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# Compressed Representation of Kohn–Sham Orbitals via Selected Columns of the Density Matrix

journal contribution

posted on 2015-04-14, 00:00 authored by Anil Damle, Lin Lin, Lexing YingGiven 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.