Real-space electronic-structure calculations with a time-saving 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 ab initio calculations. In order to demonstrate the potential power of these techniques, we present several applications for electronic structure calculations of atoms, molecules, a helical nanotube, and a fullerene bulk.