Mathematical Analysis and Numerical Approximations of Density Functional Theory Models for Metallic Systems Article Swipe
Xiaoying Dai
,
Stefano de Gironcoli
,
Bin Yang
,
Aihui Zhou
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2201.07035
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2201.07035
In this paper, we investigate the energy minimization model of the ensemble Kohn-Sham density functional theory for metallic systems, in which a pseudo-eigenvalue matrix and a general smearing approach are involved. We study the invariance and the existence of the minimizer of the energy functional. We propose an adaptive double step size strategy and the corresponding preconditioned conjugate gradient methods for solving the energy minimization model. Under some mild but reasonable assumptions, we prove the global convergence of our algorithms. Numerical experiments show that our algorithms are efficient, especially for large scale metallic systems. In particular, our algorithms produce convergent numerical approximations for some metallic systems, for which the traditional self-consistent field iterations fail to converge.
Related Topics
Concepts
Convergence (economics)
Eigenvalues and eigenvectors
Conjugate gradient method
Minification
Applied mathematics
Mathematics
Energy functional
Energy (signal processing)
Energy minimization
Mathematical optimization
Field (mathematics)
Computer science
Mathematical analysis
Physics
Economic growth
Statistics
Economics
Pure mathematics
Quantum mechanics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2201.07035
- https://arxiv.org/pdf/2201.07035
- OA Status
- green
- Cited By
- 1
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4221154358
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4221154358Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2201.07035Digital Object Identifier
- Title
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Mathematical Analysis and Numerical Approximations of Density Functional Theory Models for Metallic SystemsWork title
- Type
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preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2022Year of publication
- Publication date
-
2022-01-18Full publication date if available
- Authors
-
Xiaoying Dai, Stefano de Gironcoli, Bin Yang, Aihui ZhouList of authors in order
- Landing page
-
https://arxiv.org/abs/2201.07035Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2201.07035Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2201.07035Direct OA link when available
- Concepts
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Convergence (economics), Eigenvalues and eigenvectors, Conjugate gradient method, Minification, Applied mathematics, Mathematics, Energy functional, Energy (signal processing), Energy minimization, Mathematical optimization, Field (mathematics), Computer science, Mathematical analysis, Physics, Economic growth, Statistics, Economics, Pure mathematics, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
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2025: 1Per-year citation counts (last 5 years)
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.self-consistent | 110 |
| abstract_inverted_index.pseudo-eigenvalue | 22 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 4 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/7 |
| sustainable_development_goals[0].score | 0.8799999952316284 |
| sustainable_development_goals[0].display_name | Affordable and clean energy |
| citation_normalized_percentile |