**Preface***.* **Chapter** **1:** **The Role of Theory in the Physical Sciences***.*

1.0 Introduction*.*

1.1 What is the role of theory in science?

1.2 The gas laws of Boyle and Gay-Lussac*.*

1.3 An absolute zero of temperature*.*

1.4 The gas equation of Van der Waals*.*

1.5 Physical laws*.*

1.6 Laws, postulates, hypotheses, etc.

1.7 Theory at the end of the 19th century*.*

1.8 Bibliography and further reading*.*

**Chapter** **2:** **From Classical to Quantum Mechanics***.*

2.0 Introduction.

2.1 The motion of the planets: Tycho Brahe and Kepler*.*

2.2 Newton, Lagrange and Hamilton*.*

2.3 The power of classical mechanics*.*

2.4 The failure of classical physics*.*

2.5 The black-body radiator and Planck’s quantum hypothesis*.*

2.6 The photoelectric effect*.*

2.7 The emission spectra of atoms*.*

2.8 de Broglie’s proposal*.*

2.9 The Schrödinger equation*.*

2.10 Bibliography and further reading*.*

**Chapter** **3:** **The Application of Quantum Mechanics***.*

3.0 Introduction*.*

3.1 Observables, operators, eigenfunctions and eigenvalues*.*

3.2 The Schrödinger method*.*

3.3 An electron on a ring*.*

3.4 Hückel’s (4*N* + 2) rule: aromaticity*.*

3.5 Normalisation and orthogonality*.*

3.6 An electron in a linear box*.*

3.7 The linear and angular momenta of electrons confined within a one-dimensional box or on a ring*.*

3.8 The eigenfunctions of different operators*.*

3.9 Eigenfunctions, eigenvalues and experimental measurements*.*

3.10 More about measurement: the Heisenberg uncertainty principle*.*

3.11 The commutation of operators*.*

3.12 Combinations of eigenfunctions and the superposition of states*.*

3.13 Operators and their formulation*.*

3.14 Summary*.*

3.15 Bibliography and further reading*.*

**Chapter** **4:** **Angular Momentum***.*

4.0 Introduction*.*

4.1 Angular momentum in classical mechanics*.*

4.2 The conservation of angular momentum.

4.3 Angular momentum as a vector quantity*.*

4.4 Orbital angular momentum in quantum mechanics*.*

4.5 Spin angular momentum*.*

4.6 Total angular momentum*.*

4.7 Angular momentum operators and eigenfunctions*.*

4.8 Notation*.*

4.9 Some examples*.*

4.10 Bibliography and further reading*.*

**Chapter** **5:** **The Structure and Spectroscopy of the Atom***.*

5.0 Introduction*.*

5.1 The eigenvalues of the hydrogen atom*.*

5.2 The wave functions of the hydrogen atom*.*

5.3 Polar diagrams of the angular functions*.*

5.4 The complete orbital wave functions*.*

5.5 Other one-electron atoms*.*

5.6 Electron spin*.*

5.7 Atoms and ions with more than one electron*.*

5.8 The electronic states of the atom*.*

5.9 Spin-orbit coupling*.*

5.10 Selection rules in atomic spectroscopy*.*

5.11 The Zeeman effect*.*

5.12 Bibliography and further reading*.*

**Chapter** **6:** **The Covalent Chemical Bond***.*

6.0 Introduction*.*

6.1 The binding energy of the hydrogen molecule*.*

6.2 The Hamiltonian operator for the hydrogen molecule*.*

6.3 The Born–Oppenheimer approximation*.*

6.4 Heitler and London: The valence bond (VB) model*.*

6.5 Hund and Mulliken: the molecular orbital (MO) model*.*

6.6 Improving the wave functions.

6.7 Unification: Ionic structures and configuration interaction.

6.8 Electron correlation*.*

6.9 Bonding and antibonding Mos*.*

6.10 Why is there no He–He Bond?

6.11 Atomic orbital overlap*.*

6.12 The Homonuclear diatomic molecules from lithium to fluorine*.*

6.13 Heteronuclear diatomic molecules*.*

