Energy window stochastic density functional theory

Ming Chen; Roi Baer; Daniel Neuhauser; Eran Rabani

doi:10.1063/1.5114984

Energy window stochastic density functional theory

J Chem Phys. 2019 Sep 21;151(11):114116. doi: 10.1063/1.5114984.

Authors

Ming Chen¹, Roi Baer², Daniel Neuhauser³, Eran Rabani¹

Affiliations

¹ Department of Chemistry, University of California and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
² Fritz Haber Center of Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.
³ Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA.

PMID: 31542024
DOI: 10.1063/1.5114984

Abstract

Linear scaling density functional theory is important for understanding electronic structure properties of nanometer scale systems. Recently developed stochastic density functional theory can achieve linear or even sublinear scaling for various electronic properties without relying on the sparsity of the density matrix. The basic idea relies on projecting stochastic orbitals onto the occupied space by expanding the Fermi-Dirac operator and repeating this for N_χ stochastic orbitals. Often, a large number of stochastic orbitals are required to reduce the statistical fluctuations (which scale as N_χ ^-1/2) below a tolerable threshold. In this work, we introduce a new stochastic density functional theory that can efficiently reduce the statistical fluctuations for certain observable and can also be integrated with an embedded fragmentation scheme. The approach is based on dividing the occupied space into energy windows and projecting the stochastic orbitals with a single expansion onto all windows simultaneously. This allows for a significant reduction of the noise as illustrated for bulk silicon with a large supercell. We also provide theoretical analysis to rationalize why the noise can be reduced only for a certain class of ground state properties, such as the forces and electron density.