Towards grid-based O(N) density-functional theory methods:: Optimized nonorthogonal orbitals and multigrid acceleration

We have formulated and implemented a real-space ab initio method for electronic structure calculations in terms of nonorthogonal orbitals defined on a grid. A multigrid preconditioner is used to improve the steepest descent directions used in the iterative minimization of the energy functional. Unoccupied or partially occupied states are included using a density matrix formalism in the subspace spanned by the nonorthogonal orbitals. The freedom introduced by the nonorthogonal real-space description of the orbitals allows for localization constraints that linearize the cost of the most expensive parts of the calculations, while keeping a fast convergence rate for the iterative minimization with multigrid acceleration. Numerical tests for carbon nanotubes show that very accurate results can be obtained for localization regions with radii of 8 bohr. This approach, which substantially reduces the computational cost for very large systems, has been implemented on the massively parallel Gray T3E computer and tested on carbon nanotubes containing more than 1000 atoms.