Kernel polynomial method for a nonorthogonal electronic-structure calculation of amorphous diamond

Röder, Heinrich; Silver, R.N.; Drabold, D. A.; Dong, Jianjun

doi:10.1103/physrevb.55.15382

Cited by 101 publications

(42 citation statements)

References 15 publications

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“…Some of the techniques we use, based on the stochastic trace formula. 20 , have been developed for tight-binding electronic structure [21][22][23] , for molecular electronics 24 and for multi-exciton generation in nanocrsytals 25 . The success of sDFT in reducing the scaling comes at a price of introducing a stochastic error in all its predictions, including forces, and that precludes application to ab initio molecular dynamics.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium configurations of large nanostructures using the embedded saturated-fragments stochastic density functional theory

Arnon

Rabani

Neuhauser

et al. 2017

The Journal of Chemical Physics

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An ab initio Langevin dynamics approach is developed based on stochastic density functional theory (sDFT) within a new embedded saturated fragment formalism, applicable to covalently bonded systems. The forces on the nuclei generated by sDFT contain a random component natural to Langevin dynamics and its standard deviation is used to estimate the friction term on each atom by satisfying the fluctuation-dissipation relation. The overall approach scales linearly with system size even if the density matrix is not local and is thus applicable to ordered as well as disordered extended systems. We implement the approach for a series of silicon nanocrystals (NCs) of varying size with a diameter of up to 3nm corresponding to N e = 3000 electrons and generate a set of configurations that are distributed canonically at a fixed temperature, ranging from cryogenic to room temperature. We also analyze the structure properties of the NCs and discuss the reconstruction of the surface geometry.

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Section: Introductionmentioning

confidence: 99%

Equilibrium configurations of large nanostructures using the embedded saturated-fragments stochastic density functional theory

Arnon

Rabani

Neuhauser

et al. 2017

The Journal of Chemical Physics

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“…This problem is especially relevant if the diagonalization of the overlap matrix is performed in real space and when one uses an overlap matrix which is necessarily approximate due to the finite cutoff imposed on the range of the matrix elements or due to the Slater-Koster two-center approximation used in parametrizing them. One commonly-used fix to this problem is to add a diagonal matrix with small elements to make the overlap matrix positive definite [81]. The orthogonal Laewdin hamiltonian matrix is obtained by sandwiching the original hamiltonian matrix with A matrices:…”

Section: Laewdin Orthogonalizationmentioning

confidence: 99%

Tight‐binding parameters from the full‐potential linear muffin‐tin orbital method: A feasibility study on NiAl

Djajaputra

Cooper

2003

Physica Status Solidi (b)

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We have examined a method of direct extraction of accurate tight-binding parameters from an ab-initio band-structure calculation. The linear muffin-tin potential method, in its full-potential implementation, has been used to provide the hamiltonian and overlap matrix elements in the momentum space. These matrix elements are Fourier transformed to real space to produce the tight-binding parameters. The feasibility of this method has been tested on the intermetallic alloy NiAl, using spd orbitals for each atom. The parameters generated for this alloy have been used as input to a real-space calculation of the local density of states using the recursion method.

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“…Another notable approximation lies in the computation of the moments µ k . The sequence µ k is not readily available and can be only approximated [144,181]. The various methods proposed in the literature consist of using probabilistic arguments for this purpose.…”

Section: Use Of Orthogonal Polynomialsmentioning

confidence: 99%

“…There are, however, situations where the use of orthogonal polynomials can be very cost-effective. In [144] the density of states (DOS) is computed using this strategy. One starts with a density of eigenvalues in R n which in the form of a sum of Dirac functions:…”

Section: Use Of Orthogonal Polynomialsmentioning

confidence: 99%

Numerical Methods for Electronic Structure Calculations of Materials

Saad¹,

Chelikowsky²,

Shontz³

2010

SIAM Rev.

263

166

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The goal of this article is to give an overview of numerical problems encountered when determining the electronic structure of materials and the rich variety of techniques used to solve these problems. The paper is intended for a diverse scienti£c computing audience. For this reason, we assume the reader does not have an extensive background in the related physics. Our overview focuses on the nature of the numerical problems to be solved, their origin, and on the methods used to solve the resulting linear algebra or nonlinear optimization problems. It is common knowledge that the behavior of matter at the nanoscale is, in principle, entirely determined by the Schrödinger equation. In practice, this equation in its original form is not tractable. Successful, but approximate, versions of this equation, which allow one to study nontrivial systems, took about £ve or six decades to develop. In particular, the last two decades saw a ¤urry of activity in developing effective software. One of the main practical variants of the Schrödinger equation is based on what is referred to as Density Functional Theory (DFT). The combination of DFT with pseudopotentials allows one to obtain in an ef£cient way the ground state con£guration for many materials. This article will emphasize pseudopotentialdensity functional theory, but other techniques will be discussed as well.

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Kernel polynomial method for a nonorthogonal electronic-structure calculation of amorphous diamond

Cited by 101 publications

References 15 publications

Equilibrium configurations of large nanostructures using the embedded saturated-fragments stochastic density functional theory

Equilibrium configurations of large nanostructures using the embedded saturated-fragments stochastic density functional theory

Tight‐binding parameters from the full‐potential linear muffin‐tin orbital method: A feasibility study on NiAl

Numerical Methods for Electronic Structure Calculations of Materials

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