Timesaving double-grid method for real-space electronic-structure calculations

We present a simple and efficient technique in ab initio electronic-structure calculation utilizing real-space double grid with a high density of grid points in the vicinity of nuclei. This technique promises to greatly reduce the overhead for performing the integrals that involve nonlocal parts of pseudopotentials, while keeping a high degree of accuracy. our procedure gives rise to no Pulay forces, unlike other real-space methods using adaptive coordinates. Moreover; we demonstrate the potential power of the method by calculating several properties of atoms and molecules.