A large number of mixed main-group–transition-metal clusters can be understood with isolobal ideas and the electron-counting rules. However, there is a growing number that cannot. These clusters are more closely related to metal clusters than main-group clusters. In this chapter we begin with a survey of the “rule-abiding” mixed-element clusters with emphasis on variety rather than comprehensiveness. Why a cursory survey? Because with a solid background of main-group and transition-metal cluster behavior under our belts, the isolobal analogy permits a ready understanding of mixed systems that follow the rules. Understanding permits prediction of possible stoichiometry and structure thereby generating goals for future synthesis.

It is the second compound type that constitutes an interesting challenge to our views of cluster electronic structure. With this compound type we encounter a structural response arising from main-group and transition-metal atom competition within the context of a molecular cluster. This competition generates both cluster shapes invariant to change in electron count as well as new cluster-structure types associated with unusual electron counts. Both pose a problem of interpretation. But the problem is a worthwhile one as structures that deviate from the electron-counting rules contain information on the electronic factors that underlie cluster chemistry in general. “Failure” of the rules actually constitutes a gateway leading to compounds with hybrid properties not accessible with either pure main-group or transition-metal clusters. Useful chemistry is all about properties and the more ways we develop to vary and control properties the better off we are.

A chemist's approach to understanding matter is conveniently divided into three stages. First, fixed stoichiometric relationships between the atomic constituents of matter exist in molecular compounds and in many compounds with extended structures. Hence, the composition of a pure substance provides initial definition to a new substance. Given the atomic nature of substances, it provides direct information on structure. In a historical sense, other early means of characterization were physical ones, e.g., melting point or dipole moment, and sensual, e.g., color or taste. As a consequence, they are less directly related to structure. In the second stage, geometric relationships between the constituent atoms as well as spectroscopic and theoretical information on electronic structure add dimensions and shape to the composition data. Finally, reaction chemistry, i.e., reaction stoichiometries, rates and mechanisms, provides connections between compound types as well as generating new substances for which the whole process begins again.

Stable compounds are the most thoroughly characterized and provide the corpus of chemistry. However, “stability” is one of the definable, but casually used, terms of chemistry. Stability is associated with energy, and energy and structure are inextricably combined. A chemist, well educated in a given area, has a good understanding of both energy and structure. In a practical sense, stable for the inorganic chemist is often defined empirically by isolation and storage at room temperature. Most stable is often implied by the term, but it is not always clear that the most stable (thermodynamic) products have been characterized in a given reaction.

The conceptual connection between cluster and solid-state chemistries is the unifying theme of the first seven chapters. Complementary empirical connections between cluster and solid-state chemistries are emphasized in this final chapter. That is, the synthesis of solid-state materials from molecular precursors including clusters permits the strengths of molecular synthesis to be used in the development of new materials. On the other hand, the utilization of Zintl clusters as novel reagents in solution permits the advantages of thermodynamically driven solid-state synthesis to be transferred to the production of clusters in solution. Most of the examples discussed could have been included in earlier chapters, but are gathered here to serve as a review as well as a stimulus to creative thought for future research in cluster and materials chemistries.

Cluster precursors to new solid-state phases

In this section we give examples of molecular clusters used as precursors to new dense phases or to new porous networks.

III/VI Semiconductor synthesis

Traditional solid-state syntheses at high temperatures are guided by thermodynamics expressed in phase diagrams in distinct contrast to much of molecular chemistry that utilizes kinetics to guide synthesis. We viewed clusters as fragments of bulk solids stabilized by ligands; however, not all clusters can be viewed as building blocks of known bulk structures, e.g., icosahedral clusters. Hence, metastable phases not accessible by conventional solid-state synthesis might arise from cluster precursors. In other words, the structure of a cluster building block could determine the nature of the first-formed solid phase.

The structural chemistry of main-group and transition-metal clusters has been set forth in the last two chapters. What more can be said about molecular clusters? Quite a bit, in fact. Although broad similarities between p-block and d-block cluster chemistries exist, we have illustrated important differences in structural preferences. The intriguing question, then, is what happens if p-block and d-block elements compete in a single cluster environment? Will the preferences of one element type dominate the other or will the merging of metal and main-group fragments generate possibilities not accessible to main-group or transition-metal systems alone. Perhaps clusters with novel hybrid properties will result.

But there is another perspective to mixed clusters. The transition-metal chemist sees the main-group fragment as a complex “ligand” through which structure and chemistry at the metal centers is perturbed. A p-block chemist may rather view metals as tools to systematically vary the structure and reactivity of a coordinated main-group moiety. Neither the cluster perspective nor the metal-complex view is wrong: one chooses a perspective optimal for the problem at hand. In this chapter we explore mixed p-block/d-block compounds as metal–ligand complexes with an emphasis on connections to organometallic chemistry. In Chapter 5 the focus will be the complementary cluster view.

