PEXSI-Σ: A Green's function embedding method for Kohn-Sham density functional theory

2016/06/02 by Xiantao Li, Lin Lin, Li, Xiantao +3
Materials Science · Physics and Astronomy · #Advanced Chemical Physics Studies #Chemical Physics (physics.chem-ph) #Chemical and Physical Properties of Materials #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Graphene research and applications #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1606.00515

openalex publication_date 2016/06/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

Abstract

In this paper, we propose a new Green's function embedding method called PEXSI-Σ for describing complex systems within the Kohn-Sham density functional theory (KSDFT) framework, after revisiting the physics literature of Green's function embedding methods from a numerical linear algebra perspective. The PEXSI-Σ method approximates the density matrix using a set of nearly optimally chosen Green's functions evaluated at complex frequencies. For each Green's function, the complex boundary conditions are described by a self energy matrix Σ constructed from a physical reference Green's function, which can be computed relatively easily. In the linear regime, such treatment of the boundary condition can be numerically exact. The support of the Σ matrix is restricted to degrees of freedom near the boundary of computational domain, and can be interpreted as a frequency dependent surface potential. This makes it possible to perform KSDFT calculations with O(N²) computational complexity, where N is the number of atoms within the computational domain. Green's function embedding methods are also naturally compatible with atomistic Green's function methods for relaxing the atomic configuration outside the computational domain. As a proof of concept, we demonstrate the accuracy of the PEXSI-Σ method for graphene with divacancy and dislocation dipole type of defects using the DFTB+ software package.

Citations

• Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach
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