Ideas of Quantum Chemistry

Ideas of Quantum Chemistry

2nd Edition - November 12, 2013

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  • Author: Lucjan Piela
  • eBook ISBN: 9780444594570
  • Hardcover ISBN: 9780444594365

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Description

Ideas of Quantum Chemistry shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. From the Schroedinger equation to electronic and nuclear motion to intermolecular interactions, this book covers the primary quantum underpinnings of chemical systems. The structure of the book (a TREE-form) emphasizes the logical relationships among various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field. Ideas of Quantum Chemistry has both textbook and reference work aspects. Like a textbook, the material is organized into digestible sections with each chapter following the same structure. It answers frequently asked questions and highlights the most important conclusions and the essential mathematical formulae in the text. In its reference aspects, it has a broader range than traditional quantum chemistry books and reviews virtually all of the pertinent literature. It is useful both for beginners as well as specialists in advanced topics of quantum chemistry. An appendix on the Internet supplements this book.

Key Features

  • Presents the widest range of quantum chemical problems covered in one book
  • Unique structure allows material to be tailored to the specific needs of the reader
  • Informal language facilitates the understanding of difficult topics

Readership

For chemistry undergraduates and graduates, professors, researchers and in particular those studying quantum chemistry - from beginners to professionals. Also beneficial to those involved in biology, biotechnology, physics, astronomy, material sciences.

Table of Contents

  • Dedication

    Sources of Photographs and Figures

    Introduction

    We and the Universe A Potent Interaction

    What Do We Know?

    Narrow Temperature Range

    An Unusual Mission of Chemistry

    Book Guidelines

    Chapter Organization

    Chapter 1. The Magic of Quantum Mechanics

    Abstract

    Where Are We?

    An Example

    What Is It All About?

    Why Is This Important?

    What Is Needed?

    Classical Works

    1.1 History of a Revolution

    1.2 Postulates of Quantum Mechanics

    1.3 The Heisenberg Uncertainty Principle

    1.4 The Copenhagen Interpretation of the World

    1.5 Disproving the Heisenberg Principle–Einstein-Podolsky-Rosen’s Recipe

    1.6 Schrödinger’s Cat

    1.7 Bilocation

    1.8 The Magic of Erasing the Past

    1.9 A Test for a Common Sense: The Bell Inequality

    1.10 Photons Violate the Bell Inequality

    1.11 Teleportation

    1.12 Quantum Computing

    Summary

    Main Concepts, New Terms

    From the Research Front

    Ad Futurum

    Additional Literature

    Questions

    Answers

    Chapter 2. Schrödinger Equation

    Abstract

    Where Are We?

    An Example

    What Is It All About?

    Why Is This Important?

    What Is Needed?

    Classical Works

    2.1 Symmetry of the Hamiltonian and Its Consequences

    2.2 Schrödinger Equation for Stationary States

    2.3 The Time-Dependent Schrödinger Equation

    2.4 Evolution After Switching a Perturbation

    Summary

    From the Research Front

    Ad Futurum

    Additional Literature

    Questions

    Answers

    Chapter 3. Beyond the Schrödinger Equation

    Abstract

    Where Are We?

    An Example

    What Is It All About?

    Why Is This Important?

    What Is Needed?

    Classical Works

    3.1 A Glimpse of Classical Relativity Theory

    3.2 Toward Relativistic Quantum Mechanics

    3.3 The Dirac Equation

    3.4 The Hydrogen-like Atom in Dirac Theory

    3.5 Toward Larger Systems

    3.6 Beyond the Dirac Equation…

    Summary

    Main Concepts, New Terms

    From the Research Front

    Ad Futurum

    Additional Literature

    Questions

    Answers

    Chapter 4. Exact Solutions–Our Beacons

    Abstract

    Where Are We?

    An Example

    What Is It All About?

    Why Is This Important?

    What Is Needed?

