not affect charge neutrality argument, so the third diagram vanishes. To generalize, we expect a diagram to vanish if any ρ-circle in the diagram is joined by only one Ψ-bond. The fourth diagram above is the first in this series: