title: Sublinear scaling for time-dependent stochastic density functional theory.
abstract: A stochastic approach to time-dependent density functional theory is developed for computing the absorption cross section and the random phase approximation (RPA) correlation energy. The core idea of the approach involves time-propagation of a small set of stochastic orbitals which are first projected on the occupied space and then propagated in time according to the time-dependent Kohn-Sham equations. The evolving electron density is exactly represented when the number of random orbitals is infinite, but even a small number (≈16) of such orbitals is enough to obtain meaningful results for absorption spectrum and the RPA correlation energy per electron. We implement the approach for silicon nanocrystals using real-space grids and find that the overall scaling of the algorithm is sublinear with computational time and memory.
authors.affiliation: Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA.
authors.forename: Yi
authors.initials: Y
authors.lastname: Gao
authors.affiliation: Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA.
authors.forename: Daniel
authors.initials: D
authors.lastname: Neuhauser
authors.affiliation: Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.
authors.forename: Roi
authors.initials: R
authors.lastname: Baer
authors.affiliation: Department of Chemistry, University of California and Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: Eran
authors.initials: E
authors.lastname: Rabani