    Classical Works

    4.1 Free Particle

    4.2 Box with Ends

    4.3 Cyclic Box

    4.4 Carbon Nanotubes

    4.5 Single Barrier

    4.6 The Magic of Two Barriers

    4.7 Harmonic Oscillator

    4.8 Morse Oscillator

    4.9 Rigid Rotator

    4.10 Hydrogen-Like Atom

    4.11 What Do All These Solutions Have in Common?

    4.12 Hooke Helium Atom (Harmonium)

    4.13 Hooke Molecules

    4.14 Charming SUSY and New Solutions

    4.15 Beacons and Pearls of Physics

    Summary

    Main Concepts, New Terms

    From the Research Front

    Ad Futurum

    Additional Literature

    Questions

    Answers

    Chapter 5. Two Fundamental Approximate Methods

    Abstract

    Where Are We?

    An Example

    What Is It All About?

    Why Is This Important?

    What Is Needed?

    Classical Works

    5.1 Variational Method

    5.2 Perturbational Method

    Summary

    Main Concepts, New Terms

    From the Research Front

    Ad Futurum

    Additional Literature

    Questions

    Answers

    Chapter 6. Separation of Electronic and Nuclear Motions

    Abstract

    Where Are We?

    An Example

    What Is It All About?

    Why Is This Important?

    What Is Needed?

    Classical Works

    6.1 Separation of the Center-of-Mass Motion

    6.2 Exact (Non-Adiabatic) Theory

    6.3 Adiabatic Approximation

    6.4 Born-Oppenheimer Approximation

    6.5 Vibrations of a Rotating Molecule

    6.6 Basic Principles of Electronic, Vibrational, and Rotational Spectroscopy

    6.7 Approximate Separation of Rotations and Vibrations

    6.8 Understanding the IR Spectrum: HCl

    6.9 A Quasi-Harmonic Approximation

    6.10 Polyatomic Molecule

    6.11 Types of States

    6.12 Adiabatic, Diabatic, and Non-Adiabatic Approaches

    6.13 Crossing of Potential Energy Curves for Diatomics

    6.14 Polyatomic Molecules and Conical Intersection

    6.15 Beyond the Adiabatic Approximation

    Summary

    Main Concepts, New Terms

    From the Research Front

    Ad Futurum

    Additional Literature

    Questions

    Answers

    Chapter 7. Motion of Nuclei

    Abstract

    Where Are We?

    An Example

    What Is It All About?

    Why Is This Important?

    What Is Needed?

    Classical Works

    7.1 Rovibrational Spectra–An Example of Accurate Calculations: Atom–Diatomic Molecule

    7.2 Force Fields (FF)

    7.3 Local Molecular Mechanics (MM)

    7.4 Global Molecular Mechanics

    7.5 Small Amplitude Harmonic Motion–Normal Modes

    7.6 Molecular Dynamics (MD)

    7.7 Simulated Annealing

    7.8 Langevin Dynamics

    7.9 Monte Carlo Dynamics

    Example: Conformational Autocatalysis as a Model of Prion Disease Propagation

    7.10 Car-Parrinello Dynamics

    7.11 Cellular Automata

    Summary

    Main Concepts, New Terms

    From the Research Front

    Ad Futurum

    Additional Literature

    Questions

    Answers

    Chapter 8. Orbital Model of Electronic Motion in Atoms and Molecules

    Abstract

    Where Are We?

    An Example

    What Is It All About?

    Why Is This Important?

    What Is Needed?

    Classical Works

    8.1 Hartree-Fock Method–A Bird’s-Eye View

    8.2 Toward the Optimal Spinorbitals and the Fock Equation

    8.3 Total Energy in the Hartree-Fock Method

    8.4 Computational Technique: Atomic Orbitals as Building Blocks of the Molecular Wave Function

    8.5 Back to the Basics

    8.6 Mendeleev Periodic Table

    8.7 The Nature of the Chemical Bond

    8.8 Excitation Energy, Ionization Potential, and Electron Affinity (RHF Approach)

    8.9 Toward Chemical Picture–Localization of MOs

    8.10 A Minimal Model of a Molecule

    8.11 Valence Shell Electron Pair Repulsion (VSEPR) Algorithm

    8.12 The Isolobal Analogy

    Summary

    Main Concepts, New Terms

    From the Research Front

    Ad Futurum

    Additional Literature

    Questions

    Answer

    Chapter 9. Orbital Model of Electronic Motion in Periodic Systems

    Abstract

    Where Are We?

