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This chapter summarizes developments in the study of (transition) metal clusters held by metal-metal bonds. Similar to the case of boranes and carboranes, electron-counting rules have been devised to correlate the bonding and structure of metal clusters. Three sections are devoted to clusters with two to seven metal atoms, followed by a section on iso-bond valence and iso-structural series. The final section covers selected areas of metal-metal interaction, including aurophilicity, argentophilicity, metal string molecules, and metal-based infinite chains and networks.

Even though hydrogen is the ‘simplest’ atom in the Periodic Table, it has a very rich structural chemistry with eight bonding types. This chapter discusses the nature of the hydrogen bond, non-conventional hydrogen bonds (X-H···π, X-H···M, X-H···H-E, etc.), hydride complexes, molecular hydrogen coordination compounds, and σ-bond complexes.

This chapter covers the structural chemistry of Groups 1 and 2 elements, except hydrogen. For Group 1 metals, special attention is paid to the oxides, lithium nitride, inorganic alkali metal complexes, methyllithium compounds, π-complexes of lithium, sodium and potassium, alkalides and electrides, etc. For the Group 2 metals, the coverage includes their complexes, nitrides, low-valent oxides and nitrides, polymeric chains, Grignard reagents, metallocenes, etc. The chapter concludes with a section on the alkali and alkaline-earth metal complexes with inverse crown structures.

This chapter applies the group theoretic technique introduced in Chapter 6 to a number of chemically interesting problems. These problems include molecular orbital treatment of AHn (n = 2-6) molecules and cyclic conjugated polyenes (with and without d-orbital participation), construction of hybrid orbitals, relationship between molecular orbital and hybridization theories, molecular vibrations, etc. A large number of worked examples have been selected to illustrate that group theory can be used to simplify the physical problem and yield solutions of chemical significance. The advantage of this method becomes more obvious when the symmetry of the chemical system increases. Indeed, for highly symmetric molecules, very complex problems can have simple and elegant solutions. Even for less symmetric systems, symmetry arguments can still lead to meaningful results and conclusions that cannot be easily obtained otherwise.

This chapter covers the electronic structure of coordination complexes, using the language of group theory throughout. The bonding of these complexes ranges from ionic (crystal field theory, or CFT) to covalent (molecular orbital theory). In CFT, group theory is employed to derive the terms split from a given atomic electronic state under the influence of a set of ligands. Other topics discussed include Orgel diagrams, Tanabe-Sugano diagrams, correlation of weak and strong field approximations, spin-orbit interaction (double group), etc. Regarding molecular orbital theory, techniques used in Chapters 3 and 7 are applied to coordination complexes, with the metal d-orbitals now playing a central role. These theories are then used to interpret a number of electronic spectra of complexes selected from the literature. The chapter concludes with sections on vibronic interaction in complexes and on the f-orbitals and their crystal field splitting patterns.

This chapter first discusses the difference between semi-empirical and ab initio methods, then devotes most of the remaining pages to ab initio calculations. Each ab initio calculation is defined by two ‘parameters’: the basis set employed and the level of electron correlation adopted. These two topics are discussed in some detail. Density functional theory is also discussed, which has gained popularity in recent years. After describing these computational methods, a brief assessment on the performance of various levels of theory in yielding structural parameters, vibrational frequencies, and energetic quantities is given. Finally, a few examples are selected from recent literature to show how computations complement experiments to arrive at meaningful conclusions.

Following an extensive discussion on the symmetry of crystals in the previous chapter, a large number of crystal structures of inorganic compounds are collected in this chapter to familiarize readers with the most common space groups. The basic crystal structures introduced include cubic closest packing (NaCl, CaF2, cubic ZnS, spinel compounds, etc.), hexagonal closest packing (hexagonal ZnS, NiAS, CdI2, α-Al2O3, rutile, etc.), body-centered cubic packing (α-AgI, CsCl, etc.). The final two sections of the chapter cover perovskite structure, including superconductors belonging to this structural type, and magnetic materials such as SmCo5, Sm2Co17 and Nd2Fe14B.

