  Much work has gone into the construction of quasicontinuum energies that
reduce the coupling error along the interface between atomistic and continuum
regions. The largest consistency errors are typically pointwise
$O(\frac{1}{\eps})$ errors, and in some cases this has been reduced to
pointwise O(1) errors. In this paper we show that one cannot create a coupling
method using a finite-range coupling interface that has o(1)-consistency in the
interface, and we use this to give an upper bound on the order of convergence
in discrete $w^{1,p}$-norms in 1D.
