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

Standard orbital-free density functional theory (OFDFT) scales quadratically with system size beyond a few thousand atoms due to ionic energy terms, but with cardinal B-spline approximations, OFDFT can be made to scale fully linearly for all system sizes. To the right is shown the total time required to optimize the electron density and to then calculate the total energy, forces, and stress tensor for fixed ion positions and cell shapes within OFDFT, for systems of bulk aluminum on a single processor.