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

If the electronic structure of a given material is known, then many physical and chemical properties can be accurately determined without resorting to experiment. However, determining the electronic structure of a realistic material is a difficult numerical problem. The chief obstacle faced by computational materials and computer scientists is obtaining a highly accurate solution to a complex eigenvalue problem. We illustrate a new numerical method for calculating the electronic structure of materials. The method is based on discretizing the pseudopotential density functional method (PDFM) in real space. The eigenvalue problem within this method can involve large, sparse matrices with up to thousands of eigenvalues required. An efficient and accurate solution depends increasingly on complex data structures that reduce memory and time requirements, and on parallel computing. This approach has many advantages over traditional plane wave solutions, e.g., no fast Fast Fourier Transforms (FFTs) are needed and, consequently, the method is easy to implement on parallel platforms. We demonstrate this approach for localized systems such as atomic clusters.