PEXSI-$\Sigma$: a Green’s function embedding method for Kohn–Sham density functional theory

Li, Xiantao; Lin, Lin; Lu, Jianfeng

doi:10.4310/amsa.2018.v3.n2.a3

Cited by 11 publications

(13 citation statements)

References 58 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3.31 × 10 −2 6.33 × 10 −3 1.13 × 10 −3 9.75 × 10 −4 11 2.88 × 10 −2 6.31 × 10 −3 1.12 × 10 −3 9.04 × 10 −4 13 2.86 × 10 −2 6.63 × 10 −3 1.03 × 10 −3 7.90 × 10 −4 15 1.83 × 10 −2 4.40 × 10 −3 6.73 × 10 −4 5.68 × 10 −4 19 1.73 × 10 −2 3.12 × 10 −3 5.23 × 10 −4 4.13 × 10 −4 Table 6.5: Errors for the anthracene molecule for different bath (and system) sizes. 25 N s Table 6.6: Errors of the energy and forces for the anthracene molecule for different bath (and system) sizes. PET when the system and bath are treated using the same level of theory.…”

Section: Discussionmentioning

confidence: 99%

“…Thus, it can be applicable even when H is a dense matrix such as in the planewave discretization, or when explicit access to H is not readily available. This is in contrast to, e.g., the widely used Green's function embedding methods (see, e.g., [3,37,35,19,25]), where explicit access to H is usually required to compute Green's functions of the form G(z) := (z − H) −1 . In addition, when a large basis set such as a planewave discretization is used, even storing the Green's functions can be challenging.…”

mentioning

confidence: 99%

“…In addition, when a large basis set such as a planewave discretization is used, even storing the Green's functions can be challenging. However, when a small basis set is used, and H is a sparse matrix, Green's function embedding methods can be combined with fast algorithms [25] to yield a lower computational complexity than that of PET. It may also perform better for systems with small gaps.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Projection-Based Embedding Theory for Solving Kohn--Sham Density Functional Theory

Lin¹,

Zepeda-Núñez²

2019

Multiscale Model. Simul.

Self Cite

View full text Add to dashboard Cite

Quantum embedding theories are playing an increasingly important role in bridging different levels of approximation to the many-body Schrödinger equation in physics, chemistry and materials science. In this paper, we present a linear algebra perspective of the recently developed projection based embedding theory (PET) [Manby et al, J. Chem. Theory Comput. 8, 2564, 2012, restricted to the context of Kohn-Sham density functional theory. By partitioning the global degrees of freedom into a "system" part and a "bath" part, and by choosing a proper projector from the bath, PET is an in-principle exact formulation to confine the calculation to the system part only, and hence can be performed with reduced computational cost. Viewed from the perspective of domain decomposition methods, one particularly interesting feature of PET is that it does not enforce a boundary condition explicitly, and remains applicable even when the discretized Hamiltonian matrix is dense, such as in the context of the planewave discretization. In practice, the accuracy of PET depends on the accuracy of the bath projector. Based on the linear algebra reformulation, we develop a first order perturbation correction to the projector from the bath to improve its accuracy. Numerical results for real chemical systems indicate that with a proper choice of reference system used to compute the bath projector, the perturbatively corrected PET can be sufficiently accurate even when strong perturbation is applied to very small systems, such as the computation of the ground state energy of a SiH 3 F molecule, using a SiH 4 molecule as the reference system. Since the dimension of Bis a diagonal matrix containing all the eigenvalues of H| B ⊥ 0 ordered non-decreasingly, and Ψ ∈ C N ×(N −N b ) is given by orthogonal columns of an unitary matrix in the subspace 6 7

show abstract

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Projection-Based Embedding Theory for Solving Kohn--Sham Density Functional Theory

Lin¹,

Zepeda-Núñez²

2019

Multiscale Model. Simul.