    An Example

    What Is It All About?

    Why Is This Important?

    What Is Needed?

    Classical Works

    9.1 Primitive Lattice

    9.2 Wave Vector

    9.3 Inverse Lattice

    9.4 First Brillouin Zone (FBZ)

    9.5 Properties of the FBZ

    9.6 A Few Words on Bloch Functions

    9.7 Infinite Crystal as a Limit of a Cyclic System

    9.8 A Triple Role of the Wave Vector

    9.9 Band Structure

    9.10 Solid-State Quantum Chemistry

    9.11 The Hartree-Fock Method for Crystals

    9.12 Long-Range Interaction Problem

    9.13 Back to the Exchange Term

    9.14 Choice of Unit Cell

    Summary

    Main Concepts, New Terms

    From the Research Front

    Ad Futurum

    Additional Literature

    Questions

    Answers

    Chapter 10. Correlation of the Electronic Motions

    Abstract

    Where Are We?

    An Example

    What Is It All About?

    Why Is This Important?

    What Is Needed?

    Classic Papers

    10.1 Correlation Cusp Condition

    10.2 The Hylleraas CI Method

    10.3 Two-Electron Systems

    10.4 Exponentially Correlated Gaussian Functions

    10.5 Electron Holes

    10.6 Static Electron Correlation

    10.7 Dynamic Electron Correlation

    10.8 Anticorrelation, or Do Electrons Stick Together in Some States?

    10.9 Valence Bond (VB) Method

    10.10 Configuration Interaction (CI) Method

    10.11 Direct CI Method

    10.12 Multireference CI Method

    10.13 Multiconfigurational Self-Consistent Field Method (MC SCF)

    10.14 Complete Active Space SCF (CAS SCF) Method

    10.15 Coupled Cluster (CC) Method

    10.16 Equation-of-Motion Coupled Cluster (EOM-CC) Method

    10.17 Many-body Perturbation Theory (MBPT)

    10.18 Møller-Plesset Version of Rayleigh-Schrödinger Perturbation Theory

    Summary

    Variational Methods Using Explicitly Correlated Wave Function

    Variational Methods with Slater Determinants

    Non-variational Method Based on Slater Determinants

    Main Concepts, New Terms

    From the Research Front

    Ad Futurum

    Additional Literature

    Questions

    Answers

    Chapter 11. Chasing Correlation Dragon: Density Functional Theory (DFT)

    Abstract

    Where Are We?

    An Example

    What Is It All About?

    Why Is This Important?

    What Is Needed?

    Classic Works

    11.1 Electronic Density–The Superstar

    11.2 Electron Density Distributions- Bader Analysis

    11.3 Two important Hohenberg-Kohn theorems

    11.4 The Kohn-Sham Equations

    11.5 Trying to Guess the Appearance of the Correlation Dragon

    11.6 On the Physical Justification for the Exchange-Correlation Energy

    11.7 Visualization of Electron Pairs: Electron Localization Function (ELF)

    11.8 The DFT Excited States

    11.9 The Hunted Correlation Dragon Before Our Eyes

    Conclusion

    Summary

    Main Concepts, New Terms

    From the Research Front

    Ad Futurum

    Additional Literature

    Questions

    Answers

    Chapter 12. The Molecule Subject to the Electric or Magnetic Field

    Abstract

    Where Are We?

    An Example

    What Is It All About?

    Why Is This Important?

    What Is Needed?