Isolobal main-group and transition-metal fragments

In the first three chapters, instances were noted where the number, symmetry characteristics and occupation numbers of the frontier orbitals of a transition-metal fragment were similar to those of a main-group fragment.

Clusters – a form of matter with structure and properties lying somewhere between those of atoms and solid-state substances – impact a substantial fraction of chemistry, drawing the attention of both inorganic and physical chemists. The larger the cluster the stronger the connection with solid-state chemistry and the greater the ramifications for modern materials science in the area of nanochemistry. The term cluster is used to designate a three-dimensional assembly of atoms and cluster structures may be found in s-, p-, and d-block element chemistries. When composed of a single element, the cluster motif complements the chains and rings of molecular catenates and the chains, sheets and networks of solid substances. Clusters are found with external ligands as well as without. Cluster structure is the focus of this text and we intend to show that cluster electronic structure serves as a bridge between molecular compounds and non-molecular solid-state compounds. These connections will become more readily apparent as the structural properties of clusters are developed.

The story begins in this chapter with the clusters of simplest geometric and electronic structure. These are clusters of p-block elements with defined stoichiometry and structure in which the cluster surface-atom valences are “terminated” with ligands. The large number known provide the factual base from which clever people have derived models that connect atomic composition with structure. In turn, these p-block models provide a foundation on which to build an understanding of more complex clusters such as condensed clusters, bare clusters and transition-metal clusters.

A modern chemist has access to good computational methods that generate numerically useful information on molecules, e.g., energy, geometry and vibrational frequencies. But we also have a collection of models based on orbital ideas incorporating concepts of symmetry, overlap and electronegativity. In this text we focus on the latter as these ideas have been a huge aid in understanding the connections between stoichiometry, geometry and electronic structure. The connections can be as simple as an electron count yielding user-friendly “rules.” Our problem here, the electronic structure of a cluster or a more extended structure of the type encountered in solid-state chemistry, requires the application of models beyond those reviewed in the Appendix. Models are like tools – they permit us to disassemble and assemble the electronic structure of molecules. For each problem we choose a model that will accomplish the task with minimum effort and maximum understanding. Just as one would not use a screwdriver to remove a hex nut, so too we cannot use highly localized models to usefully describe the electronic structures of many clusters and extended bonding systems. We must use a method that is capable of producing a sensible solution as well as one that is sufficiently versatile to treat both the bonding in small clusters and bulk materials.

The proven method we will use is one that generates solutions based on the orbitals and electrons that the atoms or molecular fragments bring to the problem.

The theme of this text, clusters as a bridge to solid-state chemistry, requires that we now consider the geometric and electronic aspects of substances that are solids. In doing so we will focus our attention initially on the nature of the atomic structures inside a bulk material; that is, we will completely ignore the surfaces. Towards the end of this chapter we will reincorporate surfaces into the problem and, in doing so, complete the bridge. The electronic-structure problem presented by periodic structures exhibiting extended bonding has been effectively dealt with in several earlier texts some of which are listed at the end of this chapter. These works go beyond what we need to establish our theme; however, the reader interested in more depth and breadth is referred to them.

Cluster molecules with extended bonding networks

As usual, let us begin with a discussion of geometric ideas relevant to a transition from molecular clusters to the solid state.

Surface vs. core atoms

In the structure of [Al69R18]3− (Figure 2.32) the number of nearest-neighbor Al atoms and bonding parameters changes in going from the outer shell made up of Al–R fragments deeper into the inner shells constructed from Al atoms alone. The internal cluster atoms display coordination numbers and inter-atomic distances more closely associated with bulk elemental Al than single-shell clusters. Is this reasonable? For the single-shell clusters discussed in preceding chapters the requirement for external ligands dominates the cluster stoichiometry/shape relationship.

1. (a) Approach: Cr possesses six valence electrons, thus ligands must be chosen to supply 12 more to satisfy the 18-electron rule, e.g., six CO ligands; Mn possesses seven valence electrons, thus ligands need to supply 11, e.g., 5 CO + 1 H. (b) This problem requires recognition of the types of bonds in the molecule and which ones, if any, are unusual. The answer to part (a) suggests the Cr–CO bonds can be adequately described as two-center donor–acceptor bonds. The Cr–H–Cr with a two-coordinate H atom is clearly the unusual situation; hence, a fragmentation into two Cr(CO)5 fragments and an H–anion is appropriate. A Cr(CO)5 fragment is a 16-electron species with an empty orbital available to accept an electron pair. The H– anion possesses one filled orbital; hence, the three orbitals (two from the metal fragments and one from H) can be used to form one bonding, one non-bonding and one antibonding three-center orbital with the bonding combination containing the two available electrons.

