Accelerating <i>ab initio</i> real-space electronic structure calculations for low-dimensional materials using an atom-sphere grid truncation method

In recent decades, the real-space finite-difference implementations of Kohn--Sham density functional theory have exhibited substantial improvements in computational efficiency for large-scale systems. However, the substantial memory consumption arising from the numerous grid points has begun to limit the widespread adoption of this method. In this study, a general method is presented---applicable to both periodic and Dirichlet boundary conditions---to reduce the number of real-space grids. This approach introduces a truncation of the real-space grids based on atomic positions, which reduces memory requirements and enables a more efficient real-space scheme tailored for simulating low-dimensional and porous materials with uneven spatial distributions. By testing the method on zero-dimensional clusters, one-dimensional tubes, two-dimensional clusters adsorbed on graphene, and three-dimensional metal-organic framework materials, a 30--73% reduction in grid points and a 36--71% reduction in computational time per step are observed for simulations with a 2 meV/atom energy difference.