ADAPTIVE-COORDINATE REAL-SPACE ELECTRONIC-STRUCTURE CALCULATIONS FOR ATOMS, MOLECULES, AND SOLIDS

We report the development of a real-space approach to electronic-struc ture calculations which utilizes adaptive curvilinear coordinates. A r egular real-space mesh would be desirable from computational considera tions because it produces a sparse, local, and highly structured Hamil tonian, which enables the effective use of iterative numerical methods and parallel-computer architectures. However, a regular real-space me sh has equal resolution everywhere. This results in an inefficient dis tribution of mesh points, since actual physical systems are inhomogene ous. To remedy this inherent inefficiency without losing the computati onal advantages of a regular mesh, we use a regular mesh in curvilinea r coordinates, which is mapped by a change of coordinates to an adapti ve mesh in Cartesian coordinates. We discuss in detail the choices inv olved in the implementation of the method, including the form and opti mization of the coordinate transformation, the expression for the disc retized Laplacian, the regularization of the ionic potential for all-e lectron calculations, the method of calculating the forces, and the al gorithms used. Band-structure calculations have been implemented by ad ding a phase shift at periodic boundary conditions. We report all-elec tron calculations for atoms and molecules with 1s and 2p valence elect rons, and pseudopotential calculations for molecules and solids.