Finite-difference-pseudopotential method: Electronic structure calculations without a basis

We present a method for performing electronic structure calculations without the explicit use of a basis. We combine a finite-difference approach with ab initio pseudopotentials. In contrast to methods which use a plane wave basis, our calculations are performed completely in ``real space. '' No artifacts such as supercell geometries need be introduced for localized systems. Although this approach is easier to implement than one with a plane wave basis, no loss of accuracy occurs. The electronic structure of several diatomic molecules, Si₂, C₂, O₂, and CO, are calculated to illustrate the utility of this method.