2. S contributes four AOs and the six H atoms contribute six AOs for a total of ten leading to ten MOs. The central atom has functions of symmetry a1g (3s) and t1u (3p), whereas the six ligand functions have symmetry-adapted combinations of a1g (3s) and t1u, and eg just like an octahedral transition-metal complex. As shown below, interaction between the central atom and the ligands generates four bonding MOs plus their antibonding partners and two non-bonding orbitals having ligand character only for atotal of ten MOs.

Of the millions of different chemical systems discovered since chemistry began, many are solids at room temperature. From the early days these solids have been classified in the four families, molecular, ionic, covalent and metallic solids, based on the nature of the forces which bind the atoms. Molecular solids are composed of groups of covalently bound atoms, i.e., molecules, held by weak charge-polarization (van der Waals) forces. In ionic solids, electrostatic attraction is the primary force binding cations and anions. Bonding in covalent solids is similar to that within molecules but extends over the whole crystallite. Metallic solids also exhibit extended bonding but, in addition, possess weakly bound, highly delocalized electrons easily moved by applied fields. Of course, this classification is somewhat artificial and many solids exhibit complex bonding in which more than one type of bonding is displayed. Molecular clusters in the solid state are naturally described nowadays with molecular-orbital models. Intermolecular interactions are weak. Although this is not true for solids with extended bonding networks, the solid-state machinery we developed in Chapter 6 shows that MO ideas smoothly transfer to crystalline solids. Hence, we have an analogous language for treating these more complex structures.

This is not a text of solid-state chemistry and the purpose of this chapter is to illustrate the use of the theoretical model of Chapter 6 with experimental examples. In doing so, we firmly establish the other foundation of our cluster bridge.

The Rowland grating

This is a grating ruled on a concave spherical mirror, in consequence of which it has a self-focusing property and needs no other optical component to produce a spectrum from a point or short line source. It is the invention of H. A. Rowland of Johns Hopkins University who gave an account of it in 1883. The rulings are the intersections of the sphere with a set of parallel, equi-spaced planes, so that the interval between rulings is not constant on the surface of the sphere, and the device, although it is a spherical mirror, has a definite optic axis.

The focusing property is as follows:

The grating is ruled on a spherical mirror of radius R. There is a circle, the Rowland circle, touching the sphere at its vertex perpendicular to the rulings and of radius R/2. The elementary theory of the grating states that monochromatic light from any point on this circle is diffracted according to the grating equation, and is subsequently focused at another point on the Rowland circle.

The theorem is not exact. There is no point focus but an approximation to the proof can be given by elementary geometry. In Fig. 9.1 the grating is displaced by an infinitesimal amount along the optic axis and intersects the Rowland circle at points x, x′. Suppose the grating constant at x is a.

The problem of photometry with silver halide emulsions is that of finding the relation between density and exposure. Density is defined as minus the logarithm of the transmission ratio, i.e. of the fraction of incident light transmitted through the emulsion to the detector (on the assumption that the response of the detector is linear). Exposure is defined as the product of incident intensity during the photographic exposure and the duration of the exposure, and it is assumed, justifiably, that the density depends only on the product.

The method of the common calibration curve is to take several photographs of the same spectrum under identical circumstances, but with different neutral-density filters, the filter densities ascending for example in factors of 2. The densities of a particular spectrum line, measured from the different exposures, will give a set of points on the calibration curve. A different spectrum line can then be interpolated on this initial line and the different exposures of this second line provide further points which extrapolate the curve at one end or the other. By continuing in this fashion with other spectrum lines, the curve can be continued, always by interpolating new initial material, gradually extending the curve in both directions as far as necessary and well beyond the linear portion.

Sensitivity calibration

There are so many variables in the optical path of a spectrograph that sensitivity calibration is necessarily totally empirical. A black body at a known temperature is the only feasible method of absolute calibration, and even then one must be sure that there has been a total suppression in the spectrograph of other orders and of scattered light. Reliable absolute calibration is such an onerous task that one must question the need for it in most circumstances. For almost all practical purposes a comparison with a standard source is sufficient. In the visible, a reasonable approximation – no more – can be obtained by making a spectrogram of a surface coated with freshly deposited magnesium oxide from burning magnesium ribbon which will scatter the light of the midday sun on a clear day. In the tropics and at moderate temperate latitudes, the midday sun is an approximation to a black body at 6000 K. Ordinary white card will not do as a scatterer, neither will a painted white matt surface because both are likely to be fluorescent under the UV solar radiation.

The resulting spectrum, after correction for the CCD pixel-to-pixel variations of sensitivity, may not look much like a textbook black body spectrum and for good reason. Firstly there are the basic variations with wavelength of the CCD overall sensitivity.