Much of Ken Wade's scientific career was devoted to developing and exploiting the chemistries of boron, aluminium, gallium and indium (the Group 13 elements). He made significant contributions to both experimental and theoretical aspects of the subject and was a highly regarded teacher and attentive research supervisor. Ken was a modest and self-critical man who had a rare ability to recognize patterns in large chemical and molecular structure data sets and express the resulting generalizations in the form of simple rules that experimental chemists could appreciate and use to predict new compounds. Ken was fascinated by the structures of cluster compounds that are based on regular polyhedral shapes. Cluster molecules generally contain groups of metal atoms linked by metal–metal bonds and located on one or more spherical shells. Since the 1960s they have attracted the attention of both academic and industrial chemists. Understanding and predicting their three-dimensional shapes raised a significant intellectual challenge for chemists. The clusters also attracted attention because they occupy an intermediate position between co-ordination compounds based on a single metal atom and the parent metal, which has an infinite number of linked metal atoms. This provided chemists with a unique opportunity to explore the evolution of their electronic and chemical properties as the cluster size increases. Ken was the first to recognize the electronic relationships connecting closo- , nido- , arachno- and hypho - clusters. These clusters are inter-related by the successive removal of vertices from a regular closo- deltahedron, i.e. a polyhedron with all the faces triangular. His ability to connect the structures of these molecules to the number of valence electrons involved in skeletal bonding represented a significant contribution to chemical bonding theories. Ken communicated his conclusions in very clearly written papers and books. This made the complexities of cluster chemistry amenable to many and especially those who did not have a strong background in quantum chemistry. The skeletal electron counting rules, or Wade's Rules, which Ken pioneered, are now very much part of the fabric of modern cluster chemistry and form an important component of modern undergraduate inorganic chemistry courses. Wade's Rules may be applied to main group and transition metal carbonyl clusters as well as clusters containing both main group and transition metal fragments. Besides providing an accessible entry into cluster chemistry for students, the rules have been used creatively by many leading synthetic chemists to discover new classes of compounds.

The valence shell electron pair repulsion theory (VSEPR) added a threedimensional interpretation of simple molecular inorganic compounds by proposing that bonds and lone pairs are both stereochemically active and together define a characteristic co-ordination polyhedron. The polyhedral skeletal electron pair theory (PSEPT) developed an analogous relationship for borane and metal carbonyl polyhedral molecules which is based on the total number of skeletal valence electrons in related closo-, nido- and arachno- deltahedral molecules. The historical development of the ideas which led to the PSEPT has been described in the Introductory Chapter of Volume 1. The electron counting rules associated with this generalisation have proved to be useful as aide-memoire for teaching inorganic chemistry since they bring together a large body of structural information for polyhedral molecules. Their simplicity provided an easily applicable, but reasonably reliable, indicator for identifying potential new targets for synthetic chemists. The fundamental question remains - "What do you do if the rules do not work?". This chapter provides an account of the steps taken when a significant group of cluster compounds were found not to comply with the rules. The gold clusters discussed in this chapter were recognised as such a group in the 1970s, but they did not follow the pattern which had been recognised earlier for polyhedral boranes and transition metal carbonyl clusters. Furthermore, as their structures were revealed by X-ray crystallography it became apparent that they provided many examples of skeletal isomerism, i.e. more than one skeletal geometry was observed for seemingly isoelectronic molecules. In addition, spectroscopic studies showed that many of the clusters were stereochemically non-rigid especially in solution. The challenge of bringing these gold clusters within the scope of PSEPT when they do not share the same structures and electron counts as metal carbonyl clusters have multiple structures and are frequently stereochemically non-rigid was not trivial. Most importantly it was not sufficient to just tinker with the numerological aspects of PSEPT but a re-examination of the fundamental quantum mechanical assumptions underlying PSEPT and reformulating it in the new context.

