Discrete discontinuous basis projection (DDBP) method for large-scale electronic structure calculations.

The large number of grid points per atom required for accurate real-space Kohn-Sham Density Functional Theory (DFT) calculations restricts their efficiency. In this work, we present an approach to accelerate such calculations several-fold, without loss of accuracy, by systematically reducing the cost of the key computational step: the determination of the Kohn-Sham orbitals spanning the occupied subspace. This is achieved by systematically reducing the dimension of the discrete eigenproblem that must be solved, through projection into a highly efficient discrete discontinuous basis. In calculations of quasi-1D, quasi-2D, and bulk metallic systems, we find that accurate energies and forces are obtained with 8–25 basis functions per atom, reducing the dimension of full-matrix eigenproblems by 1-3 orders of magnitude.