Million-Atom Molecular Dynamics Simulation by Order-N Electronic Structure Theory and Parallel Computation

Geshi, Masaaki; Hoshi, Takeo; Fujiwara, Takeo

doi:10.1143/jpsj.72.2880

Cited by 20 publications

(29 citation statements)

References 11 publications

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“…Although such simulations have been carried out thus far, 8,9,13 the investigation is still limited, owing to the system size of 10 2 atoms. In this paper, the cleavage of silicon is studied with quantum mechanical calculations for large-scale electronic structures 16,17,18,19,20,21 and we use a transferable Hamiltonian 22 in the Slater-Koster (tight-binding) form. The methodology is reviewed briefly in Appendix A.…”

Section: Introductionmentioning

confidence: 99%

Nanoscale structures formed in silicon cleavage studied with large-scale electronic structure calculations: Surface reconstruction, steps, and bending

2005

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The 10-nm-scale structure in silicon cleavage is studied by the quantum mechanical calculations for large-scale electronic structure. The cleavage process on the order of 10 ps shows surface reconstruction and step formation. These processes are studied by analyzing electronic freedom and compared with STM experiments. The discussion presents the stability mechanism of the experimentally observed mode, the (111)-(2 × 1) mode, beyond the traditional approach with surface energy. Moreover, in several results, the cleavage path is bent into the experimentally observed planes, owing to the relative stability among different cleavage modes. Finally, several common aspects between cleavage and other phenomena are discussed from the viewpoints of the nonequilibrium process and the 10-nm-scale structure.

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Section: Introductionmentioning

confidence: 99%

Nanoscale structures formed in silicon cleavage studied with large-scale electronic structure calculations: Surface reconstruction, steps, and bending

2005

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“…[7][8][9][10][11] These methods are rigorously a linear scale simulation in atom number, and were tested upto 10 6 atoms by using a standard workstation. The generalized Wannier states are defined formally as unitary transformation of the occupied eigen states, though eigen states are not actually obtained.…”

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confidence: 99%

Krylov Subspace Method for Molecular Dynamics Simulation Based on Large-Scale Electronic Structure Theory

2004

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For large scale electronic structure calculation, the Krylov subspace method is introduced to calculate the one-body density matrix instead of the eigenstates of given Hamiltonian. This method provides an efficient way to extract the essential character of the Hamiltonian within a limited number of basis set. Its validation is confirmed by the convergence property of the density matrix within the subspace. The following quantities are calculated; energy, force, density of states, and energy spectrum. Molecular dynamics simulation of Si(001) surface reconstruction is examined as an example, and the results reproduce the mechanism of asymmetric surface dimer.

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“…the generalized Wannier-state method, [4,5,6] the Krylov subspace method (the subspace diagonalization method [7] and the shifted COCG method [8]) and the generalized Wannier-state solver with parallelism. [9] These methods are ones for calculating the one-body density matrix and/or the Green's function for a given Hamiltonian. Calculation was carried out using the tight-binding formalism of the Hamiltonian.…”

Section: Density Matrix Formulationmentioning

confidence: 99%

Theory of large-scale matrix computation and applications in electronic structure calculation

Fujiwara

Hoshi

Yamamoto

2008

J. Phys.: Condens. Matter

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We review our recently developed methods for large-scale electronic structure calculations, both in one-electron theory and many-electron theory. The method are based on the density matrix representation, together with the Wannier state representation and the Krylov subspace method, in one-electron theory of a-few-tens nm scale systems. The hybrid method of quantum mechanical molecular dynamical simulation is explained. The Krylov subspace method, the CG (conjugate gradient) method and the shifted-COCG (conjugate orthogonal conjugate gradient) method, can be applied to the investigation of the ground state and the excitation spectra in many-electron theory. The mathematical foundation of the Krylov subspace method for large-scale matrix computation is focused and the key technique of the shifted-COCG method, e.g. the collinear residual and seed switching, is explained. A wide variety of applications of these extended novel algorithm is also explained. These are the fracture formation and propagation, liquid carbon and formation process of gold nanowires, together with the application to the extend Hubbard model.

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Million-Atom Molecular Dynamics Simulation by Order-N Electronic Structure Theory and Parallel Computation

Cited by 20 publications

References 11 publications

Nanoscale structures formed in silicon cleavage studied with large-scale electronic structure calculations: Surface reconstruction, steps, and bending

Nanoscale structures formed in silicon cleavage studied with large-scale electronic structure calculations: Surface reconstruction, steps, and bending

Krylov Subspace Method for Molecular Dynamics Simulation Based on Large-Scale Electronic Structure Theory

Theory of large-scale matrix computation and applications in electronic structure calculation

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