  The accurate and efficient computation of the deformation of crystalline
solids requires the coupling of atomistic models near lattice defects such as
cracks and dislocations with coarse-grained models away from the defects.
Quasicontinuum methods utilize a strain energy density derived from the
Cauchy-Born rule for the coarse-grained model.
  Several quasicontinuum methods have been proposed to couple the atomistic
model with the Cauchy-Born strain energy density. The quasi-nonlocal coupling
method is easy to implement and achieves a reasonably accurate coupling for
short range interactions. In this paper, we give a new formulation of the
quasi-nonlocal method in one space dimension that allows its extension to
arbitrary finite range interactions. We also give an analysis of the stability
and accuracy of a linearization of our generalized quasi-nonlocal method that
holds for strains up to lattice instabilities.
