Ideas of Quantum Chemistry, 2nd Edition

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