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20240623213015.0 |
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m o d |
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cr cnu---unuuu |
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230724s2023 sz o 000 0 eng d |
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|a YDX
|b eng
|e rda
|c YDX
|d GW5XE
|d EBLCP
|d OCLCQ
|d YDX
|d OCLCO
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|a 1390919242
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|a 9783031223402
|q electronic book
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|a 3031223403
|q electronic book
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|z 303122339X
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|z 9783031223396
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7 |
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|a 10.1007/978-3-031-22340-2
|2 doi
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|a (OCoLC)1390916443
|z (OCoLC)1390919242
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|a QD462.6.D45
|b D45 2023
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|a HCDD
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|a Density functional theory :
|b modeling, mathematical analysis, computational methods and applications /
|c Eric Cancès, Gero Friesecke, editors.
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| 264 |
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|a Cham, Switzerland :
|b Springfer,
|c [2023]
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| 300 |
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|a 1 online resource
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| 336 |
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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| 490 |
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|a Mathematics and Molecular Modeling
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|a Intro -- Preface -- Reference -- Prologue: Early Days of Modern DFT (1964-1979) -- Contents -- Contributors -- List of Symbols -- Parameters of the Electronic Problem -- Electron Coordinates -- Wavefunctions, Density Matrices, Densities, Orbitals -- Functionals -- Energy Levels, Eigenvalues, Energy Densities, Fermi-Dirac Function -- Potentials and Kernels -- Operators -- Matrices -- Discretization Parameters, Basis Functions, Discretized Models -- 1 Review of Approximations for the Exchange-Correlation Energy in Density-Functional Theory -- 1.1 Basics of Density-Functional Theory
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|a 1.1.1 The Many-Body Problem -- 1.1.2 The Universal Density Functional -- 1.1.3 The Kohn-Sham Scheme -- 1.1.3.1 Decomposition of the Universal Functional -- 1.1.3.2 The Kohn-Sham Equations -- 1.1.3.3 Extension to Spin Density-Functional Theory -- 1.1.4 The Generalized Kohn-Sham Scheme -- 1.2 Exact Expressions and Constraints for the Kohn-Sham Exchange and Correlation Functionals -- 1.2.1 The Exchange and Correlation Holes -- 1.2.2 The Adiabatic Connection -- 1.2.3 One-Orbital and One-Electron Spatial Regions -- 1.2.4 Coordinate Scaling -- 1.2.4.1 Uniform Coordinate Scaling
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|a 1.2.4.2 Non-uniform Coordinate Scaling -- 1.2.5 Atoms in the Limit of Large Nuclear Charge -- 1.2.6 Lieb-Oxford Lower Bound -- 1.3 Semilocal Approximations for the Exchange-CorrelationEnergy -- 1.3.1 The Local-Density Approximation -- 1.3.2 The Gradient-Expansion Approximation -- 1.3.3 Generalized-Gradient Approximations -- 1.3.4 Meta-Generalized-Gradient Approximations -- 1.4 Single-Determinant Hybrid Approximations -- 1.4.1 Hybrid Approximations -- 1.4.2 Range-Separated Hybrid Approximations -- 1.5 Multideterminant Hybrid Approximations -- 1.5.1 Double-Hybrid Approximations
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|a 1.5.2 Range-Separated Double-Hybrid Approximations -- 1.5.2.1 Range-Separated One-Parameter Double-Hybrid Approximations -- 1.5.2.2 Range-Separated Two-Parameter Double-Hybrid Approximations -- 1.6 Semiempirical Dispersion Corrections and Nonlocal van der Waals Density Functionals -- 1.6.1 Semiempirical Dispersion Corrections -- 1.6.2 Nonlocal van der Waals Density Functionals -- 1.7 Orbital-Dependent Exchange-Correlation Density Functionals -- 1.7.1 Exact Exchange -- 1.7.2 Second-Order Görling-Levy Perturbation Theory -- 1.7.3 Adiabatic-Connection Fluctuation-Dissipation Approach
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|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 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. .
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|a Description based on online resource; title from digital title page (viewed on October 12, 2023).
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| 650 |
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|a Density functionals.
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| 700 |
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|a Cancès, Eric.
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| 700 |
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|a Friesecke, Gero.
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| 776 |
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8 |
|c Original
|z 303122339X
|z 9783031223396
|w (OCoLC)1348922519
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| 830 |
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|a Mathematics and Molecular Modeling.
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| 856 |
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|u https://holycross.idm.oclc.org/login?auth=cas&url=https://link.springer.com/10.1007/978-3-031-22340-2
|y Click for online access
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|6 505-00/(S
|a 1.7.3.1 Exact Adiabatic-Connection Fluctuation-Dissipation Expression -- 1.7.3.2 Random-Phase Approximations -- Suggested Further Reading -- References -- 2 On Connecting Density Functional Approximations to Theory -- 2.1 Introduction -- 2.1.1 On approximations in DFT -- 2.1.2 Excuses -- 2.1.3 Summary -- 2.2 Schrödinger Equation and Notations -- 2.3 The Density Functional Viewpoint -- 2.3.1 The Hohenberg-Kohn Theorem -- 2.3.2 Difficulty of Producing F[ρ] -- 2.4 Practical Solutions for Density Functional Approximations -- 2.4.1 Ansatz -- 2.4.1.1 Choice of the Ansatz
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|a SPRING-ALL2023
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|a 92
|b HCD
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