Effect of cell size on the energetics of vacancies in aluminum studied via orbital-free density functional theory

We investigate the effect of cell size on the energetics of vacancies in Aluminum using orbital-free density functional theory with nonlocal kinetic-energy functionals. Extending the recently developed coarse-graining techniques based on quasicontinuum reduction to include nonlocal kinetic-energy functionals, we consider cell sizes up to a million atoms in this study. We find remarkable cell-size effects that are present in computational domains consisting up to 10(3)-10(4) atoms, even in simple defects such as vacancies. These results indicate the presence of important long-ranged interactions that have not been considered in prior electronic-structure studies of defects conducted on a few hundred atoms. These cell-size effects are more striking in the computed divacancy binding energies, where vacancies are found to repel each other in small computational cells but become attractive in larger computational cells representative of realistic vacancy concentrations.