Self Cite

View full text Add to dashboard Cite

show abstract

“…For multi-dimensional problems, a discrete boundary element method 55 can be used. 56 We will refer to these algorithms in general as selective inversion. 51…”

Section: Methods and Algorithms 21 The Density-matrix Formulationmentioning

confidence: 99%

Reduced-Order Modeling Approach for Electron Transport in Molecular Junctions

Chu

2020

J. Chem. Theory Comput.

Self Cite

View full text Add to dashboard Cite

To describe non-equilibrium transport processes in a quantum device with infinite baths, we propose to formulate the problems as a reduced-order problem. Starting with the Liouville-von Neumann equation for the density-matrix, the reduced-order technique yields a finite system with open boundary conditions. We show that with appropriate choices of subspaces, the reduced model can be obtained systematically from the Petrov-Galerkin projection. The self-energy associated with the bath emerges naturally. The results from the numerical experiments indicate that the reduced models are able to capture both the transient and steady states.(ii) the surrounding areas from contacting materials. Notable examples include quantum dots, quantum wires, and molecule-lead conjunctions. The junctions play an essential role in determining the functionality and properties of the entire device and structure, such as photovoltaic cells, 8,9 intramolecular vibrational relaxation, 10-13 infrared chromophore spectroscopy, and photochemistry. [14][15][16][17] At such a small spatial and temporal scale, modeling the transport properties and processes demands a quantum theory that directly targets the electronic structures.Such problems have been traditionally treated with the Landauer-Büttiker formalism, [18][19][20] which aims at computing the steady-state of a system interacting with two or more macroscopic electrodes, and the non-equilibrium Green's function (NEGF) approach, which, often based on the tight-binding (TB) representation, can naturally incorporate the external potential and predict the steady-state current. 21 This approach was later extended to the first-principle level 22-24 using the density-functional theory (DFT). 25,26 Due to the dynamic nature and the involvement of electron excitations, one natural computational framework for transport problems is the time-dependent density-functional theory (TDDFT), 27-31 which extends the DFT to model electron dynamics. This effort was initiated by Stefanucci and Almbladh,29,32 and Kurth et al.,27 where the wave functions are projected into the center and bath regions. An algorithm was developed to propagate the wave functions confined to the center region so that the influence from the bath is taken into account. This is later treated by using the complex absorbing potential (CAP) method 33 by Varga. 34 One computational challenge from this framework is the computation of the initial eigenstates. Kurth et al. 27 addressed this issue by diagonalizing the Green's function.However, the normalization is still nontrivial, since the wave functions also have components in the bath regions. Another issue is that the CAP method is usually developed for constant external potentials. For time-dependent scalar potentials, a gauge transformation is usually needed to express the absorbing boundary condition, 35 and it is not yet clear how this can be implemented within CAP.

show abstract

“…These include matching of the wavefunctions in different regions, e.g. surface and bulk [3], and Green function or embedding methods [4][5][6][7][8][9] have e.g. been used to treat the isolated defect/adsorbate on a surface or electronic transport between two electrodes [10].…”

Section: Introductionmentioning

confidence: 99%

Removing all periodic boundary conditions: Efficient nonequilibrium Green's function calculations

et al. 2019

View full text Add to dashboard Cite

We describe a method and its implementation for calculating electronic structure and electron transport without approximating the structure using periodic super-cells. This effectively removes spurious periodic images and interference effects. Our method is based on already established methods readily available in the non-equilibrium Green function formalism and allows for nonequilibrium transport. We present examples of a N defect in graphene, finite voltage bias transport in a point-contact to graphene, and a graphene-nanoribbon junction. This method is less costly, in terms of CPU-hours, than the super-cell approximation.

show abstract

PEXSI-$\Sigma$: a Green’s function embedding method for Kohn–Sham density functional theory

Cited by 11 publications

References 58 publications

Projection-Based Embedding Theory for Solving Kohn--Sham Density Functional Theory

Projection-Based Embedding Theory for Solving Kohn--Sham Density Functional Theory

Reduced-Order Modeling Approach for Electron Transport in Molecular Junctions

Removing all periodic boundary conditions: Efficient nonequilibrium Green's function calculations

Contact Info

Product

Resources

About