16 results
Preface
- Thomas Fehlner, University of Notre Dame, Indiana, Jean-Francois Halet, Université de Rennes I, France, Jean-Yves Saillard, Université de Rennes I, France
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- Molecular Clusters
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- 19 February 2010
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- 05 July 2007, pp ix-xii
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Summary
Who, what, where, why, when and how – the elementary prescription for a news squib is also appropriate for a preface.
Who? The book is intended primarily as a text for advanced undergraduates and graduate students. It can also serve the needs of research workers in the wide area of nanochemistry, as molecular clusters and extended solid-state materials constitute the structural “bookends” of nanoparticles: species that are not large enough to be treated with solid-state concepts but too large to follow the simple rules of molecular clusters. Those interested in a wide-ranging introduction to models of electronic structure applicable to delocalized, three-dimensional systems will also find it useful.
What? This text circumscribes a non-traditional area of inorganic chemistry. The focus is on a class of compound that exhibits cluster bonding. Emphasis is on connections between the problems of small molecular clusters, where the vast majority of atoms are found at the surface, to large crystals, where most atoms are found in the bulk. A review of bonding in molecular compounds (Chapter 1) is followed by the fundamentals of cluster bonding in p-block clusters (Chapter 2) and transition-metal clusters (Chapter 3). After making connections with organometallic chemistry (Chapter 4), mixed p–d-block clusters are developed (Chapter 5). A bonding model for periodic extended structures (Chapter 6) is developed in the style of Chapter 1. Chapter 7 then illustrates some of the similarities and differences between the bonding of clusters and related solid-state structures.
3 - Transition-metal clusters: geometric and electronic structure
- Thomas Fehlner, University of Notre Dame, Indiana, Jean-Francois Halet, Université de Rennes I, France, Jean-Yves Saillard, Université de Rennes I, France
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- Molecular Clusters
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- 19 February 2010
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- 05 July 2007, pp 85-138
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Summary
To a large extent, we expect the cluster bonding principles established for main-group clusters in Chapter 2 to carry over to transition-metal clusters. However, the AO basis sets for building MOs differ for transition metals which means that the expression of the cluster bonding principles in geometric and electronic structure will also differ. That is, the observed cluster compositions and shapes differ and these differences can be associated with the participation of the metal d functions in cluster bonding. The d functions are the “wild cards” that make transition-metal chemistry so interestingly different from main-group chemistry. In writing Chapter 3 we have assumed that the reader has a basic understanding of the principles of cluster bonding as expressed by p-block clusters (Chapter 2). Emphasis here is placed on the varied expression of d-block metal character within a cluster context. A number of monographs on metal clusters are suggested at the end of this chapter as additional reading for those interested in pursuing a topic in more depth.
Three-connect clusters
Main-group clusters that exhibit three-connect shapes can often be described using localized two-center bonds. What is the situation for metal clusters?
Localized two-center bonds
Two-center–two-electron bonding and the eight-electron rule adequately rationalize three-connect clusters like P4; hence, we expect the 18-electron rule to suffice for three-connect transition-metal clusters like tetrahedral Ir4(CO)12 (Figure 3.1) with 12 terminal carbonyl ligands. Indeed it does.
Molecular Clusters
- A Bridge to Solid-State Chemistry
- Thomas Fehlner, Jean-Francois Halet, Jean-Yves Saillard
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- 19 February 2010
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- 05 July 2007
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Clusters can be viewed as solids at the nano-scale, yet molecular cluster chemistry and solid state chemistry have traditionally been considered as separate topics. This treatment has made it conceptually difficult to appreciate commonalities of structure and bonding between the two. Using analogous models, this is the first book to form a connecting bridge. Although the focus is on clusters, sufficient attention is paid to solid-state compounds at each stage of the development to establish the interrelationship between the two topics. Comprehensive coverage of cluster types by composition, size and ligation, is provided, as is a synopsis of selected research. Written in an accessible style and highly illustrated to aid understanding, this book is suitable for researchers in inorganic chemistry, physical chemistry, materials science, and condensed matter physics.