The valence shell electron pair repulsion theory (VSEPR) provided a three-dimensional interpretation of the structures of simple molecular inorganic compounds by recognising that bonds and lone pairs are both stereochemically active and when taken together define a spherical polyhedron. The polyhedral skeletal electron pair theory (PSEPT) developed an analogous relationship for borane and metal carbonyl polyhedral molecules. Related closo-, nido- and arachno-deltahedral molecules shared the total number of skeletal valence electron pairs (sep). The historical development of the ideas which led to the PSEPT was described in the Introductory Chapter and this chapter summarises the essential features of Tensor Surface Harmonic Theory (TSHT). TSHT provided a theoretical justification for the electron counting rules which accompanied the PSEPT. TSHT was developed by Anthony Stone using the quantum mechanical solutions for a particle on a sphere to define the molecular orbitals in molecular clusters. It achieved this by describing the radial molecular orbitals using the scalar harmonic solutions and the tangential interactions on the surface of the sphere using vector harmonic solutions. For clusters where radial bonds dominate then the wave functions and solutions are analogous to the jellium model developed at approximately the same time. For main group molecular clusters and specifically the boron hydride anion clusters [BnHn](2-) it is essential to take into account the interactions between those orbitals which result from the overlap of p orbitals perpendicular to the radii of the sphere and this requires a utilisation of the vector harmonic solutions for the particle on a sphere. For transition metal clusters it is also necessary to utilise the tensor surface harmonic functions to describe the interactions between the d(delta) orbitals lying in the surface of the sphere. The group theoretical implications of TSHT are profound and have been used to account for the closo-, nido- and arachno-relationships in metal clusters, the allowed vs. forbidden nature of polytopal rearrangements and most importantly exceptions to the electron counting generalisations.

2021 marks the 50th Anniversary of the publication by Ken Wade's "The structural significance of the number of skeletal bonding electron-pairs in carboranes, the higher boranes and borane anions, and various transition metal carbonyl cluster compounds" in Chemical Communications. This paper played an important role in the development of cluster and polyhedral main group chemistry and through the isolobal analogy encouraged imaginative interconnections between main group, transition metal and organic chemistry. It has been cited more than 500 times and the rules which developed from this and related papers are introduced in all modern undergraduate inorganic textbooks. It is therefore appropriate to publish a set of reviews which illustrate the influence of these generalisations on modern inorganic chemistry and give those newer to the field an insight into how the ideas which Wade introduced evolved. The chapters also give a critical account of the limitations of the approach and suggest how the subject may develop in the future.

The discovery of the optical microscope played an important role in the scientific revolution of the seventeenth century because it enabled one to directly view objects which were invisible to the naked eye. In 1667 Robert Hooke improved the microscope invented in the previous century in Holland and used it to examine the "microscopic" appearance of snowflakes and plants. Others were able to view for themselves the presence of very small objects and the structures of plants, hair, skin, bones etc. The development of X-ray crystallography at the beginning of the twentieth century by von Laue and the Braggs played an equally important role in the scientific revolution which has shaped our lives. The technique they discovered did not enable scientists to look at the molecular world by looking through a more powerful microscope, but it provided data which when processed enabled scientists to calculate the structures of molecules and appreciate their three-dimensional structures. It provided the zeitgeist of our time that the knowledge of the structure would lead to a more profound understanding of the function and properties of that class of molecule.This chapter recounts the early history of the development of this important technique and describes how the early technical problems were overcome. It is a fascinating technique because unlike the optical microscope it required the development of a deeper understanding of the way in which the X-rays interact with the electron density in the planes of the crystal and the development of models in order to model this electron density satisfactorily. This chapter traces how these problems were overcome. In the early days, the structures of even simple organic molecules would take a PhD student several months or even years to solve the structure. In time and particularly since the 1950s, the development of more sophisticated equipment and the massive rise in computing power made it possible to solve the three-dimensional structure of an organic molecule within a few minutes with the latest detectors on a laboratory instrument. This successful trajectory has resulted in the ability to study ever more complex molecules and use smaller and smaller crystals. The structures of over a million organic and organometallic compounds are now archived in the most commonly used database, and this wealth of information creates a new set of problems for future generations of scientists.

