Density functional theory : modeling, mathematical analysis, computational methods and applications

Density functional theory : modeling, mathematical analysis, computational methods and applications / Eric Cancès, Gero Friesecke, editors.

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 syste...

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Bibliographic Details
Other Authors: Cancès, Eric, Friesecke, Gero
Format: eBook
Language:English
Published: Cham, Switzerland : Springfer, [2023]
Series:Mathematics and Molecular Modeling.
Subjects:
Density functionals.
Online Access:Click for online access
Table of Contents:
  • 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
  • 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
  • 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
  • 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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