The symmetry properties of molecules were discussed in Chapter 6, and the corresponding properties of crystals are presented here. In contrast to discrete molecules, crystals have a lattice structure with three-dimensional periodicity. Hence, additional symmetry elements such as translations, screw axes, and glide planes, which are applicable to an infinitely extended system, need to be considered. This chapter introduces the concept and nomenclature of space groups and their application in describing the structures of crystals. Examples of crystal structures for selected space groups are provided. The chapter concludes with a section on the use of space group symmetry in the determination of crystal structure. In short, the chapter gives a succinct introduction to the symmetry of crystals.

This chapter begins with a description of the characteristic properties of the lanthanide elements, including their metallic and ionic radii (lanthanide contraction), crystal structures, oxidation states, electronic states, and magnetic properties. Their oxides and halides, and the coordination geometry of their cations are discussed. The section on organometallic compounds of the lanthanides is mainly concerned with those with cyclic organic ligands such as benzene, cyclopentadienyl, or cyclooctatetraenyl groups. The chapter concludes with a section on the reduction chemistry of the +2 oxidation state.

This chapter covers the rudiments of group theory, with emphasis on the use of the character tables of molecular point groups. The chapter begins with the identification of the symmetry elements a molecule possesses, and the symmetry operations these elements generate. With such knowledge at hand, the symmetry point group of a given molecule can be readily determined. The character tables of the point groups are then introduced, and the Mulliken notation for the irreducible representations is discussed in detail. Finally, the direct product of two irreducible representations is covered. The result of the direct product is used to identify the non-zero integrals in quantum chemistry and derive the selection rules in electronic spectroscopy. No rigorous mathematics is used in treating the various theories in this chapter. Instead, abstract concepts are often illustrated with examples based on real chemical compounds or practical applications.

This chapter starts off with an in-depth discussion on the angular and radial functions of the hydrogenic orbitals. Then the ground 1s 2 and the excited 1s 12s 1 configurations of the helium atom are employed to illustrate the determinantal wavefunction and the Pauli Exclusion Principle. Some simple trial wavefunctions for helium are introduced, with emphasis on the physical meaning of the adjustable parameters. For the many-electron atoms, the L-S and j-j coupling schemes are used to derive the spectroscopic terms arising from a given atomic configuration. Examples are then given to illustrate the correlation between the terms derived by these two schemes. The chapter concludes with a section on atomic properties, including ionization energy and electron affinity, electronegativity, relativistic effect on the properties of elements.

This chapter on supramolecular chemistry is the longest one in the book. According to J.-M. Lehn, who shared the 1987 Nobel Prize in Chemistry with D. J. Cram and C. J. Pedersen, supramolecular chemistry is the study of organized entities of higher complexity (supermolecule) resulting from the association of two or more chemical species consolidated by intermolecular forces. Fundamental concepts such as the nature of intermolecular interactions, molecular recognition, self-assembly, crystal engineering, and supramolecular synthon are systematically introduced. Several examples are presented to shed light on this fascinating and ever-evolving research area.

This chapter covers the elements of Groups 17 (halogens) and 18 (noble gases) in the Periodic Table. For the elemental halogens, discussion includes their crystal structures and homopolyatomic anions and cations. The subsequent sections are on the interhalogen compounds and ions, charge-transfer complexes of halogens, the oxides and oxo compounds of halogens, etc. The final section devoted to noble-gas compounds with a comprehensive coverage on the structural chemistry of xenon.

This chapter starts off with the classification of solids, then discusses the various types of bonding or interaction in solids, including ionic bonding, metallic bonding, covalent bonding (band theory), and van der Waals interaction. Numerous examples are given for each type of bonding.

This chapter focuses on nitrogen, including the N2 molecule, all-nitrogen ions, dinitrogen complexes, nitrogen oxides and hydrides, etc. A significant portion of the chapter is devoted to the structural chemistry of phosphorus, consisting of sections on elemental phosphorus and Pn groups, the bonding types and coordination geometry of phosphorus, phosphorus-nitrogen and phosphorus-carbon compounds, etc. The chapter concludes with a section on the structural chemistry of arsenic, antimony, and bismuth, discussing their stereochemistry, clusters, and the intermolecular interactions in organoantimony and organobismuth compounds.

