Many-Body Methods for Atoms and Molecules: 1st Edition (Hardback) book cover

Many-Body Methods for Atoms and Molecules

1st Edition

By Rajat Kumar Chaudhuri, Sudip Kumar Chattopadhyay

CRC Press

238 pages | 40 B/W Illus.

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pub: 2016-10-26
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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



Born–Oppenheimer approximation

Approximate methods

Independent particle model

Configuration interaction

Electron correlation

Size-extensivity and size-consistency

Occupation Number Representation


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


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


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


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


Single-reference coupled cluster method


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


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


State universal multi-reference coupled cluster (SU-MRCC) theory

Development of state-specific theories

About the Authors

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

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Chemistry / Physical & Theoretical
SCIENCE / Nuclear Physics
SCIENCE / Physics