No abstract

We present a real-space formulation for isotropic Fourier-space preconditioners used to accelerate the self-consistent field iteration in Density Functional Theory calculations. Specifically, after approximating the preconditioner in Fourier space using a rational function, we express its realspace application in terms of the solution of sparse Helmholtz-type systems. Using the truncated-Kerker and Resta preconditioners as representative examples, we show that the proposed realspace method is both accurate and efficient, requiring the solution of a single linear system, while accelerating self-consistency to the same extent as its exact Fourier-space counterpart.

We present an approach to accelerate real-space electronic structure methods several fold, without loss of accuracy, by reducing the dimension of the discrete eigenproblem that must be solved. To accomplish this, we construct an efficient, systematically improvable, discontinuous basis spanning the occupied subspace and project the real-space Hamiltonian onto the span. In calculations on a range of systems, we find that accurate energies and forces are obtained with 8-25 basis functions per atom, reducing the dimension of the associated real-space eigenproblems by 1-3 orders of magnitude.

We present SPARC: Simulation Package for Ab-initio Real-space Calculations. SPARC can perform Kohn-Sham density functional theory calculations for isolated systems such as molecules as well as extended systems such as crystals and surfaces, in both static and dynamic settings. It is straightforward to install/use and highly competitive with stateof-the-art planewave codes, demonstrating comparable performance on a small number of processors and increasing advantages as the number of processors grows. Notably, SPARC brings solution times down to a few seconds for systems with O(100 − 500) atoms on largescale parallel computers, outperforming planewave counterparts by an order of magnitude and more.

We present M-SPARC: Matlab-Simulation Package for Ab-initio Real-space Calculations. It can perform pseudopotential spin-polarized and unpolarized Kohn-Sham Density Functional Theory (DFT) simulations for isolated systems such as molecules as well as extended systems such as crystals, surfaces, and nanowires. M-SPARC provides a rapid prototyping platform for the development and testing of new algorithms and methods in real-space DFT, with the potential to significantly accelerate the rate of advancements in the field. It also provides a convenient avenue for the accurate first principles study of small to moderate sized systems.