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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 m… Read more
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Immediately download your ebook while waiting for your print delivery. No promo code needed.
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.
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
LP