Mathematical Modeling of Properties and Structures of Crystals: From Quantum Approach to Machine Learning
The crystalline state of matter serves as a reference point in the context of studies of properties of a variety of chemical compounds. This is due to the fact that prepared crystalline solids of practically useful materials (inorganic or organic) may be utilized for the thorough characterization of...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Crystals |
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| Online Access: | https://www.mdpi.com/2073-4352/15/1/61 |
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| author | Grzegorz Matyszczak Christopher Jasiak Gabriela Rusinkiewicz Kinga Domian Michał Brzozowski Krzysztof Krawczyk |
| author_facet | Grzegorz Matyszczak Christopher Jasiak Gabriela Rusinkiewicz Kinga Domian Michał Brzozowski Krzysztof Krawczyk |
| author_sort | Grzegorz Matyszczak |
| collection | DOAJ |
| description | The crystalline state of matter serves as a reference point in the context of studies of properties of a variety of chemical compounds. This is due to the fact that prepared crystalline solids of practically useful materials (inorganic or organic) may be utilized for the thorough characterization of important properties such as (among others) energy bandgap, light absorption, thermal and electric conductivity, and magnetic properties. For that reason it is important to develop mathematical descriptions (models) of properties and structures of crystals. They may be used for the interpretation of experimental data and, as well, for predictions of properties of novel, unknown compounds (i.e., the design of novel compounds for practical applications such as photovoltaics, catalysis, electronic devices, etc.). The aim of this article is to review the most important mathematical models of crystal structures and properties that vary, among others, from quantum models (e.g., density functional theory, DFT), through models of discrete mathematics (e.g., cellular automata, CA), to machine learning (e.g., artificial neural networks, ANNs). |
| format | Article |
| id | doaj-art-beb707aeccdc4e588e9007ab340dbcc8 |
| institution | Kabale University |
| issn | 2073-4352 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Crystals |
| spelling | doaj-art-beb707aeccdc4e588e9007ab340dbcc82025-01-24T13:28:10ZengMDPI AGCrystals2073-43522025-01-011516110.3390/cryst15010061Mathematical Modeling of Properties and Structures of Crystals: From Quantum Approach to Machine LearningGrzegorz Matyszczak0Christopher Jasiak1Gabriela Rusinkiewicz2Kinga Domian3Michał Brzozowski4Krzysztof Krawczyk5Chair of Chemical Technology, Faculty of Chemistry, Warsaw University of Technology, Noakowski Str. 3, 00-664 Warsaw, PolandChair of Chemical Technology, Faculty of Chemistry, Warsaw University of Technology, Noakowski Str. 3, 00-664 Warsaw, PolandChair of Chemical Technology, Faculty of Chemistry, Warsaw University of Technology, Noakowski Str. 3, 00-664 Warsaw, PolandChair of Chemical Technology, Faculty of Chemistry, Warsaw University of Technology, Noakowski Str. 3, 00-664 Warsaw, PolandChair of Chemical Technology, Faculty of Chemistry, Warsaw University of Technology, Noakowski Str. 3, 00-664 Warsaw, PolandChair of Chemical Technology, Faculty of Chemistry, Warsaw University of Technology, Noakowski Str. 3, 00-664 Warsaw, PolandThe crystalline state of matter serves as a reference point in the context of studies of properties of a variety of chemical compounds. This is due to the fact that prepared crystalline solids of practically useful materials (inorganic or organic) may be utilized for the thorough characterization of important properties such as (among others) energy bandgap, light absorption, thermal and electric conductivity, and magnetic properties. For that reason it is important to develop mathematical descriptions (models) of properties and structures of crystals. They may be used for the interpretation of experimental data and, as well, for predictions of properties of novel, unknown compounds (i.e., the design of novel compounds for practical applications such as photovoltaics, catalysis, electronic devices, etc.). The aim of this article is to review the most important mathematical models of crystal structures and properties that vary, among others, from quantum models (e.g., density functional theory, DFT), through models of discrete mathematics (e.g., cellular automata, CA), to machine learning (e.g., artificial neural networks, ANNs).https://www.mdpi.com/2073-4352/15/1/61DFTdensity functional theorymolecular dynamicscellular automatamachine learningcrystal structure |
| spellingShingle | Grzegorz Matyszczak Christopher Jasiak Gabriela Rusinkiewicz Kinga Domian Michał Brzozowski Krzysztof Krawczyk Mathematical Modeling of Properties and Structures of Crystals: From Quantum Approach to Machine Learning Crystals DFT density functional theory molecular dynamics cellular automata machine learning crystal structure |
| title | Mathematical Modeling of Properties and Structures of Crystals: From Quantum Approach to Machine Learning |
| title_full | Mathematical Modeling of Properties and Structures of Crystals: From Quantum Approach to Machine Learning |
| title_fullStr | Mathematical Modeling of Properties and Structures of Crystals: From Quantum Approach to Machine Learning |
| title_full_unstemmed | Mathematical Modeling of Properties and Structures of Crystals: From Quantum Approach to Machine Learning |
| title_short | Mathematical Modeling of Properties and Structures of Crystals: From Quantum Approach to Machine Learning |
| title_sort | mathematical modeling of properties and structures of crystals from quantum approach to machine learning |
| topic | DFT density functional theory molecular dynamics cellular automata machine learning crystal structure |
| url | https://www.mdpi.com/2073-4352/15/1/61 |
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