1 Introduction

1.1 What Is a Molecule？

1.2 Goals and Methods

1.3 Historical Remarks

1.4 The Significance of Molecular Physics and Quantum Chemistry for Other Fields

2 Mechanical Properties of Molecules，Their Size and Mass

2.1 Molecular Sizes

2.2 The Shapes of Molecules

2.3 Molecular Masses

2.4 Specific Heat and Kinetic Energy

Problems

3 Molecules in Electric and Magnetic Fields

3.1 Dielectric Properties

3.2 Nonpolar Molecules

3.3 Polar Molecules

3.4 Index of Refraction，Dispersion

3.5 The Anisotropy of the Polarisability

3.6 Molecules in Magnetic Fields，Basic Concepts and Definitions

3.7 Diamagnetic Molecules

3.8 Paramagnetic Molecules

Problems

4 Introduction to the Theory of Chemical Bonding

4.1 A Brief Review of Quantum Mechanics

4.2 Heteropolar and Homopolar Bonding

4.3 The Hydrogen Molecule-Ion，H+ 2

4.4 The Hydrogen Molecule，H2

4.4.1 The Variational Principle

4.4.2 The Heitler-London Method

4.4.3 Covalent-Ionic Resonance

4.4.4 The Hund-Mullikan-Bloch Theory of Bonding in Hydrogen

4.4.5 Comparison of the Wavefunctions

4.5 Hybridisation

Problems

5 Symmetries and Symmetry Operations：A First Overview

5.1 Fundamental Concepts

5.2 Application to Benzene：the π-Electron Wavefunctions by the Hückel Method

5.3 The Hückel Method Revisited，The Energy of the π-Electrons

5.4 Slater Determinants

5.5 The Ethene Wavefunctions．Parity

5.6 Summary

Problems

6 Symmetries and Symmetry Operations．A Systematic Approach

6.1 Fundamentals

6.2 Molecular Point Groups

6.3 The Effect of Symmetry Operations on Wavefunctions

6.4 Similarity Transformations and Reduction of Matrices

6.5 Fundamentals of the Theory of Group Representations

6.5.1 The Concept of the Class

6.5.2 The Character of a Representation

6.5.3 The Notation for Irreducible Representations

6.5.4 The Reduction of a Representation

6.6 Summary

6.7 An Example：The H2O Molecule

Problems

7 The Multi-Electron Problem in Molecular Physics and Quantum Chemistry

7.1 Overview and Formulation of the Problem

7.1.1 The Hamiltonian and the Schr？dinger Equation

7.1.2 Slater Determinants and Energy Expectation Values

7.2 The Hartree-Fock Equation．The Self-Consistent Field（SCF）Method

7.3 The Hartree-Fock Method for a Closed Shell

7.4 The Unrestricted SCF Method for Open Shells

7.5 The Restricted SCF Method for Open Shells

7.6 Correlation Energies

7.7 Koopman's Theorem

7.8 Configuration Interactions

7.9 The Second Quantisation

7.10 Résumé of the Results of Chapters 4-7

Problems

8 Overview of Molecular Spectroscopy Techniques

8.1 Spectral Regions

8.2 An Overview of Optical Spectroscopy Methods

8.3 Other Experimental Methods

Problems

9 Rotational Spectroscopy

9.1 Microwave Spectroscopy

9.2 Diatomic Molecules

9.2.1 The Spectrum of the Rigid Rotor （Dumbbell Model）

9.2.2 Intensities

9.2.3 The Non-rigid Rotor

9.3 Isotope Effects

9.4 The Stark Effect

9.5 Polyatomic Molecules

9.6 Some Applications of Rotational Spectroscopy

Problems

10 Vibrational Spectroscopy

10.1 Infrared Spectroscopy

10.2 Diatomic Molecules：Harmonic Approximation

10.3 Diatomic Molecules．The Anharmonic Oscillator

10.4 Rotational-Vibrational Spectra of Diatomic Molecules．The Rotating Oscillator and the Rotational Structure of the Bands

