Density functional theory: modeling, mathematical analysis, computational methods, and applications
Density functional theory (DFT) provides the most widely used models for simulating molecules and materials based on the fundamental laws of quantum mechanics. It plays a central role in a huge spectrum of applications in chemistry, physics, and materials science.Quantum mechanics describes a system...
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| Weitere Verfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2023]
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| Schriftenreihe: | Mathematics and molecular modeling
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| Schlagworte: | |
| Zusammenfassung: | Density functional theory (DFT) provides the most widely used models for simulating molecules and materials based on the fundamental laws of quantum mechanics. It plays a central role in a huge spectrum of applications in chemistry, physics, and materials science.Quantum mechanics describes a system of N interacting particles in the physical 3-dimensional space by a partial differential equation in 3N spatial variables. The standard numerical methods thus incur an exponential increase of computational effort with N, a phenomenon known as the curse of dimensionality; in practice these methods already fail beyond N=2. DFT overcomes this problem by1) reformulating the N-body problem involving functions of 3N variables in terms of the density, a function of 3 variables, 2) approximating it by a pioneering hybrid approach which keeps important ab initio contributions and re-models the remainder in a data-driven way.This book intends to be an accessible, yet state-of-art text on DFT for graduate students and researchers in applied and computational mathematics, physics, chemistry, and materials science. It introduces and reviews the main models of DFT, covering their derivation and mathematical properties, numerical treatment, and applications |
| Beschreibung: | xix, 580 Seiten 235 mm |
| ISBN: | 9783031223396 |
Internformat
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| 520 | |a Density functional theory (DFT) provides the most widely used models for simulating molecules and materials based on the fundamental laws of quantum mechanics. It plays a central role in a huge spectrum of applications in chemistry, physics, and materials science.Quantum mechanics describes a system of N interacting particles in the physical 3-dimensional space by a partial differential equation in 3N spatial variables. The standard numerical methods thus incur an exponential increase of computational effort with N, a phenomenon known as the curse of dimensionality; in practice these methods already fail beyond N=2. DFT overcomes this problem by1) reformulating the N-body problem involving functions of 3N variables in terms of the density, a function of 3 variables, 2) approximating it by a pioneering hybrid approach which keeps important ab initio contributions and re-models the remainder in a data-driven way.This book intends to be an accessible, yet state-of-art text on DFT for graduate students and researchers in applied and computational mathematics, physics, chemistry, and materials science. It introduces and reviews the main models of DFT, covering their derivation and mathematical properties, numerical treatment, and applications | ||
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| spelling | Density functional theory modeling, mathematical analysis, computational methods, and applications Erid Cancès, Gero Friesecke, editors Cham, Switzerland Springer [2023] xix, 580 Seiten 235 mm txt rdacontent n rdamedia nc rdacarrier Mathematics and molecular modeling Density functional theory (DFT) provides the most widely used models for simulating molecules and materials based on the fundamental laws of quantum mechanics. It plays a central role in a huge spectrum of applications in chemistry, physics, and materials science.Quantum mechanics describes a system of N interacting particles in the physical 3-dimensional space by a partial differential equation in 3N spatial variables. The standard numerical methods thus incur an exponential increase of computational effort with N, a phenomenon known as the curse of dimensionality; in practice these methods already fail beyond N=2. DFT overcomes this problem by1) reformulating the N-body problem involving functions of 3N variables in terms of the density, a function of 3 variables, 2) approximating it by a pioneering hybrid approach which keeps important ab initio contributions and re-models the remainder in a data-driven way.This book intends to be an accessible, yet state-of-art text on DFT for graduate students and researchers in applied and computational mathematics, physics, chemistry, and materials science. It introduces and reviews the main models of DFT, covering their derivation and mathematical properties, numerical treatment, and applications Condensed matter Atoms Molecules Quantum chemistry Electronics—Materials Materials science—Data processing Mathematics Dichtefunktionalformalismus (DE-588)4258514-4 gnd rswk-swf Hardcover, Softcover / Mathematik (DE-588)4143413-4 Aufsatzsammlung gnd-content Dichtefunktionalformalismus (DE-588)4258514-4 s DE-604 Cancès, Eric edt Friesecke, Gero 1964- (DE-588)1241384444 edt Erscheint auch als Online-Ausgabe 978-3-031-22340-2 |
| spellingShingle | Density functional theory modeling, mathematical analysis, computational methods, and applications Condensed matter Atoms Molecules Quantum chemistry Electronics—Materials Materials science—Data processing Mathematics Dichtefunktionalformalismus (DE-588)4258514-4 gnd |
| subject_GND | (DE-588)4258514-4 (DE-588)4143413-4 |
| title | Density functional theory modeling, mathematical analysis, computational methods, and applications |
| title_auth | Density functional theory modeling, mathematical analysis, computational methods, and applications |
| title_exact_search | Density functional theory modeling, mathematical analysis, computational methods, and applications |
| title_exact_search_txtP | Density functional theory modeling, mathematical analysis, computational methods, and applications |
| title_full | Density functional theory modeling, mathematical analysis, computational methods, and applications Erid Cancès, Gero Friesecke, editors |
| title_fullStr | Density functional theory modeling, mathematical analysis, computational methods, and applications Erid Cancès, Gero Friesecke, editors |
| title_full_unstemmed | Density functional theory modeling, mathematical analysis, computational methods, and applications Erid Cancès, Gero Friesecke, editors |
| title_short | Density functional theory |
| title_sort | density functional theory modeling mathematical analysis computational methods and applications |
| title_sub | modeling, mathematical analysis, computational methods, and applications |
| topic | Condensed matter Atoms Molecules Quantum chemistry Electronics—Materials Materials science—Data processing Mathematics Dichtefunktionalformalismus (DE-588)4258514-4 gnd |
| topic_facet | Condensed matter Atoms Molecules Quantum chemistry Electronics—Materials Materials science—Data processing Mathematics Dichtefunktionalformalismus Aufsatzsammlung |
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