  We consider an atomistic model defined through an interaction field
satisfying a variational principle, and can therefore be considered a toy model
of (orbital free) density functional theory. We investigate
atomistic-to-continuum coupling mechanisms for this atomistic model, paying
special attention to the dependence of the atomistic subproblem on the
atomistic region boundary and the boundary conditions. We rigorously prove
first-order error estimates for two related coupling mechanisms.