5 - Main-group–transition-metal clusters
- Thomas Fehlner, University of Notre Dame, Indiana, Jean-Francois Halet, Université de Rennes I, France, Jean-Yves Saillard, Université de Rennes I, France
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- Molecular Clusters
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- 19 February 2010
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- 05 July 2007, pp 165-204
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Summary
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.
Appendix: Fundamental concepts: a concise review
- Thomas Fehlner, University of Notre Dame, Indiana, Jean-Francois Halet, Université de Rennes I, France, Jean-Yves Saillard, Université de Rennes I, France
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- Molecular Clusters
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- 05 July 2007, pp 323-348
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Summary
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.
References
- Thomas Fehlner, University of Notre Dame, Indiana, Jean-Francois Halet, Université de Rennes I, France, Jean-Yves Saillard, Université de Rennes I, France
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- Molecular Clusters
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- 05 July 2007, pp 369-370
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8 - Inter-conversion of clusters and solid-state materials
- Thomas Fehlner, University of Notre Dame, Indiana, Jean-Francois Halet, Université de Rennes I, France, Jean-Yves Saillard, Université de Rennes I, France
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- Molecular Clusters
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- 19 February 2010
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- 05 July 2007, pp 303-322
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Summary
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.
Index
- Thomas Fehlner, University of Notre Dame, Indiana, Jean-Francois Halet, Université de Rennes I, France, Jean-Yves Saillard, Université de Rennes I, France
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- Molecular Clusters
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- 05 July 2007, pp 371-378
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4 - Isolobal relationships between main-group and transition-metal fragments. Connections to organometallic chemistry
- Thomas Fehlner, University of Notre Dame, Indiana, Jean-Francois Halet, Université de Rennes I, France, Jean-Yves Saillard, Université de Rennes I, France
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- Molecular Clusters
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- 05 July 2007, pp 139-164
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Summary
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.
2 - Main-group clusters: geometric and electronic structure
- Thomas Fehlner, University of Notre Dame, Indiana, Jean-Francois Halet, Université de Rennes I, France, Jean-Yves Saillard, Université de Rennes I, France
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- Molecular Clusters
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- 19 February 2010
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- 05 July 2007, pp 33-84
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Summary
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.
1 - Introduction
- Thomas Fehlner, University of Notre Dame, Indiana, Jean-Francois Halet, Université de Rennes I, France, Jean-Yves Saillard, Université de Rennes I, France
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- Molecular Clusters
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- 05 July 2007, pp 1-32
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Summary
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.
Contents
- Thomas Fehlner, University of Notre Dame, Indiana, Jean-Francois Halet, Université de Rennes I, France, Jean-Yves Saillard, Université de Rennes I, France
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- Molecular Clusters
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- 05 July 2007, pp v-viii
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Frontmatter
- Thomas Fehlner, University of Notre Dame, Indiana, Jean-Francois Halet, Université de Rennes I, France, Jean-Yves Saillard, Université de Rennes I, France
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- Molecular Clusters
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- 05 July 2007, pp i-iv
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6 - Transition to the solid state
- Thomas Fehlner, University of Notre Dame, Indiana, Jean-Francois Halet, Université de Rennes I, France, Jean-Yves Saillard, Université de Rennes I, France
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- Molecular Clusters
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- 19 February 2010
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- 05 July 2007, pp 205-256
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Summary
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.
Problem Answers
- Thomas Fehlner, University of Notre Dame, Indiana, Jean-Francois Halet, Université de Rennes I, France, Jean-Yves Saillard, Université de Rennes I, France
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- Molecular Clusters
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Summary
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.
7 - From molecules to extended solids
- Thomas Fehlner, University of Notre Dame, Indiana, Jean-Francois Halet, Université de Rennes I, France, Jean-Yves Saillard, Université de Rennes I, France
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- Molecular Clusters
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- 05 July 2007, pp 257-302
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Summary
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.