Real-space electronic-structure calculations with timesaving double-grid technique

We present a set of efficient techniques in first-principles electronic-structure calculations utilizing the real-space finite-difference method. These techniques greatly reduce the overhead for performing integrals that involve norm-conserving pseudopotentials, solving Poisson equations, and treating models which have specific periodicities, while keeping a high degree of accuracy. Since real-space methods are inherently local, they have a lot of advantages in applicability and flexibility compared with the conventional plane-wave approach, and promise to be well suited for large and accurate {\it ab initio} calculations. In order to demonstrate the potential power of these techniques, we present several applications for electronic structure calculations of atoms, molecules and a helical nanotube.