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Ultra-large-scale electronic structure theory and numerical algorithm
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Ultra-large-scale electronic structure theory
and numerical algorithm
T. Hoshi1,2
1Department of Applied Mathematics and Physics, Tottori University;
2Core Research for Evolutional Science and Technology, Japan Science and
Technology Agency (CREST-JST)
This article is composed of two parts; In the first part (Sec.
1), the ultra-large-scale electronic structure theory is reviewed
for (i) its fundamental numerical algorithm and (ii) its role in
nano-material science. The second part (Sec. 2) is devoted to
the mathematical foundation of the large-scale electronic struc-
ture theory and their numerical aspects.
1 Large-scale electronic structure theory and
nano-material science
1.1 Overview
Nowadays electronic structure theory gives a microscopic foun-
dation of material science and provides atomistic simulations
in which electrons are treated as wavefunction within quantum
mechanics. An example is given in the upper left panel of Fig.1.
For years, we have developed fundamental theory and program
code for large-scale electronic structure calculations, particu-
larly, for nano materials. [1-6] The code was applied to several
nano materials with 102-107 atoms, whereas standard electronic
structure calculations are carried out typically with 102 atoms.
Two application studies, for silicon and gold, are shown in the
right panels and the lower left panels of Fig.1, respectively. Now
1
the code is being reorganized as a simulation package, named as
ELSES (Extra-Large-Scale Electronic Structure calculation), for
a wider range of users and applications in science and industry.
[6]
Figure 1: Upper left panel: Example of calculated electronic wavefunction
on a silicon surface (A ‘π-type’ electron state on Si(111)-2x1 surface, given by
a standard electronic structure calculation). Right panels: Application of our
code to fracture dynamics of silicon crystal. [2] In results, the fracture pat
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