Accurate simulations of metals at the mesoscale: Explicit treatment of 1 million atoms with quantum mechanics

We present a fully linear scaling (at most O(N · log(N))) and parallel algorithm for orbital-free density functional theory (OFDFT), for the first time exhibiting linear scaling in all terms (electronic and ionic). OFDFT solves directly for the electron density; consequently, the electron kinetic energy is determined using density functionals, which must be nonlocal to provide sufficient accuracy. The systematic elimination of bottlenecks within OFDFT renders the entire algorithm quasilinear scaling for all system sizes (no crossover point). Now an unprecedented number of atoms (∼1 million) can be treated explicitly quantum mechanically within OFDFT with a modest number of processors, opening up the door to treatment of ever more complex features in materials (precipitates, dislocations, etc.) without introducing empirical assumptions.