First-Principles Calculations for Extremely Large Systems by Parallel Computations Based on the Order-N3 Real-Space Density-Functional Theory

We have recently developed a first-principles density-functional program code based on the real-space finite-difference method in order to perform the calculations with massively parallel computers efficiently. In addition to the efficient parallel implementation, several computational improvements have also been performed, and thereby the computational costs of the Gram-Schmidt procedure and the Rayleigh-Ritz diagonalization are substantially reduced. We have performed the first-principles calculations for the system of 10,000 Si atoms with our real-space density-functional code, and demonstrated that it is possible to obtain a self-consistent electronic structure of 10,000-atom system by a few days with a massively parallel cluster of TFLOPS performance.