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Updated: May 23, 2026
08:04
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
An order-N electronic structure theory with generalized eigenvalue equations and its application to a
T Hoshi1, S Yamamoto, T Fujiwara
1Department of Applied Mathematics and Physics, Tottori University, Tottori, Japan. hoshi@damp.tottori-u.ac.jp
Summary
The multiple Arnoldi method enables large-scale electronic structure calculations using generalized eigenvalue equations. This computational approach efficiently simulates materials with millions of atoms on standard hardware.
Area of Science:
- Computational Physics
- Materials Science
- Linear Algebra
Background:
- Large-scale electronic structure calculations are computationally intensive.
- Generalized eigenvalue equations are common in quantum mechanics and materials simulations.
- Existing methods face scalability challenges for systems with many atoms.
Purpose of the Study:
- To introduce a novel linear algebraic theory, the multiple Arnoldi method.
- To enable efficient, large-scale (order-N) electronic structure calculations.
- To implement and validate the method for finite-temperature molecular dynamics simulations.
Main Methods:
- Developed the multiple Arnoldi method based on linear algebra.
- Solved simultaneous linear equations (zS - H)x = b using multiple Krylov subspaces.
- Implemented the method in the ELSES simulation package for tight-binding Hamiltonians.
Main Results:
- Successfully performed large-scale electronic structure calculations.
- Achieved simulations with up to 10(7) atoms on a single workstation.
- Demonstrated parallel efficiency using up to 1024 CPU cores.
Conclusions:
- The multiple Arnoldi method provides a scalable approach for electronic structure computations.
- The ELSES package facilitates large-scale simulations of metallic and insulating materials.
- The method shows significant potential for advancing materials science research.
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