Numerical aspect of large-scale electronic state calculation for flexible device material

Numerical aspects of large-scale electronic state calculation are explored on flexible organic device materials. Physical theory, numerical method and real application studies are discussed in the context of application-algorithm-architecture co-design. An application study was carried out for disordered organic thin film. Participation ratio, a measure for the spatial extension of electronic wavefunction is focused on, since it is crucial for device property. A data scientific research is reported for a classification problem of disordered organic polymers, in which participation ratio is used as descriptor. These application studies indicate the potential need of purpose-specific solvers for internal eigenpairs.

[1]  R. Martin,et al.  Electronic Structure: Basic Theory and Practical Methods , 2004 .

[2]  D. Thouless,et al.  Electrons in disordered systems and the theory of localization , 1974 .

[3]  Hiroto Imachi,et al.  Hybrid Numerical Solvers for Massively Parallel Eigenvalue Computations and Their Benchmark with Electronic Structure Calculations , 2015, J. Inf. Process..

[4]  Takao Someya,et al.  Human-friendly organic integrated circuits , 2011 .

[5]  T. Sakurai,et al.  A projection method for generalized eigenvalue problems using numerical integration , 2003 .

[6]  A Marek,et al.  The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science , 2014, Journal of physics. Condensed matter : an Institute of Physics journal.

[7]  R. S. Mulliken.  Electronic Population Analysis on LCAO–MO Molecular Wave Functions. I , 1955 .

[8]  Fumiyoshi Shoji,et al.  Extremely Scalable Algorithm for 108-atom Quantum Material Simulation on the Full System of the K Computer , 2016, 2016 7th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA).

[9]  R. J. Bell.  The dynamics of disordered lattices , 1972 .

[10]  Dongjin Lee,et al.  Solution of the k-th eigenvalue problem in large-scale electronic structure calculations , 2017, J. Comput. Phys..

[11]  T. Someya,et al.  Thermally stable, highly efficient, ultraflexible organic photovoltaics , 2018, Proceedings of the National Academy of Sciences.

[12]  Satoshi Watanabe,et al.  Design principle for increasing charge mobility of π-conjugated polymers using regularly localized molecular orbitals , 2013, Nature Communications.

[13]  Junmei Wang,et al.  Development and testing of a general amber force field , 2004, J. Comput. Chem..

[14]  R. J. Bell,et al.  Atomic vibrations in vitreous silica , 1970 .

[15]  Yohei Akiyama,et al.  Novel linear algebraic theory and one-hundred-million-atom electronic structure calculation on the K computer , 2013, 1307.3218.

[16]  Eric Polizzi,et al.  A Density Matrix-based Algorithm for Solving Eigenvalue Problems , 2009, ArXiv.

[17]  Matthias Scheffler,et al.  Ab initio molecular simulations with numeric atom-centered orbitals , 2009, Comput. Phys. Commun..

[18]  G. Gelinck,et al.  Flexible active-matrix displays and shift registers based on solution-processed organic transistors , 2004, Nature materials.

[19]  Hiroyuki Matsui,et al.  Distribution of localized states from fine analysis of electron spin resonance spectra in organic transistors. , 2010, Physical review letters.

[20]  Yamamoto,et al.  Scaling properties of wave functions and transport coefficients in quasicrystals. , 1996, Physical review. B, Condensed matter.

[21]  Franz Wegner,et al.  Inverse participation ratio in 2+ε dimensions , 1980 .

[22]  T. Fujiwara,et al.  Domain boundary formation in helical multishell gold nanowires , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[23]  T. Fujiwara,et al.  An order-N electronic structure theory with generalized eigenvalue equations and its application to a ten-million-atom system , 2012, Journal of physics. Condensed matter : an Institute of Physics journal.

[24]  Richard M. Martin.  Electronic Structure: Frontmatter , 2004 .

[25]  D. van der Spoel,et al.  GROMACS: A message-passing parallel molecular dynamics implementation , 1995 .

[26]  Zhenan Bao,et al.  Organic Field-Effect Transistors , 2007 .

[27]  Kazuyuki Tanaka,et al.  EigenKernel , 2019, Japan journal of industrial and applied mathematics.

[28]  Chao Yang,et al.  A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems , 2015, SIAM J. Sci. Comput..