1st Edition

Many-Body Methods for Atoms and Molecules

    256 Pages 40 B/W Illustrations
    by CRC Press

    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.

    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

    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