= Alternating-charge chain cohesive energy
{title2=$u(R)=-\alpha q^2/(4\pi\epsilon_0R)+2A/R^n$}
For a large one-dimensional chain of alternating charges, $\alpha=2\ln2$ is the <Madelung constant>. Summing the Coulomb interaction about one ion and dividing by two avoids double counting; per ion pair the result is $-\alpha q^2/(4\pi\epsilon_0R)$. There are two nearest-neighbour bonds per pair, so a repulsion $A/R^n$ per bond gives the displayed second term. If $A>0,n>1$, $R_0^{n-1}=8\pi\epsilon_0nA/(\alpha q^2)$ is a stable minimum with $u_0=-(1-1/n)\alpha q^2/(4\pi\epsilon_0R_0)$.
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