Electronic structure methods for predicting the properties of materials: Grids in space

If the electronic structure of a given material is known, then many physica l and chemical properties can be accurately determined without resorting to experiment. However, determining the electronic structure of a realistic m aterial is a difficult numerical problem. The chief obstacle faced by compu tational materials and computer scientists is obtaining a highly accurate s olution to a complex eigenvalue problem. We illustrate a new numerical meth od for calculating the electronic structure of materials. The method is bas ed on discretizing the pseudopotential density functional method (PDFM) in real space. The eigenvalue problem within this method can involve large, sp arse matrices with up to thousands of eigenvalues required. An efficient an d accurate solution depends increasingly on complex data structures that re duce memory and time requirements, and on parallel computing. This approach has many advantages over traditional plane wave solutions, e.g., no fast F ast Fourier Transforms (FFTs) are needed and, consequently, the method is e asy to implement on parallel platforms. We demonstrate this approach for lo calized systems such as atomic clusters.