Takeo Hoshi

Linear algebraic calculation of the 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 Greens 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 Greens function, and dynamically, at each step in dynamical simulations. The method is applied to both a semiconductor and a metal.

Theory of Composite-Band Wannier States and Order-N Electronic-Structure Calculations

From the order-N electronic-structure formulation, a Hamiltonian is derived, of which the lowest eigen state is the generalized or composite-band Wannier state. This Hamiltonian maps the locality of the Wannier state to that of a virtual impurity state and to a perturbation from a bonding orbital. These theories are demonstrated in the diamond-structure solids, where the Wannier states are constructed by a practical order-N algorithm with the Hamiltonian. The results give a prototypical picture of the Wannier states in covalent-bonded systems.

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

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

Dynamical Brittle Fractures of Nanocrystalline Silicon using Large-Scale Electronic Structure Calculations

(111)

Krylov subspace method for molecular dynamics simulation based on large-scale electronic structure theory

-

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

(2 x 1)

Fully-Selfconsistent Electronic-Structure Calculation Using Nonorthogonal Localized Orbitals within a Finite-Difference Real-Space Scheme and Ultrasoft Pseudopotential

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.

Solution of generalized shifted linear systems with complex symmetric matrices

A hybrid scheme between large-scale electronic structure calculations is developed and applied to nanocrystalline silicon with more than 10 5 atoms. Dynamical fracture processes are simulated under external loads in the [001] direction. We show how the fracture propagates anisotropically on the (001) plane and reconstructed surfaces appear with asymmetric dimers. Step structures are formed in larger systems, which is explained by the beginning of a crossover between nanoscale and macroscale samples.

Hybrid Numerical Solvers for Massively Parallel Eigenvalue Computations and Their Benchmark with Electronic Structure Calculations

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.

A Numerical Method for Calculating the Green's Function Arising from Electronic Structure Theory

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 (2000) 3773]. 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 2 � 10 6 atoms is 3.0 min 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.