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

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

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

Theoretical analysis of GaAs/AlGaAs quantum dots in quantum wire array for intermediate band solar cell

A GaAs quantum dot (QD) array embedded in a AlGaAs host material was fabricated using a strain-free approach, through combination of neutral beam etching and atomic hydrogen-assisted molecular beam epitaxy regrowth. In this work, we performed theoretical simulations on a GaAs/AlGaAs quantum well, GaAs QD and QD array based intermediated band solar cell (IBSC) using a combined multiband k·p and drift-diffusion transportation method. The electronic structure, IB band dispersion, and optical transitions, including absorption and spontaneous emission among the valence band, intermediate band, and conduction band, were calculated. Based on these results, maximum conversion efficiency of GaAs/AlGaAs QD array based IBSC devices were calculated by a drift-diffusion model adapted to IBSC under the radiative recombination limit

Identification of hot-spot residues in protein-protein interactions by computational docking

<p>Abstract</p> <p>Background</p> <p>The study of protein-protein interactions is becoming increasingly important for biotechnological and therapeutic reasons. We can define two major areas therein: the structural prediction of protein-protein binding mode, and the identification of the relevant residues for the interaction (so called 'hot-spots'). These hot-spot residues have high interest since they are considered one of the possible ways of disrupting a protein-protein interaction. Unfortunately, large-scale experimental measurement of residue contribution to the binding energy, based on alanine-scanning experiments, is costly and thus data is fairly limited. Recent computational approaches for hot-spot prediction have been reported, but they usually require the structure of the complex.</p> <p>Results</p> <p>We have applied here normalized interface propensity (<it>NIP</it>) values derived from rigid-body docking with electrostatics and desolvation scoring for the prediction of interaction hot-spots. This parameter identifies hot-spot residues on interacting proteins with predictive rates that are comparable to other existing methods (up to 80% positive predictive value), and the advantage of not requiring any prior structural knowledge of the complex.</p> <p>Conclusion</p> <p>The <it>NIP </it>values derived from rigid-body docking can reliably identify a number of hot-spot residues whose contribution to the interaction arises from electrostatics and desolvation effects. Our method can propose residues to guide experiments in complexes of biological or therapeutic interest, even in cases with no available 3D structure of the complex.</p