10.5 The Vibrational Spectra of Polyatomic Molecules

10.6 Applications of Vibrational Spectroscopy

10.7 Infrared Lasers

10.8 Microwave Masers

Problems

11 The Quantum-Mechanical Treatment of Rotational and Vibrational Spectra

11.1 The Diatomic Molecule

11.1.1 The Born-Oppenheimer Approximation

11.1.2 Justification of the Approximations

11.2 The Rotation of Tri-and Polyatomic Molecules

11.2.1 The Expression for the Rotational Energy

11.2.2 The Symmetric Top

11.2.3 The Asymmetric Top

11.3 The Vibrations of Tri-and Polyatomic Molecules

11.4 Symmetry and Normal Coordinates

11.5 Summary

Problems

12 Raman Spectra

12.1 The Raman Effect

12.2 Vibrational Raman Spectra

12.3 Rotational Raman Spectra

12.4 The Influence of Nuclear Spins on the Rotational Structure

Problems

13 Electronic States

13.1 The Structure of Band Spectra

13.2 Types of Bonding

13.3 Electronic States of Diatomie Molecules

13.4 Many-Electron States and Total Electronic States of Diatomic Molecules

13.5 An Example：the Electronic States of H2

Problems

14 The Electronic Spectra of Molecules

14.1 Vibrational Structure of the Band Systems of Small Molecules；The Franck-Condon Principle

14.2 The Rotational Structure of Electronic Band Spectra in Small Molecules；Overview and Selection Rules

14.3 The Rotational Structure of the Band Spectra of Small Molecules；Fortrat Diagrams

14.4 Dissociation and Predissociation

14.5 Applications of Band Spectra of Smaller Molecules

14.6 The Electronic Spectra of Larger Molecules

Problems

15 Further Remarks on the Techniques of Molecular Spectroscopy

15.1 The Absorption of Light

15.2 Radiationless Processes

15.3 The Emission of Light

15.4 Cold Molecules

15.5 Dye Lasers

15.6 High-Resolution Two-Photon Spectroscopy

15.7 Ultrashort Pulse Spectroscopy

15.8 Photoelectron Spectroscopy

15.9 High-Resolution Photoelectron Spectroscopy

Problems

16 The Interaction of Molecules with Light：Quantum-Mechanical Thatment

16.1 An Overview

16.2 Time-Dependent Perturbation Theory

16.3 Spontaneous and Stimulated Emission and the Absorption of Light by Molecules

16.3.1 The Form of the Hamiltonian

16.3.2 Wavefunctions of the Initial and Final States

16.3.3 The General Form of the Matrix Elements

16.3.4 Transition Probabilities and the Einstein Coefficients

16.3.5 The Calculation of the Absorption Coefficient

16.3.6 Transition Moments，Oscillator Strengths，and Spatial Averaging

16.4 The Franck-Condon Principle

16.5 Selection Rules

16.6 Summary

17 Theoretical Tratment of the Raman Effect and the Elements of Nonlinear Optics

17.1 Time-Dependent Perturbation Theory in Higher Orders

17.2 Theoretical Description of the Raman Effect

17.3 Two-Photon Absorption

18 Nuclear Magnetic Resonance

18.1 Fundamentals of Nuclear Resonance

18.1.1 Nuclear Spins in a Magnetic Field

18.1.2 Detection of Nuclear Resonance

18.2 Proton Resonance in Molecules

18.2.1 The Chemical Shift

18.2.2 Fine Structure and the Direct Nuclear Spin-Spin Coupling

18.2.3 Fine Structure and the Indirect Spin-Spin Coupling Between Two Nuclei

18.2.4 The Indirect Spin-Spin Interaction Among Several Nuclei

18.3 Dynamic Processes and Relaxation Times

18.4 Nuclear Resonance with Other Nuclei

18.5 Two-Dimensional Nuclear Resonance

18.5.1 The Basic Concepts

18.5.2 The Quantum-mechanical Theory of COSY

18.5.3 The Investigation of Dynamic Processes Using 2-Dimensional Exchange Spectroscopy，in particular NOESY

18.6 Applications of Nuclear Magnetic Resonance

Problems

19 Electron Spin Resonance

19.1 Fundamentals

19.2 The g-Factor

19.3 Hyperfine Structure

19.4 Fine Structure

19.5 Calculation of the Fine Structure Tensor and the Spin Wavefunctions of Triplet States

19.6 Double Resonance Methods：ENDOR

19.7 Optically Detected Magnetic Resonance（ODMR）

19.8 Applications of ESR

Problems

20 Macromolecules，Biomolecules，and Supermolecules

20.1 Their Significance for Physics，Chemistry，and Biology

20.2 Polymers

20.3 Molecular Recognition，Molecular Inclusion

20.4 Energy Transfer，Sensitisation

20.5 Molecules for Photoreactions in Biology

20.6 Molecules as the Basic Units of Life

20.7 Molecular Functional Units

Problems

21 Experiments on and with Single Molecules

21.1 Introduction：Why？

21.2 The Imaging of Single Molecules with X-ray and Electron Beam Methods

21.3 Scanning Tunnel and Atomic Force Microscopes

21.4 Optical Spectroscopy of Single Molecules

21.4.1 Overview

21.4.2 Experimental Methods

21.4.3 Single-Molecule Spectroscopy with Relatively Limited Resolution：Spatial Selection

21.4.4 Measurements with a High Spectral Resolution at Low Temperatures：Spectral Selection

21.4.5 Some Experimental Results

21.5 The Electrical Conductivity ofMolecules

21.5.1 Molecular Wires

21.5.2 Experimental Results

22 Molecular Electronics and Other Applications

22.1 What Is It？

22.2 Molecules as Switching Elements

22.3 Molecular Electrical Conductors

22.4 Molecular Wires

22.5 Molecules as Energy Conductors

22.6 Molecular Electronic Functional Units

22.7 Nanotubes

22.8 Molecular Storage Elements，Hole-Burning

22.9 Electroluminescence and Light-Emitting Diodes

22.10 The Future：Intelligent Molecular Materials

Problems

Appendix

A.1 The Calculation of Expectation Values Using Wavefunctions Represented by Determinants

A.1.1 Calculation of Determinants

A.1.2 Calculation of Expectation Values

A.2 Calculation of the Density of Radiation

Bibliography

Subject Index