Process Chemistry for Burner Product From Graphite Fuels Containing Niobium.

Paige, B.E.; Evans, T.L.

doi:10.2172/4740167

1971

DOI: 10.2172/4740167

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Process Chemistry for Burner Product From Graphite Fuels Containing Niobium.

B.E. Paige¹,

T.L. Evans²

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2021

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“…Lanczos methods.-Lanczos methods are adapted from power methods to efficiently calculate a small number of eigenvalues and eigenvectors of a large-dimensional Hermitian matrix [33,34]. They are particularly suited for dealing with large sparse Hamiltonians where only shortrange interactions are considered.…”

mentioning

confidence: 99%

An $O(N)$ $Ab~initio$ Calculation Scheme for Large-Scale Moiré Structures

Zhang,

Regnault,

Bernevig

et al. 2021

Preprint

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We present a two-step method and the implemented code specifically tailored for band structure calculation of the small-angle moiré-pattern materials. These materials contain tens of thousands of atoms in a unit cell and the existing ab initio codes usually fail to do this within a finite amount of time without simplifying approximations. Our method can dramatically reduce the computational cost. Firstly, the self-consistent field calculation for ground state is performed with O(N ) Krylov subspace method implemented in OpenMX, which is an ab initio package based on localized pseudoatomic orbitals (PAOs) and pseudo-potential method. Secondly, the crystal momentum dependent Bloch Hamiltonian is constructed from the Hamiltonian matrix elements in PAO basis set obtained in the first step and only selected eigenvalues of it is solved with Lanczos and shift-invert techniques. The computational cost increases linearly with the number of atoms per unit cell instead of cubically (O(N 3 )) in other generally used ab initio packages. By systematically tuning two key parameters, the cutoff radius for electron hopping interaction and the dimension of Krylov subspace, we obtained the band structures for both rigid and corrugated twisted bilayer graphene structures at θ = 2.00 • , θ = 1.61 • , θ = 1.41 • and θ = 1.08 • with improved accuracy in affordable costs both in time and computer resources. They are in good agreement with those from tight binding models, continuum models, and plane-wave pseudo-potential based ab initio calculations, as well as the experimental observations. Our method has taken the advantages of O(N ) method, local atomic orbital basis method, and Lanczos technique. This will play a crucial role in other twisted two-dimensional materials with much more complex band structures than graphene, when the continuum model or effective tight-binding model is hard to construct.

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mentioning

confidence: 99%

An $O(N)$ $Ab~initio$ Calculation Scheme for Large-Scale Moiré Structures

Zhang,

Regnault,

Bernevig

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

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Process Chemistry for Burner Product From Graphite Fuels Containing Niobium.

Cited by 1 publication

References 1 publication

An $O(N)$ $Ab~initio$ Calculation Scheme for Large-Scale Moiré Structures

An $O(N)$ $Ab~initio$ Calculation Scheme for Large-Scale Moiré Structures

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