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Updated: May 31, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Nonlinear algorithm for the solution of the Kohn-Sham equations in solids.

Jian Wang¹, Yu Wang, Shaoying Yu

¹School of Science, Huzhou University, Zhejiang 313000, People's Republic of China.

Journal of Physics. Condensed Matter : an Institute of Physics Journal

|June 22, 2011

Summary

This study introduces a new Full Approximation Storage (FAS) multigrid method for solving complex electronic structure problems. The FAS scheme directly addresses self-consistency in calculations, improving efficiency for materials like Silicon and Aluminum.

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Last Updated: May 31, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

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Published on: May 27, 2020

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Published on: April 8, 2020

Area of Science:

Computational Physics
Materials Science
Quantum Chemistry

Background:

Traditional methods linearize Kohn-Sham equations, requiring iterative potential updates.
This linearization can be computationally intensive for electronic structure calculations.

Purpose of the Study:

To apply the Full Approximation Storage (FAS) nonlinear multigrid scheme to Kohn-Sham equations.
To directly solve the nonlinear self-consistent problem for pseudopotential band structure calculations.
To improve the efficiency of electronic structure calculations.

Main Methods:

The Full Approximation Storage (FAS) multigrid algorithm was implemented.
The FAS scheme directly solves the nonlinear self-consistent problem, bypassing traditional linearization.
Eigenvalue problems are integrated within the FAS framework, evolving with the self-consistent density correction.

Main Results:

The FAS scheme was successfully applied to pseudopotential band structure calculations.
Demonstrated calculations for Silicon (Si) and Aluminum (Al) using the new method.
The method directly computes self-consistent density errors and applies corrections via coarse grid solutions.

Conclusions:

The Full Approximation Storage (FAS) scheme offers a direct and potentially more efficient approach to solving Kohn-Sham equations.
This nonlinear multigrid method integrates self-consistency and eigenvalue solutions within a unified framework.
The approach shows promise for accelerating electronic structure calculations in materials science.