An order-N electronic structure theory with generalized eigenvalue equations and its application to a ten-million-atom system

A linear-algebraic theory called 'multiple Arnoldi method' is presented and realizes large-scale (order-N) electronic structure calculation with generalized eigen-value equations. A set of linear equations, in the form of (zS-H) x = b, are solved simultaneously with multiple Krylov subspaces. The method is implemented in a simulation package ELSES (http://www.elses.jp) with tight-binding-form Hamiltonians. A finite-temperature molecular dynamics simulation is carried out for metallic and insulating materials. A calculation with $10^7$ atoms was realized by a workstation. The parallel efficiency is shown upto 1,024 CPU cores.Comment: 9 pages, 3 figures. To appear in J. Phys.: Condens. Matte

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$^5$ 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

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

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

Elaboration and characterization of Fe1–xO thin films sputter deposited from magnetite target

Majority of the authors report elaboration of iron oxide thin films by reactive magnetron sputtering from an iron target with Ar–O2 gas mixture. Instead of using the reactive sputtering of a metallic target we report here the preparation of Fe1–xOthin films, directly sputtered froma magnetite target in a pure argon gas flow with a bias power applied. This oxide is generally obtained at very low partial oxygen pressure and high temperature.We showed that bias sputtering which can be controlled very easily can lead to reducing conditions during deposition of oxide thin film on simple glass substrates. The proportion of wustite was directly adjusted bymodifying the power of the substrate polarization. Atomic force microscopy was used to observe these nanostructured layers. Mössbauer measurements and electrical properties versus bias polarization and annealing temperature are also reported

Efficient and Accurate Linear Algebraic Methods for Large-scale Electronic Structure Calculations with Non-orthogonal Atomic Orbitals

The need for large-scale electronic structure calculations arises recently in the field of material physics and efficient and accurate algebraic methods for large simultaneous linear equations become greatly important. We investigate the generalized shifted conjugate orthogonal conjugate gradient method, the generalized Lanczos method and the generalized Arnoldi method. They are the solver methods of large simultaneous linear equations of one-electron Schr\"odinger equation and maps the whole Hilbert space to a small subspace called the Krylov subspace. These methods are applied to systems of fcc Au with the NRL tight-binding Hamiltonian (Phys. Rev. B {\bf 63}, 195101 (2001)). We compare results by these methods and the exact calculation and show them equally accurate. The system size dependence of the CPU time is also discussed. The generalized Lanczos method and the generalized Arnoldi method are the most suitable for the large-scale molecular dynamics simulations from the view point of CPU time and memory size.Comment: 13pages, 7figure

From nonwetting to prewetting: the asymptotic behavior of 4He drops on alkali substrates

We investigate the spreading of 4He droplets on alkali surfaces at zero temperature, within the frame of Finite Range Density Functional theory. The equilibrium configurations of several 4He_N clusters and their asymptotic trend with increasing particle number N, which can be traced to the wetting behavior of the quantum fluid, are examined for nanoscopic droplets. We discuss the size effects, inferring that the asymptotic properties of large droplets correspond to those of the prewetting film

O(N) methods in electronic structure calculations

Linear scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high performance computers. The linear scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas is then discussed. The applications of linear scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear scaling methods are discussed.Comment: 85 pages, 15 figures, 488 references. Resubmitted to Rep. Prog. Phys (small changes

Monitoring Voltage-Dependent Charge Displacement of Shaker B-IR K+ Ion Channels Using Radio Frequency Interrogation

Here we introduce a new technique that probes voltage-dependent charge displacements of excitable membrane-bound proteins using extracellularly applied radio frequency (RF, 500 kHz) electric fields. Xenopus oocytes were used as a model cell for these experiments, and were injected with cRNA encoding Shaker B-IR (ShB-IR) K+ ion channels to express large densities of this protein in the oocyte membranes. Two-electrode voltage clamp (TEVC) was applied to command whole-cell membrane potential and to measure channel-dependent membrane currents. Simultaneously, RF electric fields were applied to perturb the membrane potential about the TEVC level and to measure voltage-dependent RF displacement currents. ShB-IR expressing oocytes showed significantly larger changes in RF displacement currents upon membrane depolarization than control oocytes. Voltage-dependent changes in RF displacement currents further increased in ShB-IR expressing oocytes after ∼120 µM Cu2+ addition to the external bath. Cu2+ is known to bind to the ShB-IR ion channel and inhibit Shaker K+ conductance, indicating that changes in the RF displacement current reported here were associated with RF vibration of the Cu2+-linked mobile domain of the ShB-IR protein. Results demonstrate the use of extracellular RF electrodes to interrogate voltage-dependent movement of charged mobile protein domains — capabilities that might enable detection of small changes in charge distribution associated with integral membrane protein conformation and/or drug–protein interactions