The earlier chapter recounted the early history of the development of X-ray crystallography and described how the early technical problems were overcome. It is a fascinating technique because unlike the optical microscope, it required the development of a deeper understanding of the way in which the X-rays interact with the electron density in the planes of the crystal and the development of theories which were able to quantitatively model it. The following sections deal with how the use of these techniques has led to structural chemistry becoming a very important aspect of modern chemistry. In the early days, the structures of even simple organic molecules would take a PhD student several months or even years to solve the structure. Since the 1950s the development of more sophisticated equipment and the massive rise in computing power made it possible to solve the three-dimensional structure of an organic molecule within hours if not minutes. This successful trajectory has resulted in the ability to study ever more complex molecules and use smaller and smaller crystals. The structures of over a million organic and organo-metallic compounds are now archived in the most commonly used database, and this wealth of information creates a new set of problems for future generations of scientists. This chapter introduces the techniques which have developed to help the chemist use the vast amount of data and the theoretical models which have helped them make use of the data to further their research activities.

Kossel and Lewis' description of the chemical bonding in ionic and covalent compounds in 1916 made an important contribution, which connected the Periodic Table to modern valence theory. In a 1919 paper Langmuir made the perceptive observation that neutral molecules, which had the same number of electrons, e.g. N2 and CO and N2O and CO2, had remarkably similar physico-chemical properties. Inorganic chemists have used this isoelectronic principle to interconnect a wide range of compounds and thereby explore the implications of the Periodic Table.

The 150th anniversary of the publication of The Principles of Chemistry by Mendeleev has been declared "The International Year of the Periodic Table" by the United Nations and is being marked by a multitude of events around the world. There is no doubt that the Periodic Table occupies an iconic position not only for chemistry but more generally as a symbol of scientific endeavour. The proposal of a Periodic Table could not have happened without an understanding of what is required for a substance to be defined as a chemical element and the discovery of sufficient elements to provide a reasonably large sample to attempt to find an ordered pattern. This chapter traces how the first metals were discovered approximately 7,000 years ago and proved to be sufficiently useful to initiate the copper, bronze and iron ages. This journey initially was based on practical considerations but eventually developed into recognised methods of careful and controlled experimentation, observation and theoretical thinking which we now associate with the Scientific Revolution. The practical and conceptual progress made internationally resulted in the discovery and purification of 98 elements which occur naturally on earth and organised them in a logical order in a Periodic Table, which is recognisable by chemists throughout the world. Furthermore, an understanding of the fundamental nature of elements in terms of atoms, whose properties are governed by quantum mechanical principles, led to the synthesis and characterisation of elements not found on earth. Indeed, one in six of the elements in the current Periodic Table is man-made and were made in high technology laboratories since 1940.

The replacement of precious metals by base metals in homogeneous catalysis is of great interest due to their high natural abundance and generally lower toxicity. However, in many cases the reactivity of secondand third-row transition metals cannot easily be transferred to first-row metals due to fundamental differences in electronic structure and bonding, which affect key elementary steps of homogeneous catalysis, like oxidative addition or reductive elimination. These formally multielectron redox steps are often less favorable for 3d metal complexes for various reasons, such as a preference for higher spin states resulting in lower metal-ligand bond dissociation energies. This tutorial review covers the recent efforts to make up for these problems and establish first-row metal homogeneous catalysts with “noble metal-like” reactivity by the use of functional ligands. Such ligands enable the replacement of challenging, metal-centered multielectron redox steps, e.g., by ligand-centered redox activity or alternative, redox-neutral ways of M. Fritz and S. Schneider (*) Universität Göttingen, Institut für Anorganische Chemie, Göttingen, Germany e-mail: sven.schneider@chemie.uni-goettingen.de substrate activation, such as heterolytic H–E cleavage. These concepts will be discussed in the context of recent milestones, which also emphasize that the alternative mechanistic scenarios do not only allow for use of base metals in homogeneous catalysis but offer unprecedented reactivities and selectivities.

