LEADER 04881nam 22008055 450 001 9910735774803321 005 20240509130142.0 010 $a3-031-22340-3 024 7 $a10.1007/978-3-031-22340-2 035 $a(MiAaPQ)EBC30654998 035 $a(Au-PeEL)EBL30654998 035 $a(DE-He213)978-3-031-22340-2 035 $a(PPN)272253928 035 $a(CKB)27675139000041 035 $a(EXLCZ)9927675139000041 100 $a20230718d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDensity Functional Theory $eModeling, Mathematical Analysis, Computational Methods, and Applications /$fedited by Eric Cancès, Gero Friesecke 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (595 pages) 225 1 $aMathematics and Molecular Modeling 311 08$aPrint version: Cancès, Eric Density Functional Theory Cham : Springer International Publishing AG,c2023 9783031223396 327 $aChapter 1. Review of approximations for the exchange-correlation energy in density-functional theory -- Chapter 2. On connecting density functional approximations to theory -- Chapter 3. Universal functionals in density functional theory -- Chapter 4. The strong-interaction limit of density functional theory -- Chapter 5. Moreau?Yosida regularization in DFT -- Chapter 6. Thermodynamic limits of electronic systems -- Chapter 7. Numerical methods for Kohn?Sham models: discretization, algorithms, and error analysis -- Chapter 8. Recent progress in evaluating the Kohn?Sham map -- Chapter 9. Augmented plane wave methods for full-potential calculations -- Chapter 10. Finite Element Methods for Density Functional Theory -- Chapter 11. Flexibilities of wavelets as a computational basis set for large-scale electronic structure calculations -- Chapter 12. Accurate approximations of density functional theory for large systems with applications to defects in crystalline solids -- Glossary -- Notation. 330 $aDensity 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 by 1) 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. . 410 0$aMathematics and Molecular Modeling 606 $aMathematics 606 $aCondensed matter 606 $aAtoms 606 $aMolecules 606 $aQuantum chemistry 606 $aElectronics$xMaterials 606 $aMaterials science$xData processing 606 $aMathematics 606 $aCondensed Matter Physics 606 $aAtomic, Molecular and Chemical Physics 606 $aQuantum Chemistry 606 $aElectronic Materials 606 $aComputational Materials Science 606 $aTeoria del funcional de densitat$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematics. 615 0$aCondensed matter. 615 0$aAtoms. 615 0$aMolecules. 615 0$aQuantum chemistry. 615 0$aElectronics$xMaterials. 615 0$aMaterials science$xData processing. 615 14$aMathematics. 615 24$aCondensed Matter Physics. 615 24$aAtomic, Molecular and Chemical Physics. 615 24$aQuantum Chemistry. 615 24$aElectronic Materials. 615 24$aComputational Materials Science. 615 7$aTeoria del funcional de densitat 676 $a510 676 $a541.28 700 $aCancès$b Eric$01378497 701 $aFriesecke$b Gero$01378498 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910735774803321 996 $aDensity Functional Theory$93417111 997 $aUNINA