Valency

This book was written after one of us published two editions of a smaller book (Atomic Structure and Valency by R. D. Brown, 1961 and 1966) and from the experiences of all three of us teaching a first-year university course in valency at Monash University. Our object has been to give enough of an historical introduction to quantum mechanics to enable a student to grasp the fundamental ideas without being subjected to much mathematical formalism. We have also tried to avoid making erroneous statements in the interest of simplicity (e. g" the widespread tendency to ignore the difference between 2Pl, 2po, 2p-l and 2px, 2py, 2p z) because these lead to irritation and confusion of the better students, when they proceed to further studies of chemical quantum mechanics. The topics we have chosen to expand upon-i. e. , energy levels of electrons in atoms, energetic considerations of bonding in diatomic molecules, and packing of ions in the simplest solid state structures­ we believe form a good basis for students to progress to more complicated systems in a qualitative way. Both space and the intended level ofthe book have necessitated that the experimental section on spectroscopic and diffrac­ tion methods be very introductory. Again we believe that it is essential for a student to have some acquaintance with this, if the whole subject is to have a firm basis.

1 Introduction.- SI Units.- Derived SI Units.- Prefixes for Fractions and Multiples of SI Units.- Units Contrary to SI.- Energy Units in Valency.- Classical Forms of Energy.- Problems.- 2 Gross Atomic Structure.- The Early Clues.- The Rutherford Experiment.- Discovery of the Neutron and Periodic Classification of the Elements.- Problems.- 3 Atomic Theory.- Two Spanners in the Works.- The Michelson-Morley Experiment.- Blackbody Radiation.- Dual Nature of Light and Matter.- The Wavelength of Sally Brown.- The Wavelength of an Electron.- The Spectrum of Atomic Hydrogen.- The Bohr Theory of Atomic Structure.- Stationary States Confirmed.- The Demise of the Bohr Theory.- The Standing Waves of a Vibrating Guitar String.- The Standing Waves of a Vibrating Drum Head.- A Wavelike Equation Applied to Matter.- Solutions to Schroedinger’s Wave Equation.- The Heisenberg Uncertainty Principle.- Quantum-mechanical Hydrogen Atom.- The 1s Orbital.- The 2s and 2p Orbitals.- The 3s, 3p, and 3d Orbitals.- n = 4 Orbitals.- The Ground State of the Hydrogen Atom.- Other One-electron Atoms.- Summary.- Problems.- 4 Many-electron Atoms.- Experiments Leading to Determination of Energies of Electrons in Atoms.- Electron Spin and the Pauli Principle.- Energy Levels of Many-electron Atoms.- Helium, Z = 2.- Lithium, Z = 3.- Beryllium to Neon.- From Sodium on.- The Periodic Table.- Trends in Ionization Potential.- Electron Configurations of Doubly Charged First-transition-series Ions.- Atomic Size.- Electron Affinities.- Summary.- Problems.- 5 Molecular Theory and Chemical Bonds.- Energy Changes and the Chemical Bond.- Valency and Quantum Mechanics.- Combinations of Atomic Ions.- Ion Clusters.- Review of Ionic Bonding.- The Covalent Bond.- The Virial Theorem and Molecular Stability.- The Forces in H2/+.- The Molecular Orbitals 1s? and 1s?*.- The Molecules H2/+, H2, He2/+, and He2.- H2/+.- H2.- H2/+.- He2.- The Molecular Orbitals 2s?, 2s?*, 2pz?, 2pz?*, 2px?, 2px?*, 2py?, and 2py?*.- Li2.- Be2.- B2.- C2.- N2.- O2.- F2.- Ne2.- Diatomic Molecular Ions.- Heteronuclear Diatomic Molecules.- The LiH Molecule.- The HF Molecule.- The CO and NO Molecules.- Experimentally Measurable Molecular Parameters.- Bond Lengths.- Interbond Angles.- Bond Energies.- Dipole Moments.- Magnetism.- Electron Sharing and the Completed Valence-shell Principle.- Resonance.- Geometric Distribution of Bonds in Space.- Valence-bond Theory and Valence States.- Hybridization.- sp2 Hybrid Orbitals.- sp3 Hybrid Orbitals.- Other Hybrid Orbitals.- Delocalized Molecular Orbitals.- ?- and ?-Molecular Orbitals in Polyatomic Molecules.- Crystal-field Theory.- Crystal Fields, Spectra, and Magnetic Properties.- Van der Waals Forces.- Hydrogen Bonds.- Summary.- Problems.- 6 The Solid State.- Ionic Solids.- Metals.- Molecular Crystals.- Covalent Solids.- Crystal Structures.- Close-packed Structures.- The Equivalence of CCP and FCC Unit Cell.- The Unit Cell of HCP.- Sites in Close-Packed Structures.- Body-centered Cubic Lattice.- The Diamond Lattice.- Structures of Elements and Compounds.- The Elements.- Ionic Crystals.- Radius Ratio and Crystal Structures.- Covalent Solids.- Three-dimensional Giant Molecules.- Layer Lattices.- Chain Lattices.- Molecular Lattices.- A Biological Macromolecule, DNA.- Problems.- 7 Experimental Methods of Valency.- Spectroscopic Methods.- Rotational Transitions.- Vibrational-rotational Transitions.- Electronic Transitions.- Microwave Spectroscopy.- Infrared Spectroscopy.- Visible-ultraviolet Spectroscopy.- Nuclear Magnetic Resonance Spectroscopy.- Mass Spectroscopy.- Diffraction Techniques.- Problems.- Appendix I: Angular Momentum and the Bohr Atom.- Appendix II: Spherical Polar Coordinates.- Appendix III: Atomic Orbitals and Magnetic Quantum Numbers.