Many-Body Methods for Atoms and Molecules  book cover
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Many-Body Methods for Atoms and Molecules




ISBN 9781482211900
Published October 26, 2016 by CRC Press
238 Pages - 40 B/W Illustrations

 
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Book Description

Brings Readers from the Threshold to the Frontier of Modern Research

Many-Body Methods for Atoms and Molecules addresses two major classes of theories of electron correlation: the many-body perturbation theory and coupled cluster methods. It discusses the issues related to the formal development and consequent numerical implementation of the methods from the standpoint of a practicing theoretician. The book will enable readers to understand the future development of state-of-the-art multi-reference coupled cluster methods as well as their perturbative counterparts.

The book begins with an introduction to the issues relevant to the development of correlated methods in general. It next gives a formally rigorous treatment of aspects that pave the foundation toward the theoretical development of methods capable of tackling problems of electronic correlation. The authors go on to cover perturbation theory first in a fundamental way and then in the multi-reference context. They also describe the idea of state-specific theories, Fock space-based multi-reference coupled cluster methods, and basic issues of the single-reference coupled cluster method. The book concludes with state-of-the-art methods of modern electronic structure.

Table of Contents

Introduction
Background
Born–Oppenheimer approximation
Approximate methods
Independent particle model
Configuration interaction
Electron correlation
Size-extensivity and size-consistency

Occupation Number Representation
Background
Creation and annihilation operators
Occupation number representation of operators
Evaluation of matrix elements
Normal order product of ordinary operators
Hole-particle formalism and Fermi vacuum
Evaluation of Hamiltonian elements between reference states
Normal order product for Fermi vacuum
Normal product form of quantum mechanical operators
Graphical representation of normal product operators

Perturbation Theory
Background
Rayleigh–Schrödinger perturbation theory: traditional approach
Projection operator-based formulation of perturbation theory
Brillouin-Wigner perturbation theory
Rayleigh–Schrödinger perturbation theory
Wave operator-based formulation of Rayleigh–Schrödinger perturbation theory
Factorization theorem and cancellation of unlinked terms
Choice of zeroth order Hamiltonian H0
Intruder state problems in Rayleigh–Schrödinger perturbation theory
Comparison of Brillouin–Wigner and Rayleigh–Schrödinger perturbation theories

Multi-Reference Perturbation Theory
Introduction
Choice of Fermi vacuum and the hole-particle states
Multi-configuration self-consistent field method
Improved virtual orbital complete active space configuration method
Classification of perturbative methods
Formal multi-reference perturbation theory for complete model space
Multi-reference perturbation theory for incomplete model space
Intermediate Hamiltonian methods
Effective valence shell Hamiltonian method

State-Specific Perturbation Theory
Background
Multi-reference Moller–Plesset second-order perturbation theory
Multi-configuration quasi-degenerate perturbation theory
Complete active space second order perturbation theory
Multi-state complete active space second order perturbation theory

Coupled Cluster Method
Introduction
Single-reference coupled cluster method
Extensivity
Relation with full configuration interaction (FCI) method
Coupled cluster equation for doubles (CCD) and singles and doubles (CCSD) approximations
Evaluation of the matrix elements for the couple cluster doubles equations
Diagrammatic representation of coupled cluster doubles (CCD) matrix elements
Emergence of many-body perturbation theory from CC method
Other variants of CC theory

Fock Space Multi-Reference Coupled Cluster Method
Background
Choice of wave operator for multi-reference systems
Connectivity of the effective Hamiltonian
Fock space coupled cluster theory for energy difference
Systematic generation of cluster equations for various valence sectors
Equation of motion coupled cluster method
Relationship between FSMRCC and EOMCC
Numerical examples
Intermediate Hamiltonian-based multi-reference coupled cluster theory

Hilbert Space Coupled Cluster Theory
Introduction
State universal multi-reference coupled cluster (SU-MRCC) theory
Development of state-specific theories

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Author(s)

Biography

Dr. Rajat Kumar Chaudhuri is a professor at the Indian Institute of Astrophysics. His research interests lie at the interface of chemistry and physics with principal areas of focus on the development and applications of ab initio theories of atomic and molecular systems and theoretical spectroscopy. He has published over 150 scientific articles in the realm of theoretical chemistry.

Dr. Sudip Kumar Chattopadhyay is a professor of chemistry at the Indian Institute of Engineering Science and Technology, where he teaches basic and advanced quantum mechanics and quantum chemistry. His research interests include the development of electronic structure theories and their application to problems of broad chemical interest. He has also been working in the field of chemical dynamics in condensed phases. Dr. Chattopadhyay has published over 100 articles in journals of international repute