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

dc.contributor.author Li, X
dc.contributor.author Lin, L
dc.contributor.author Lu, Jianfeng
dc.date.accessioned 2017-04-23T15:47:13Z
dc.date.available 2017-04-23T15:47:13Z
dc.date.issued 2017-04-23
dc.identifier http://arxiv.org/abs/1606.00515v2
dc.identifier.uri https://hdl.handle.net/10161/14057
dc.description.abstract In this paper, we propose a new Green's function embedding method called PEXSI-$\Sigma$ 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-$\Sigma$ 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 $\Sigma$ 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 $\Sigma$ 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 $\mathcal{O}(N^2)$ 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-$\Sigma$ method for graphene with divacancy and dislocation dipole type of defects using the DFTB+ software package.
dc.subject physics.comp-ph
dc.subject physics.comp-ph
dc.subject math.NA
dc.subject physics.chem-ph
dc.title PEXSI-$Σ$: A Green's function embedding method for Kohn-Sham density functional theory
dc.type Journal article
pubs.author-url http://arxiv.org/abs/1606.00515v2
pubs.organisational-group Chemistry
pubs.organisational-group Duke
pubs.organisational-group Mathematics
pubs.organisational-group Physics
pubs.organisational-group Trinity College of Arts & Sciences


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