(EAM), which work best for late transition and noble fcc metals, the indirect (“through-substrate") interactions are expected to be strong only when the adatoms share common substrate nearest neighbors; then the interaction should be repulsive and proportional to the number of shared substrate atoms.[@TLE-Unertl] (Longer range pair interactions and multisite non-pairwise interactions are generally very-to-negligibly small in such calculations; they probably underestimate the actual values of these interactions since there is no Fermi surface in this picture, and it is the Fermi wavevector that dominates long-range interactions.) If the NN and NNN interactions on Cu(001) were purely indirect, we would then predict $\epsilon_2 \!=\! \scriptstyle{\frac{1}{2}}\textstyle{\epsilon_1} \! > \! 0$. However, whenever direct interactions (due to covalent effects between the nearby adatoms) are important, they overwhelm the indirect interaction. At NN separation, which is the bulk NN spacing, direct interactions must be significant, explaining why $\epsilon_1$ can be attractive. It is not obvious from such general arguments whether there are significant direct interactions between Cu adatoms at NNN separations. (For Pt atoms on Pt(100), the only homoepitaxial case in which $\epsilon_2$ was computed semiempirically, EAM calculations[@WDF] gave $\epsilon_2/|\epsilon_1|$ = 0.2, less than half the ratio predicted by counting substrate neighbors, but 