title: Compressed Representation of Kohn-Sham Orbitals via Selected Columns of the Density Matrix.
abstract: Given a set of Kohn-Sham orbitals from an insulating system, we present a simple, robust, efficient, and highly parallelizable method to construct a set of optionally orthogonal, localized basis functions for the associated subspace. Our method explicitly uses the fact that density matrices associated with insulating systems decay exponentially along the off-diagonal direction in the real space representation. We avoid the usage of an optimization procedure, and the localized basis functions are constructed directly from a set of selected columns of the density matrix (SCDM). Consequently, the core portion of our localization procedure is not dependent on any adjustable parameters. The only adjustable parameters present pertain to the use of the SCDM after their computation (for example, at what value should the SCDM be truncated). Our method can be used in any electronic structure software package with an arbitrary basis set. We demonstrate the numerical accuracy and parallel scalability of the SCDM procedure using orbitals generated by the Quantum ESPRESSO software package. We also demonstrate a procedure for combining the orthogonalized SCDM with Hockney's algorithm to efficiently perform Hartree-Fock exchange energy calculations with near-linear scaling.
authors.affiliation: Institute for Computational and Mathematical Engineering, Stanford University , Stanford, California, United States.
authors.forename: Anil
authors.initials: A
authors.lastname: Damle
authors.affiliation: Department of Mathematics, University of California, Berkeley , Berkeley, California, United States.|Computational Research Division, Lawrence Berkeley National Laboratory , Berkeley, California, United States.
authors.forename: Lin
authors.initials: L
authors.lastname: Lin
authors.affiliation: Institute for Computational and Mathematical Engineering, Stanford University , Stanford, California, United States.|Department of Mathematics, Stanford University , Stanford, California, United States.
authors.forename: Lexing
authors.initials: L
authors.lastname: Ying