 Alternating-charge chain cohesive energy

For a large one-dimensional chain of alternating charges, $\alpha =2\ln 2$ is the Madelung constant. Summing the Coulomb interaction about one ion and dividing by two avoids double counting; per ion pair the result is $-\alpha q^2/(4\pi {ϵ}_{0}R)$. There are two nearest-neighbour bonds per pair, so a repulsion $A/R^n$ per bond gives the displayed second term. If $A>0,n>1$, $R_0^{n-1}=8\pi {ϵ}_{0}nA/(\alpha q^2)$ is a stable minimum with $u_0=-(1-1/n)\alpha q^2/(4\pi {ϵ}_0{R}_0)$.