The 150th anniversary of the publication of The Principles of Chemistry by Mendeleev has been declared “The International Year of the Periodic Table” by the United Nations and is being marked by a multitude of events around the world. There is no doubt that the Periodic Table occupies an iconic position not only for chemistry but more generally as a symbol of scientific endeavour. The proposal of a Periodic Table could not have happened without an understanding of what is required for a substance to be defined as a chemical element and the discovery of sufficient elements to provide a reasonably large sample to attempt to find an ordered pattern. This chapter traces how the first metals were discovered approximately 7,000 years ago and proved to be sufficiently useful to initiate the copper, bronze and iron ages. This journey initially was based on practical considerations but eventually developed into recognised methods of careful and controlled experimentation, observation and theoretical thinking which we now associate with the Scientific Revolution. The practical and conceptual progress made internationally resulted D. M. P. Mingos (*) Inorganic Chemistry Laboratory, Oxford University, Oxford, UK e-mail: Michael.mingos@seh.ox.ac.uk in the discovery and purification of 98 elements which occur naturally on earth and organised them in a logical order in a Periodic Table, which is recognisable by chemists throughout the world. Furthermore, an understanding of the fundamental nature of elements in terms of atoms, whose properties are governed by quantum mechanical principles, led to the synthesis and characterisation of elements not found on earth. Indeed, one in six of the elements in the current Periodic Table is man-made and were made in high technology laboratories since 1940.

In order to understand the launching in 1966 of Structure and Bonding, it is necessary to appreciate the factors which contributed to the emergence of inorganic chemistry as an equal branch of chemistry. A variety of social and economic factors contributed to the transformation of inorganic chemistry from an essentially descriptive subject into an intellectual equal of organic and physical chemistry. The aims and distinctive features of Structure and Bonding are identified with reference to the initial preface and the composition of the editorial board. The research interests and characteristics of some of the founding editorial board members are introduced and used as a basis for highlighting the important topics which were covered in the initial 50 volumes. Subsequent changes in the character of the journal are reviewed and used to introduce the present anniversary volume.

The seminal papers of Lewis and Kossel in 1916 are put into a historical perspective. Mendeleev’s periodic table, Thompson’s discovery of the electron, Ramsay and Raleigh’s discovery of the noble gases, Rutherford’s model of the atom and Bohr’s description of the stationary orbitals for the electrons in atoms all paid an important role in providing the background for Lewis and Kossel’s proposal that the chemical bond originated either from the transfer of electrons or the sharing of electron pairs. These insights depended on the attainment of inert gas configurations by the atoms either directly by electron transfer or electron-pair sharing. The model incorporated an evolutionary gene which has enabled it to survive and grow by incorporating subsequent developments in quantum physics. The simplicity of the model has resulted in the development of a notation, which is universally used by chemists and has evolved to plot the course of chemical reactions and predict their regioselectivities. Its initial limitations are discussed, and the way in which they have been overcome by an orbitally based model is recounted. The model has been repeatedly enriched by quantum mechanically based theoretical studies.

Chemical structure and bonding. The scope of the series spans the entire Periodic Table and addresses structure and bonding issues associated with all of the elements. It also focuses attention on new

The study of gold cluster compounds originated from Malatesta's syntheses of tertiaryphosphine derivatives in the 1960s and was greatly extended between 1970 and 2000. Single crystal X-ray studies defined the major structural classes and led to the development of a theoretical model which accounted for their closed shell requirements in terms of their topological features and proved to be sufficiently flexible to be extended to related heteronuclear cluster compounds. Since the turn of the century the range of gold cluster compounds has been greatly extended by the study of organothiolato-gold cluster compounds. The structures of these compounds have revealed that the gold atoms combine with the organothiolato-ligands to generate a novel class of metallo-organothiolato-ligands which protect and stabilise the inner core of gold atoms. These developments originally suggested that the phosphine and organothiolato-clusters defined quite distinct classes of gold clusters, but recent structural and theoretical developments have reconciled many of these differences. This review summarises the structures of all the clusters of gold and suggests a theoretical model which effectively unites the broad structural properties of the two classes of compound. This model is based on the united atom model for diatomics developed by Mulliken and the compression co-ordinate is related to the interpenetration of icosahedral and cuboctahedral pseudo-spherical clusters. The predicted closed shell requirements agree well with the results of structural determinations.

