Density Functional Theory : Modeling, Mathematical Analysis, Computational Methods, and Applications / edited by Eric Cancès, Gero Friesecke.

Format:

Book

Author/Creator:

Cancès, Eric.

Contributor:

Friesecke, Gero.

Series:

Mathematics and Molecular Modeling, 3005-0294

Language:

English

Subjects (All):

Mathematics.

Condensed matter.

Atoms.

Molecules.

Quantum chemistry.

Electronics--Materials.

Electronics.

Materials science--Data processing.

Materials science.

Condensed Matter Physics.

Atomic, Molecular and Chemical Physics.

Quantum Chemistry.

Electronic Materials.

Computational Materials Science.

Local Subjects:

Mathematics.

Condensed Matter Physics.

Atomic, Molecular and Chemical Physics.

Quantum Chemistry.

Electronic Materials.

Computational Materials Science.

Physical Description:

1 online resource (595 pages)

Edition:

1st ed. 2023.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2023.

Summary:

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. .

Contents:

Chapter 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.

Notes:

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Cancès, Eric Density Functional Theory

ISBN:

9783031223402

3031223403

OCLC:

1391441251