    Classical Works

    12.1 Hellmann-Feynman Theorem

    12.2 The Molecule Immobilized in an Electric Field

    12.3 How to Calculate the Dipole Moment

    12.4 How to Calculate the Dipole Polarizability

    12.5 A Molecule in an Oscillating Electric Field

    12.6 Magnetic Dipole Moments of Elementary Particles

    12.7 NMR Spectra–Transitions Between the Nuclear Quantum States

    12.8 Hamiltonian of the System in the Electromagnetic Field

    12.9 Effective NMR Hamiltonian

    12.10 The Ramsey Theory of the NMR Chemical Shift

    12.11 The Ramsey Theory of the NMR Spin-Spin Coupling Constants

    12.12 Gauge-Invariant Atomic Orbitals (GIAOs)

    Summary

    Electric Phenomena

    Magnetic Phenomena

    Main Concepts, New Terms

    From the Research Front

    Ad Futurum

    Additional Literature

    Questions

    Answers

    Chapter 13. Intermolecular Interactions

    Abstract

    Where Are We?

    An Example

    What Is It All About?

    Why Is This Important?

    What Is Needed?

    Classical Works

    Intermolecular Interactions (Theory)

    13.1 Idea of the Rigid Interaction Energy

    13.2 Idea of the Internal Relaxation

    13.3 Interacting Subsystems

    13.4 Binding Energy

    13.5 Dissociation Energy

    13.6 Dissociation Barrier

    13.7 Supermolecular Approach

    13.8 Perturbational Approach

    13.9 Symmetry Adapted Perturbation Theories (SAPT)

    13.10 Convergence Problems and Padé Approximants

    13.11 Non-additivity of Intermolecular Interactions

    13.12 Idea of Molecular Surface

    13.13 Decisive Forces

    13.14 Construction Principles

    Summary

    Main Concepts, New Terms

    From the Research Front

    Ad Futurum

    Additional Literature

    Questions

    Answers

    Chapter 14. Chemical Reactions

    Abstract

    Where Are We?

    An Example

    What Is It All About?

    Why Is This Important?

    What Is Needed?

    Classical Works

    14.1 Hypersurface of the Potential Energy for Nuclear Motion

    14.2 Chemical Reaction Dynamics (A Pioneers’ Approach)

    14.3 Accurate Solutions (Three Atoms)

    14.4 Intrinsic Reaction Coordinate (IRC) or Statics

    14.5 Reaction Path Hamiltonian Method

    14.6 Acceptor-Donor (AD) Theory of Chemical Reactions

    14.7 Symmetry-Allowed and Symmetry-Forbidden Reactions

    14.8 Barrier for the Electron-Transfer Reaction

    Summary

    Main Concepts, New Terms

    From the Research Front

    Ad Futurum

    Additional Literature

    Questions

    Answers

    Chapter 15. Information Processing–The Mission of Chemistry

    Abstract

    Where Are We?

    An Example

    What Is It All About?

    Why Is This Important?

    What Is Needed?