6.14 Charge distribution*.*

6.15 Hybridisation and resonance*.*

6.16 Resonance and the valence bond theory*.*

6.17 Molecular geometry*.*

6.18 Computational developments*.*

6.19 Bibliography and further reading*.*

**Chapter** **7:** **Bonding, Spectroscopy and Magnetism in Transition-Metal Complexes***.*

7.0 Introduction*.*

7.1 Historical development*.*

7.2 The crystal field theory*.*

7.3 The electronic energy levels of transition-metal complexes*.*

7.4 The electronic spectroscopy of transition-metal complexes*.*

7.5 Pairing energies; low-spin and high-spin complexes*.*

7.6 The magnetism of transition-metal complexes*.*

7.7 Covalency and the ligand field theory*.*

7.8 Bibliography and further reading*.*

**Chapter** **8:** **Spectroscopy***.*

8.0 The interaction of radiation with matter*.*

8.1 Electromagnetic radiation*.*

8.2 Polarised light*.*

8.3 The electromagnetic spectrum*.*

8.4 Photons and their properties*.*

8.5 Selection rules*.*

8.6 The quantum mechanics of transition probability*.*

8.7 The nature of the time-independent interaction.

8.8 Spectroscopic time scales.

8.9 Quantum electrodynamics*.*

8.10 Spectroscopic units and notation*.*

8.11 The Einstein coefficients*.*

8.12 Bibliography and further reading*.*

**Chapter** **9:** **Nuclear Magnetic Resonance Spectroscopy***.*

9.0 Introduction*.*

9.1 The magnetic properties of atomic nuclei*.*

9.2 The frequency region of NMR spectroscopy*.*

9.3 The NMR selection rule*.*

9.4 The chemical shift*.*

9.5 Nuclear spin–spin coupling*.*

9.6 The energy levels of a nuclear spin system*.*

9.7 The intensities of NMR spectral lines*.*

9.8 Quantum mechanics and NMR spectroscopy*.*

9.9 Bibliography and further reading*.*

**Chapter** **10:** **Infrared Spectroscopy***.*

10.0 Introduction*.*

10.1 The origin of the infrared spectra of molecules*.*

10.2 Simple harmonic motion*.*

10.3 The quantum-mechanical harmonic oscillator*.*

10.4 Rotation of a diatomic molecule*.*

10.5 Selection rules for vibrational and rotational transitions*.*

10.6 Real diatomic molecules*.*

10.7 Polyatomic molecules*.*

10.8 Anharmonicity*.*

10.9 The *ab-initio* calculation of IR spectra*.*

10.10 The special case of near infrared spectroscopy*.*

10.11 Bibliography and further reading*.*

**Chapter** **11:** **Electronic Spectroscopy***.*

11.0 Introduction*.*

11.1 Atomic and molecular orbitals*.*

11.2 The spectra of covalent molecules*.*

11.3 Charge transfer (CT) spectra*.*

11.4 Many-electron wave functions*.*

11.5 The 1s^{1}2s^{1} configuration of the helium atom; singlet and triplet states*.*

11.6 The Π-electron spectrum of benzene*.*

11.7 Selection rules*.*

11.8 Slater determinants (Appendix 6)*.*

11.9 Bibliography and further reading*.*

**Chapter** **12:** **Some Special Topics***.*

12.0 Introduction*.*

12.1 The Hückel molecular orbital (HMO) theory.

12.2 Magnetism in chemistry*.*

12.3 The band theory of solids*.*

12.4 Bibliography and further reading*.*

**Appendices.**

1. Fundamental Constants and Atomic Units*.*

2. The Variation Method and the Secular Equations*.*

3. Energies and Wave Functions by Matrix Diagonalisation*.*

4. Perturbation Theory*.*

5. The Spherical Harmonics and Hydrogen Atom Wave Functions.

6. Slater Determinants*.*

7. Spherical Polar Co-ordinates*.*

8. Numbers: Real, Imaginary and Complex*.*

9. Dipole and Transition Dipole Moments*.*

10. Wave Functions for the 3F States of d2 using Shift Operators*.*

**Index.**