Linear Scaling 3D Fragment Method for Large-scale Electronic Structure Calculations

We present a linear scaling 3 dimensional fragment (LS3DF) method that uses a novel decomposition and patching scheme to do ab initio density functional theory (DFT) calculations for large systems. This method cancels out the artificial boundary effects that arise from the spatial decomposition. As a result, the LS3DF results are essentially the same as the original full-system DFT results with errors smaller than the errors introduced by other sources of numerical approximations. In addition, the resulting computational times are thousands of times smaller than conventional DFT methods, making calculations with 100,000 atom systems possible. The LS3DF method is applicable to insulator and semiconductor systems, which covers a current gap in the DOE’s materials science code portfolio for large-scale ab initio simulations.