    Classical Works

    15.1 Multilevel Supramolecular Structures (Statics)

    15.2 Chemical Feedback–A Steering Element (Dynamics)

    15.3 Information and Informed Matter

    Summary

    Main Concepts, New Terms

    From the Research Front

    Ad Futurum

    Additional Literature

    Question

    Answers

    Appendix A. Reminding Matrices and Determinants

    Matrices

    Determinants

    Appendix B. A Few Words on Spaces, Vectors, and Functions

    Vector Space

    Euclidean Space

    Unitary Space

    Hilbert Space

    Linear Operator

    Adjoint Operator

    Hermitian Operator

    Unitary Operator

    Eigenvalue Equation

    Commutation and Eigenvalues

    Appendix C. Group Theory in Spectroscopy

    Group

    Representations

    Group Theory and Quantum Mechanics

    Integrals Important in Spectroscopy

    Appendix D. A Two-State Model

    Appendix E. Dirac Delta Function

    Approximations to

    Properties of

    An Application of the Dirac Delta Function

    Appendix F. Translation versus Momentum and Rotation versus Angular Momentum

    The Form of the Operator

    Hamiltonian Commutes with the Total Momentum Operator

    Hamiltonian, and Do Commute

    Rotation and Translation Operators Do Not Commute

    Conclusion

    Appendix G. Vector and Scalar Potentials

    Maxwell Equations

    Arbitrariness of Potentials and

    Choice of Potentials and for a Uniform Magnetic Field

    Practical Importance of this Choice

    Vector Potential Causes the Wave Function to Change Phase

    The Incredible Aharonov-Bohm Effect

    Appendix H. Optimal Wave Function for the Hydrogen-Like Atom

    Appendix I. Space- and Body-Fixed Coordinate Systems

    Appendix J. Orthogonalization

    Schmidt Orthogonalization

    Löwdin Symmetric Orthogonalization

    Appendix K. Diagonalization of a Matrix

    Appendix L. Secular Equation

    Secular Equation and Normalization

    Chapter M. Slater-Condon Rules

    Antisymmetrization Operator

    Slater-Condon Rules

    A Simple Trick Used in the Proofs

    I Slater-Condon Rule

    Special Case: Double Occupation

    II Slater-Condon Rule

    III Slater-Condon Rule

    IV Slater-Condon Rule

    Appendix N. Lagrange Multipliers Method

    Appendix O. Penalty Function Method

    Appendix P. Molecular Integrals with Gaussian Type Orbitals 1s

    Do These Formulas Work?

    Appendix Q. Singlet and Triplet States for Two Electrons

    Appendix R. The Hydrogen Molecular Ion in the Simplest Atomic Basis Set

    Bonding and Antibonding Orbital Energy

    Appendix S. Population Analysis

    Mulliken Population Analysis

    Other Population Analyses

    Multipole Representation

    Appendix T. Dipole Moment of a Lone Pair

    Appendix U. Second Quantization

    Vacuum State

    Creation and Annihilation of Electron

    Operators in the Second Quantization

    One-Electron Operators

    Two-Electron Operators

    Appendix V. Hydrogen Atom in Electric Field–The Variational Approach

    Appendix W. NMR Shielding and Coupling Constants–Derivation

    Shielding Constants

    Coupling Constants

    Appendix X. Multipole Expansion

    What Is the Multipole Expansion For?

    Coordinate System

    Multipole Series and the Multipole Operators of a Particle

    Multipole Moment Operators for Many Particles

    Examples

    The Multipoles Depend on the Coordinate System Chosen

    Interaction Energy of Non-pointlike Multipoles

    What Is ?

    Properties of the Multipole Expansion

    Convergence of the Multipole Expansion

    Appendix Y. Pauli Deformation

    Case

    Case

    Two Large Molecules

    Two Final Remarks

    Appendix Z. Acceptor-Donor Structure Contributions in the MO Configuration

    Acronyms

    Tables

    Name Index

    Subject Index

Product details

  • No. of pages: 1078
  • Language: English
  • Copyright: © Elsevier 2013
  • Published: November 12, 2013
  • Imprint: Elsevier
  • eBook ISBN: 9780444594570
  • Hardcover ISBN: 9780444594365

About the Author

Lucjan Piela

Professor Piela received his bachelor degree in 1960 from the histroric Konarski College in his home town of Rzeszow, Poland. In 1965, he graduated with a Masters of Science from the University of Warsaw and, after obtaining his Ph.D. from the same university 5 years later, went on to became a professor in 1976. In addition to his work in Warsaw, he has carried out research in the Centre Européen de Calcul Atomique et Moléculaire (France), Facultés Universitaires de Namur (Belgium) and Cornell University (USA). In addition to being the author of about hundred papers published in international journals, Professor Piela is an elected member of the Academie Royale des Sciences, Lettres et Beaux-Arts de Belgique, and a member of the European Academy of Sciences.

Affiliations and Expertise

Department of Chemistry, University of Warsaw, Warsaw, Poland

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