Quantum mechanics for chemists

This book is designed to provide a basic understanding of the principles of quantum mechanics.  It is assumed that the reader will have a qualitative understanding of the general features of atomic and molecular orbitals, probably from a course on chemical bonding (frequently given in the first year). The approach is rather different from that adopted in most books on QM, in that the Schrödinger wave equation is introduced at a fairly late stage, after students have become familiar with the application of de Broglie-type wavefunctions to free particles and particles in a box. Likewise, the Hamiltonian operator and the concept of eigenfunctions and eigenvalues are not introduced until the last two chapters of the book, where approximate solutions to the wave equation for many-electron atoms and molecules are discussed. In this way, students receive a gradual introduction to the basic concepts of quantum mechanics.

1. Particle-Wave Duality. 1.1 Introduction. 1.2 Particle Properties of Electromagnetic Waves. 1.3 Wave Properties of matter. 1.4 Matte Waves. 2. Particle in a One-dimensional Box. 2.1 Allowed Wavefunctions and Energies. 2.2 Normalization. 2.3 Probability Distributions of the Wavefunctions. 2.4 Seminconductor Quantum Wells. 2.5 Electrons in Conjugated Molecules. 3. Uncertainty Arising from the Wave Nature of Matter. 3.1 Uncertainty in the Diffraction of Particles. 3.2 Diffraction of Electrons through Double Slits. 3.3 Uncertainty with a Particle-in-a-box. 3.4 Statement of the Heisenberg Uncertainty Principle. 3.5 Application to an Electron Beam. 3.6 The Wavefunction of a Localized Electron. 4. The One-dimensional Schrödinger Wave Equation and Some of Its Applications. 4.1 The One-dimensional Schrödinger Equation. 4.2 The One-dimensional Harmonic Oscillator. 4.3 Quantum Mechanical Tunnelling. 5. Rotational Motion. 5.1 Circular Motion in a Fixed Plane. 5.2 Rotation in Three Dimensions. 5.3 Spin. 6. The Hydrogen Atom. 6.1 Introduction. 6.2 The Hydrogen Spectrum and the Quantization of Energy. 6.3 The Bohr Theory. 6.4 Formulation of the Schrödinger Wave Equation for Hydrogen-like Atoms. 6.5 The Radial Wave Equation. 6.6 The Full Hydrogen Atom Wavefunctions. 7. Further Concepts in Quantum Mechanics and their Application to Many-electron Atoms. 7.1 The Hamilatonian Operator. 7.2 Application to the Motion of a Single Particle. 7.3 Eigenfunctions and Eigenvalues. 7.4 The Wave Equation for the Helium Atom. 7.5 Electron Spin. 7.6 The Orbital Approximation for Lithium. 7.7 Electron Shielding or the Nuclear charge in Many-electron Atoms. 7.8 The Use of Self-consistent Field Methods to Obtain Atoms Orbitals. 7.9 Electron Correlation Energy. 7.10 The Elements of the Periodic Table. 7.11 Hunds Rule. 7.12 Ionization Energies of the Elements. 8. The Structure of Molecules. 8.1 Introduction. 8.2 Trial Wavefunctions and their Associated Energies. 8.3 The Variation Principle. 8.4 The Hamiltonian Operator for the Hydrogen Molecule-ion. 8.5 The Born-Oppenheimer Approximation. 8.6 Molecular Orbitals for the Hydrogen Molecule-ion. 8.7 The Hydrogen Molecule. 8.8 Molecular Orbitals for Other Diatomic Molecules. 8.9 Molecular Orbitals for Homonuclear Diatomic Molecules. 8.10 Application of MO Theory to Heteronuclear Diatomic Molecules. 8.11 Hybridization in Polyatomic Molecules. 8.12 Bonding in the Water Molecule. 8.13 Hückel Molecular Orbital Theory. Answers to Problems. Subject Index.