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We describe a massively parallel implementation of the recently developeddiscontinuous Galerkin density functional theory (DGDFT) [J. Comput. Phys.2012, 231, 2140] method, for efficient large-scale Kohn-Sham DFT basedelectronic structure calculations. The DGDFT method uses adaptive local basis(ALB) functions generated on-the-fly during the self-consistent field (SCF)iteration to represent the solution to the Kohn-Sham equations. The use of theALB set provides a systematic way to improve the accuracy of the approximation.It minimizes the number of degrees of freedom required to represent thesolution to the Kohn-Sham problem for a desired level of accuracy. Inparticular, DGDFT can reach the planewave accuracy with far fewer numbers ofdegrees of freedom. By using the pole expansion and selected inversion (PEXSI)technique to compute electron density, energy and atomic forces, we can makethe computational complexity of DGDFT scale at most quadratically with respectto the number of electrons for both insulating and metallic systems. We showthat DGDFT can achieve 80% parallel efficiency on 128,000 high performancecomputing cores when it is used to study the electronic structure oftwo-dimensional (2D) phosphorene systems with 3,500-14,000 atoms. This highparallel efficiency results from a two-level parallelization scheme that wewill describe in detail.

DGDFT: A Massively Parallel Method for Large Scale Density Functional Theory Calculations