3,294 research outputs found
Accuracy control in ultra-large-scale electronic structure calculation
Numerical aspects are investigated in ultra-large-scale electronic structure
calculation. Accuracy control methods in process (molecular-dynamics)
calculation are focused. Flexible control methods are proposed so as to control
variational freedoms, automatically at each time step, within the framework of
generalized Wannier state theory. The method is demonstrated in silicon
cleavage simulation with 10^2-10^5 atoms. The idea is of general importance
among process calculations and is also used in Krylov subspace theory, another
large-scale-calculation theory.Comment: 8 pages, 3 figures. To appear in J.Phys. Condens. Matter. A preprint
PDF file in better graphics is available at
http://fujimac.t.u-tokyo.ac.jp/lses/index_e.htm
Large-scale electronic-structure theory and nanoscale defects formed in cleavage process of silicon
Several methods are constructed for large-scale electronic structure
calculations. Test calculations are carried out with up to 10^7 atoms. As an
application, cleavage process of silicon is investigated by molecular dynamics
simulation with 10-nm-scale systems. As well as the elementary formation
process of the (111)-(2 x 1) surface, we obtain nanoscale defects, that is,
step formation and bending of cleavage path into favorite (experimentally
observed) planes. These results are consistent to experiments. Moreover, the
simulation result predicts an explicit step structure on the cleaved surface,
which shows a bias-dependent STM image.Comment: 4 page 4 figures. A PDF file with better graphics is available at
http://fujimac.t.u-tokyo.ac.jp/lses
Million-atom molecular dynamics simulation by order-N electronic structure theory and parallel computation
Parallelism of tight-binding molecular dynamics simulations is presented by
means of the order-N electronic structure theory with the Wannier states,
recently developed (J. Phys. Soc. Jpn. 69,3773 (2000)). An application is
tested for silicon nanocrystals of more than millions atoms with the
transferable tight-binding Hamiltonian. The efficiency of parallelism is
perfect, 98.8 %, and the method is the most suitable to parallel computation.
The elapse time for a system of atoms is 3.0 minutes by a
computer system of 64 processors of SGI Origin 3800. The calculated results are
in good agreement with the results of the exact diagonalization, with an error
of 2 % for the lattice constant and errors less than 10 % for elastic
constants.Comment: 5 pages, 3 figure
Krylov Subspace Method for Molecular Dynamics Simulation based on Large-Scale Electronic Structure Theory
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.Comment: 7 pages, 3 figures; corrected typos; to be published in Journal of
the Phys. Soc. of Japa
Large-scale electronic structure theory for simulating nanostructure process
Fundamental theories and practical methods for large-scale electronic
structure calculations are given, in which the computational cost is
proportional to the system size. Accuracy controlling methods for microscopic
freedoms are focused on two practical solver methods, Krylov-subspace method
and generalized-Wannier-state method. A general theory called the
'multi-solver' scheme is also formulated, as a hybrid between different solver
methods. Practical examples are carried out in several insulating and metallic
systems with 10^3-10^5 atoms. All the theories provide general guiding
principles of constructing an optimal calculation for simulating nanostructure
processes, since a nanostructured system consists of several competitive
regions, such as bulk and surface regions, and the simulation is designed to
reproduce the competition with an optimal computational cost.Comment: 19 pages, 6 figures. To appear in J. Phys. Cond. Matt. A preprint PDF
file in better graphics is available at
http://fujimac.t.u-tokyo.ac.jp/lses/index_e.htm
Linear Algebraic Calculation of Green's function for Large-Scale Electronic Structure Theory
A linear algebraic method named the shifted
conjugate-orthogonal-conjugate-gradient method is introduced for large-scale
electronic structure calculation. The method gives an iterative solver
algorithm of the Green's function and the density matrix without calculating
eigenstates.The problem is reduced to independent linear equations at many
energy points and the calculation is actually carried out only for a single
energy point. The method is robust against the round-off error and the
calculation can reach the machine accuracy. With the observation of residual
vectors, the accuracy can be controlled, microscopically, independently for
each element of the Green's function, and dynamically, at each step in
dynamical simulations. The method is applied to both semiconductor and metal.Comment: 10 pages, 9 figures. To appear in Phys. Rev. B. A PDF file with
better graphics is available at http://fujimac.t.u-tokyo.ac.jp/lses
Dynamical brittle fractures of nanocrystalline silicon using large-scale electronic structure calculations
A hybrid scheme between large-scale electronic structure calculations is
developed and applied to nanocrystalline silicon with more than 10 atoms.
Dynamical fracture processes are simulated under external loads in the [001]
direction. We shows that the fracture propagates anisotropically on the (001)
plane and reconstructed surfaces appear with asymmetric dimers. Step structures
are formed in larger systems, which is understood as the beginning of a
crossover between nanoscale and macroscale samples.Comment: 10 pages, 4 figure
Timesaving Double-Grid Method for Real-Space Electronic-Structure Calculations
We present a simple and efficient technique in ab initio electronic-structure
calculation utilizing real-space double-grid with a high density of grid points
in the vicinity of nuclei. This technique promises to greatly reduce the
overhead for performing the integrals that involves non-local parts of
pseudopotentials, with keeping a high degree of accuracy. Our procedure gives
rise to no Pulay forces, unlike other real-space methods using adaptive
coordinates. Moreover, we demonstrate the potential power of the method by
calculating several properties of atoms and molecules.Comment: 4 pages, 5 figure
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