Gradient Flow Based Discretized Kohn-Sham Density Functional Theory Article Swipe
Xiaoying Dai
,
Qiao Wang
,
Aihui Zhou
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1907.06321
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1907.06321
In this paper, we propose and analyze a gradient flow based Kohn-Sham density functional theory. First, we prove that the critical point of the gradient flow based model can be a local minimizer of the Kohn-Sham total energy. Then we apply a midpoint scheme to carry out the temporal discretization. It is shown that the critical point of the Kohn-Sham energy can be well-approximated by the scheme. In particular, based on the midpoint scheme, we design an orthogonality preserving iteration scheme to minimize the Kohn-Sham energy and show that the orthogonality preserving iteration scheme produces approximations that are orthogonal and convergent to a local minimizer under reasonable assumptions. Finally, we report numerical experiments that support our theory.
Related Topics
Concepts
Kohn–Sham equations
Discretization
Balanced flow
Orthogonality
Mathematics
Midpoint
Scheme (mathematics)
Energy functional
Flow (mathematics)
Point (geometry)
Applied mathematics
Critical point (mathematics)
Mathematical analysis
Density functional theory
Energy (signal processing)
Mathematical optimization
Geometry
Physics
Quantum mechanics
Statistics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1907.06321
- https://arxiv.org/pdf/1907.06321
- OA Status
- green
- Cited By
- 3
- References
- 32
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2956460414
All OpenAlex metadata
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https://openalex.org/W2956460414Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.1907.06321Digital Object Identifier
- Title
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Gradient Flow Based Discretized Kohn-Sham Density Functional TheoryWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2019Year of publication
- Publication date
-
2019-07-15Full publication date if available
- Authors
-
Xiaoying Dai, Qiao Wang, Aihui ZhouList of authors in order
- Landing page
-
https://arxiv.org/abs/1907.06321Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1907.06321Direct 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
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https://arxiv.org/pdf/1907.06321Direct OA link when available
- Concepts
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Kohn–Sham equations, Discretization, Balanced flow, Orthogonality, Mathematics, Midpoint, Scheme (mathematics), Energy functional, Flow (mathematics), Point (geometry), Applied mathematics, Critical point (mathematics), Mathematical analysis, Density functional theory, Energy (signal processing), Mathematical optimization, Geometry, Physics, Quantum mechanics, StatisticsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
3Total citation count in OpenAlex
- Citations by year (recent)
-
2023: 2, 2021: 1Per-year citation counts (last 5 years)
- References (count)
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32Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.prove | 17 |
| abstract_inverted_index.shown | 52 |
| abstract_inverted_index.total | 36 |
| abstract_inverted_index.under | 105 |
| abstract_inverted_index.First, | 15 |
| abstract_inverted_index.design | 75 |
| abstract_inverted_index.energy | 60, 85 |
| abstract_inverted_index.paper, | 2 |
| abstract_inverted_index.report | 110 |
| abstract_inverted_index.scheme | 43, 80, 93 |
| abstract_inverted_index.analyze | 6 |
| abstract_inverted_index.density | 12 |
| abstract_inverted_index.energy. | 37 |
| abstract_inverted_index.propose | 4 |
| abstract_inverted_index.scheme, | 73 |
| abstract_inverted_index.scheme. | 66 |
| abstract_inverted_index.support | 114 |
| abstract_inverted_index.theory. | 14, 116 |
| abstract_inverted_index.Finally, | 108 |
| abstract_inverted_index.critical | 20, 55 |
| abstract_inverted_index.gradient | 8, 24 |
| abstract_inverted_index.midpoint | 42, 72 |
| abstract_inverted_index.minimize | 82 |
| abstract_inverted_index.produces | 94 |
| abstract_inverted_index.temporal | 48 |
| abstract_inverted_index.Kohn-Sham | 11, 35, 59, 84 |
| abstract_inverted_index.iteration | 79, 92 |
| abstract_inverted_index.minimizer | 32, 104 |
| abstract_inverted_index.numerical | 111 |
| abstract_inverted_index.convergent | 100 |
| abstract_inverted_index.functional | 13 |
| abstract_inverted_index.orthogonal | 98 |
| abstract_inverted_index.preserving | 78, 91 |
| abstract_inverted_index.reasonable | 106 |
| abstract_inverted_index.experiments | 112 |
| abstract_inverted_index.particular, | 68 |
| abstract_inverted_index.assumptions. | 107 |
| abstract_inverted_index.orthogonality | 77, 90 |
| abstract_inverted_index.approximations | 95 |
| abstract_inverted_index.discretization. | 49 |
| abstract_inverted_index.well-approximated | 63 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/7 |
| sustainable_development_goals[0].score | 0.8100000023841858 |
| sustainable_development_goals[0].display_name | Affordable and clean energy |
| citation_normalized_percentile |