Title A Mathematical Introduction to Electronic Structure Theory
Author Lin Lin, Jianfeng Lu
ISBN 9781611975796
List price USD 44.00
Price outside India Available on Request
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Binding Paperback
No of pages 134
Book size 178 x 254 mm
Publishing year 2019
Original publisher SIAM - Society for Industrial and Applied Mathematics (Eurospan Group)
Published in India by .
Exclusive distributors Viva Books Private Limited
Sales territory India, Sri Lanka, Bangladesh, Pakistan, Nepal, .
Status New Arrival
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Based on first principle quantum mechanics, electronic structure theory is widely used in physics, chemistry, materials science, and related fields and has recently received increasing research attention in applied and computational mathematics. This book provides a self-contained, mathematically oriented introduction to the subject and its associated algorithms and analysis. It will help applied mathematics students and researchers with minimal background in physics understand the basics of electronic structure theory and prepare them to conduct research in this area. 

A Mathematical Introduction to Electronic Structure Theory begins with an elementary introduction of quantum mechanics, including the uncertainty principle and the Hartree–Fock theory, which is considered the starting point of modern electronic structure theory. The authors then provide an in-depth discussion of two carefully selected topics that are directly related to several aspects of modern electronic structure calculations: density matrix based algorithms and linear response theory. Chapter 2 introduces the Kohn–Sham density functional theory with a focus on the density matrix based numerical algorithms, and Chapter 3 introduces linear response theory, which provides a unified viewpoint of several important phenomena in physics and numerics. An understanding of these topics will prepare readers for more advanced topics in this field. The book concludes with the random phase approximation to the correlation energy.



Chapter 1: Basic Theory of quantum mechanics • Finite dimensional quantum systems • Schrödinger equation in the real space • Hydrogen atom • Periodic systems • Tensor product spaces: Twin spin -½ particles • Identical particles

Chapter 2: Density functional theory: Formulation and algorithms • Hartee-Fock theory • Kohn-Sham density functional theory • Nonlinear eigenvalue problem • Self-consistent field iteration • Density matrix formulation • Extension to finite temperature • Density matrix algorithms • Brillouin zone sampling for periodic systems • Localization • Geometry optimization and ab initio molecular dynamics • Time-dependent density functional theory

Chapter 3: Linear response theory • Perturbation of Green’s function • Perturbation of the density matrix • Density functional perturbation theory • Applications of density functional perturbation theory • Exponential decay of the Green’s function • Time-dependent density functional perturbation theory • Casida formalism • Random phase approximation

A. Notations and preliminaries

A.1 Notation • A.2 Spherical harmonics • A.3 Equalities in complex analysis

B. Selected references for further reading



About the Authors:

Lin Lin is an associate professor in the department of mathematics at the University of California, Berkeley, and is a faculty scientist at Lawrence Berkeley National Laboratory. He is a recipient of the Sloan Fellowship, the National Science Foundation CAREER Award, the Department of Energy Early Career Award, and the SIAM Computational Science and Engineering (CSE) Early Career Award. His research focuses on the development of efficient numerical methods for electronic structure calculations. 

Jianfeng Lu is an associate professor of mathematics, physics, and chemistry at Duke University, where he works in mathematical analysis and algorithm development for problems and challenges arising from computational physics, theoretical chemistry, and materials science. His work has been recognized by a Sloan Fellowship, a National Science Foundation Career Award, and the IMA Prize in Mathematics and its Applications.

Target Audience:

The book is written for advanced undergraduate and beginning graduate students, specifically those with mathematical backgrounds but without a prior knowledge of quantum mechanics, and can be used for self-study by researchers, instructors, and other scientists. The book can also serve as a starting point to learn about many-body perturbation theory, a topic at the frontier of the study of interacting electrons. People interested in physics, chemistry, materials science, and related fields along with applied and computational mathematics.

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