This chapter discusses the basic organic crystal structures, starting with the allotropes of carbon. It then covers the (aliphatic, aromatic, and fullerenic) compounds of carbon and the bonding in these compounds. The abnormal carbon-carbon single bonds, complexes containing a naked carbon atom, and complexes containing naked dicarbon ligands are discussed. The subsequent sections are on the chemistry of silicon (including silicates, silicide, etc.), halides, oxides, polyatomic anions, and organometallic compounds of the heavier members of Group 14 (germanium, tin, and lead).

About 80% of this chapter is devoted to the particularly rich structural chemistry of boron. There are sections on elemental boron, metal and non-metal borides, boranes and carboranes, boric acids, and borates. In the section on boranes and carboranes, electron-counting rules are introduced to account for the relationship between the bonding and structures of these compounds. For the remaining Group 13 elements, there are sections on their organometallic compounds with novel features (such as bridged structures, M-M bonding, π bonding, etc.) and on naked anionic metalloid clusters.

This chapter covers the rudiments of quantum theory, including the dual nature of light and matter, the Uncertainty Principle and probability concept, the electronic wavefunction, and the probability density function. Numerical examples are given to show that given the electronic wavefunction of a system, the probability of finding an electron in a volume element around a certain point in space can be readily calculated. Finally, the electronic wave equation, the Schrödinger equation, is introduced. This discussion is followed by the solution of a few particle-in-a-box problems, with the ‘box’ having the shape of a wire (one-dimensional), a cube, a ring, or a triangle. Where possible, the solutions of these problems are then applied to a chemical system.

This chapter focuses on the first two elements of the group: oxygen and sulfur. There is a section each on dioxygen and ozone, oxygen and dioxygen coordination compounds, and structure of water and ices (including protonated water species). For sulfur, coverage includes its allotropes and polyatomic sulfur species, metal complexes with sulfide anions as ligands, and oxides and oxoacids of sulfur. Finally, there is a section on the allotropes and stereochemistry of selenium and tellurium, as well as the polyatomic anions and cations of these elements.

This text is an updated English version of a class-tested textbook originally published in Chinese in 2006. Its contents are based on the lecture notes of several courses taught by the authors at The Chinese University of Hong Kong and Peking University. These courses include Chemical Bonding, Structure and Properties of Matter, Advanced Inorganic Chemistry, Quantum Chemistry, Group Theory, and Chemical Crystallography. This book consists of three parts. Part I reviews the basic theories of chemical bonding, with chapters on elementary quantum theory, atomic structure, bonding in molecules, bonding in solids, and computational chemistry. Part II introduces point groups and space groups, and their applications to the study of discrete molecules and crystals. A large number of worked examples are provided in order to illustrate the usefulness and elegance of the symmetry concept. Part III constitutes about half of the book and it gives a succinct description of the structural chemistry of the elements in the Periodic Table. The main-group elements are covered in seven chapters and three other chapters deal with the rare-earth elements, transition-metal clusters and supramolecular systems. The selected systems, many of them from recent literature, are used to elucidate various aspects of structure and bonding presented in Parts I and II, and to expound the current research trends in structural inorganic chemistry

This chapter covers covalent bonding in small molecules, starting from hydrogen molecule ions and hydrogen molecules, and then proceeding to homonuclear and heteronuclear diatomic molecules, and linear triatomics. Using the hydrogen molecule as the prototype, the bonding of this molecule is treated by the molecular orbital and valence bond theories. The difference between these two models is discussed in detail. In addition, since both methods are approximate, refinement of the approximation will lead to identical results. The hybridization theory is also discussed, and several systems that may be effectively dealt with by this theory are provided. The chapter concludes with a discussion of the Hückel molecular orbital treatment of conjugated polyenes. The wavefunctions of the polyenes are used to predict the products of the cyclization reactions of the polyenes.