The Yukawa closure for hard spheres is
g i j ( r ) ≡ h i j ( r ) + 1 = 0 r < σ i j = ( σ i + σ j ) / 2 {\displaystyle g_{ij}(r)\equiv h_{ij}(r)+1=0~~~~~~~~r<\sigma _{ij}=(\sigma _{i}+\sigma _{j})/2}
and
c i j ( r ) = ∑ n = 1 K i j r e − z n r σ i j < r {\displaystyle c_{ij}(r)=\sum _{n=1}{\frac {K_{ij}}{r}}e^{-z_{n}r}~~~~~~\sigma _{ij}<r}
