A parallel eigensolver: Using spectrum slicing method to solve the KohnSham problem for large systems

Solving the Kohn–Sham equation within density functional theory (DFT) finds extensive use in solving for the electronic structure of a variety of condensed materials, including complex biomolecules, nanostructures and interfacial systems. PARSEC, a real-space pseudopotential DFT code developed by our group, routinely solves the electronic structure problem for localized and extended systems of thousands of atoms using Chebyshev polynomial subspace filtering; however, many systems of interest contain tens of thousands of atoms, where the computational demands of orthonormalization can overwhelm current machines. In an effort to address this numerical constraint, we add an additional level of parallelism to our eigensolver by focusing on spectrum slicing. Spectrum slicing assigns energy windows to eigenpairs and treats each window as an independent task, which may be assigned to groups of processing units. We will demonstrate the advantages of this approach for a large (over 20,000 atoms) silicon nanocrystal with and without defects.