Cobalt boryl complexes, which have only been sporadically reported, can be accessed systematically with remarkable (but controllable) variation in the nature of the M-B bond. Complexes incorporating a very strong trans σ-donor display unparalleled inertness, reflected in retention of the M-B bond even in the presence of extremely strong acid. By contrast, the use of the strong π-acceptor CO in the trans position, results in significant Co-B elongation and to labilization of the boryl ligand via unprecedented CO migratory insertion. Such chemistry provides a pathway for the generation of coordinative unsaturation, thereby enabling ligand substitution and/or substrate assimilation. Alkene functionalization by boryl transfer, a well-known reaction for noble metals such as Rh or Pt, can thus be effected by an 18-electron base-metal complex.

Abstract This review provides a theoretical underpinning of previously published definitions of ambidentate, ambivalent and ambiphilic ligands. The study encompasses ambivalent ligands such as NO, NR, N2R; ambiphilic molecules such as SO2, I2 and ambiphilic transition metal complexes, e.g. [Pt(PCy3)2]. These ambivalent molecules adopt alternative geometries which depend primarily on the number of electrons which they formally donate or accept. The theoretical analysis focuses initially on those complexes where the same ligand displays ambivalent properties within the same molecule in order to define the energetics of their interconversion. These square-pyramidal complexes provide a test-bed for generating data which throws light on the relative abilities of ambivalent ligands to adopt linear or bent geometries. The ligands were compared with NO and their relative abilities were placed in the following order PO > PH2 > N2H > SO2 > NO > NH2 > NS. The linear nitrosyl ligand does not exert a trans-influence and this property has been contrasted with the nitrido-ligand which shows a large trans-influence. The conversion of NO to a non-linear geometry results in a strong trans-influence and this has significant catalytic and biological importance. Calculations on octahedral palladium complexes have been used to order the trans-influences of ambivalent ligands when they adopt their alternative symmetry signatures. The relative trans-influences are NO > PH2 > NS > N2H > NH2. The interconversion of linear and bent dinitrosyls provides an interesting inorganic example of valence tautomerism and this is noted as a general characteristic of ambivalent and ambiphilic ligands. The soft energy surface associated with these interconversions leads to the experimentally verified fluxional process. The energetics of adduct formation by ambiphilic ligands has been studied using a series of SO2 complexes of palladium and platinum and the results contrasted with adducts of SO2 with main group Lewis acids and bases. The isomers {(PH3)2M(SO2) p}16 and {(PH3)2M(SO2) np}14 are calculated to have very similar energies and the relative stabilities of analogous isomers may be manipulated by varying the bite angle of the phosphine ligands in {[(PH2)2CnH2n]M(SO2)}.

The very strong reducing capabilities of the boryllithium nucleophile (THF)2Li{B(NDippCH)2} (1, Dipp = 2,6-iPr2C6H3) render impractical its use for the direct introduction of the {B(NDippCH)2} ligand via metathesis chemistry into the immediate coordination sphere of transition metals (d(n), with n ≠ 0 or 10). Instead, 1 typically reacts with metal halide, amide and hydrocarbyl electrophiles either via electron transfer or halide abstraction. Evidence for the formation of M-B bonds is obtained only in the case of the d(5) system [{(HCDippN)2B}Mn(THF)(μ-Br)]2. Lower oxidation state metal carbonyl complexes such as Fe(CO)5 and Cr(CO)6 react with 1 via nucleophilic attack at the carbonyl carbon atom to give boryl-functionalized Fischer carbene complexes Fe(CO)4{C(OLi(THF)3)B(NDippCH)2} and Cr(CO)5{C(OLi(THF)2)B(NDippCH)2}. Although C-to-M boryl transfer does not occur for these formally anionic systems, more labile charge neutral bora-acyl derivatives of the type LnM{C(O)B(NDippCH)2} [LnM = Mn(CO)5, Re(CO)5, CpFe(CO)2] can be synthesized, which cleanly lose CO to generate M-B bonds. From a mechanistic standpoint, an archetypal organometallic mode of reactivity, carbonyl extrusion, has thus been shown to be applicable to the boryl ligand class, with (13)C isotopic labeling studies confirming a dissociation/migration pathway. These proof-of-methodology synthetic studies can be extended beyond boryl complexes of the group 7 and 8 metals (for which a number of versatile synthetic routes already exist) to provide access to complexes of cobalt, which have hitherto proven only sporadically accessible.