ABSTRACT:We describe the development and applications of a new electronic structure method that uses a real-space grid as a basis. Multigrid techniques provide preconditioning and convergence acceleration at all length scales and therefore lead to Ž . particularly efficient algorithms. The salient points of our implementation include: i new compact discretization schemes in real space for systems with cubic, orthorhombic, Ž . and hexagonal symmetry and ii new multilevel algorithms for the iterative solution of Kohn᎐Sham and Poisson equations. The accuracy of the discretizations was tested by direct comparison with plane-wave calculations, when possible, and the results were in excellent agreement in all cases. These techniques are very suitable for use on massively Ž . parallel computers and in O N methods. Tests on the Cray-T3D have shown nearly Ž . linear scaling of the execution time up to the maximum number of processors 512 . The above methodology was tested on a large number of systems, such as the C molecule, 60 diamond, Si and GaN supercells, and quantum molecular dynamics simulations for Si. Large-scale applications include a simulation of surface melting of Si and investigations of electronic and structural properties of surfaces, interfaces, and biomolecules.
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