ABSTRACT

Density-functional theory has provided insights into various materials properties in the recent decade. However, its computational complexity has made other aspects, especially those involving defects, beyond reach. Here, we present a method that enables the study of multi-million atom clusters using orbital-free density-functional theory with no spurious physics or restrictions on geometry. The key ideas are (i) a real-space formulation, (ii) a nested finite-element implementation of the formulation and (iii) a systematic means of adaptive coarse-graining retaining full resolution where necessary and coarsening elsewhere with no patches, assumptions or structure. We demonstrate the method, its accuracy under modest computational cost and the physical insights it offers by studying one and two vacancies in aluminum crystals consisting of millions of atoms.