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.