Efficient large-scale real-space electronic structure calculations
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Calculations involving the electronic structure of matter provides valuable insight in understanding and predicting a wide range of materials properties. Over the course of the last few decades, Density Functional Theory (DFT) has been a reliable and popular ab-initio method. The plane-wave basis is commonly employed for solving the DFT problem. However, the need for periodicity limits the effectiveness of the plane-wave basis in studying localized or partially periodic systems. Furthermore, efficient utilization of modern large-scale computer architectures is particularly challenging due to the non-locality of the basis. Real-space methods for solving the DFT problem provide an attractive alternative. In this work we present an accurate and efficient real-space formulation and parallel implementation of Density Functional Theory (DFT) for performing ab-initio simulations of isolated clusters (molecules and nanostructures), periodic (infinite crystals) and partially periodic systems (slabs and nanowires). Using the finite-difference representation, local reformulation of the electrostatics, the Chebyshev polynomial filtered self-consistent field iteration, and a reformulation of the non-local component of the force, we develop SPARC (Simulation Package for Ab-initio Real-space Calculations), a framework that enables the efficient evaluation of energies and atomic forces to within chemical accuracies in DFT. Through selected examples consisting of a variety of elements, we demonstrate that the developed framework obtains exponential convergence in energy and forces with domain size; systematic convergence in the energy and forces with mesh-size to reference plane-wave result at comparably high rates; forces that are consistent with the energy, both free from any noticeable `egg-box' effect; and accurate ground-state properties including equilibrium geometries and vibrational spectra. We also demonstrate the weak and strong scaling behavior of SPARC and compare with well-established and optimized plane-wave and other real-space implementations of DFT for systems consisting up to thousands of electrons. Overall, the developed framework is able to accurately and efficiently simulate the electronic structure of a wide range of material systems and represents an attractive alternative to existing codes for practical DFT simulations.