  We compute a rigorous asymptotic expansion of the energy of a point defect in
a 1D chain of atoms with second neighbour interactions. We propose the Confined
Lennard-Jones model for interatomic interactions, where it is assumed that
nearest neighbour potentials are globally convex and second neighbour
potentials are globally concave. We derive the {\Gamma}-limit for the energy
functional as the number of atoms per period tends to infinity and derive an
explicit form for the first order term in a {\Gamma}-expansion in terms of an
infinite cell problem. We prove exponential decay properties for minimisers of
the energy in the infinite cell problem, suggesting that the perturbation to
the deformation introduced by the defect is confined to a thin boundary layer.
