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

Gamma-expansion for a 1D Confined Lennard-Jones model with point defect