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

Specific antigen of tumor cell transformed by DNA extracted from SV-40 virus

In the immunofluorescent study it has been revealed that rabbit sera immunized with transformed cells induced by SV-40 DNA, produce circulating antibody capable of re:lcting with intranuclear antigens synthesized by SV-40 complyte virus transforming process, In addition, the result confirmed that SV-40 DNA replicates DNA-containing viruses in the host cell and that also the genome coding for the synthesis of SV-40 tumor antigen is resposible for viral DNA.</p

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