  The regular Cauchy--Born method is a useful and efficient tool for analyzing
bulk properties of materials in the absence of defects. However, the method
normally fails to capture surface effects, which are essential to determining
material properties at small length scales. In this paper, we present a
corrector method that improves upon the prediction for material behavior from
the Cauchy--Born method over a small boundary layer at the surface of a 1D
material by capturing the missed surface effects. We justify the separation of
the problem into a bulk response and a localized surface correction by
establishing an error estimate, which vanishes in the long wavelength limit.
