Polyhedral skeletal electron pair approach

The energy decomposition analysis (EDA) is a powerful method for a quantitative interpretation of chemical bonds in terms of three major components. The instantaneous interaction energy ΔEint between two fragments A and B in a molecule A–B is partitioned in three terms, namely (1) the quasiclassical electrostatic interaction ΔEelstat between the fragments; (2) the repulsive exchange (Pauli) interaction ΔEPauli between electrons of the two fragments having the same spin, and (3) the orbital (covalent) interaction ΔEorb which comes from the orbital relaxation and the orbital mixing between the fragments. The latter term can be decomposed into contributions of orbitals with different symmetry which makes it possible to distinguish between σ, π, and δ bonding. After a short introduction into the theoretical background of the EDA we present illustrative examples of main group and transition metal chemistry. The results show that the EDA terms can be interpreted in chemically meaningful way thus providing a bridge between quantum chemical calculations and heuristic bonding models of traditional chemistry. The extension to the EDA–Natural Orbitals for Chemical Valence (NOCV) method makes it possible to breakdown the orbital term ΔEorb into pairwise orbital contributions of the interacting fragments. The method provides a bridge between MO correlations diagrams and pairwise orbital interactions, which have been shown in the past to correlate with the structures and reactivities of molecules. There is a link between frontier orbital theory and orbital symmetry rules and the quantitative charge- and energy partitioning scheme that is provided by the EDA–NOCV terms. The strength of the pairwise orbital interactions can quantitatively be estimated and the associated change in the electronic structure can be visualized by plotting the deformation densities.

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Energy decomposition analysis

Metals and organic molecules are at the opposite sides in chemistry. Thus one may think that chemical bonding models, such as aromaticity, developed in organic chemistry will not be applicable in systems involving metallic elements. Yet in recent years there have been significant advances in extending the aromaticity and antiaromaticity concepts into the realm of metal clusters and alloys. These new developments have shown that aromaticity and antiaromaticity in metal systems have frequently multiple nature, being o-aromatic/antiaromatic and n-aromatic/antiaromatic, which is not found in organic aromatic/antiaromatic molecules.

http://casey.brown.edu/chemistry/research/LSWang/publications/209.pdf

All-Metal Aromaticity and Antiaromaticity

Weak attractive interactions between closed shell metal ions have been increasingly studied in the last few years and are generally designated as metallophilic interactions. They are best evidenced in the solid state where structural data obtained by X-ray diffraction provide precise information about the distance between the metals involved. The strength of such metal–metal interactions has been compared to that of hydrogen bonding (ca. 7–11 kcal mol−1) and is clearly sufficient to bring about novel bonding and structural features and confer interesting physical properties such as luminescence, polychromism, magnetism or one-dimensional electrical conductivity. The Cu(I)–Cu(I), Ag(I)–Ag(I) and Au(I)–Au(I) interactions have been increasingly observed and the latter have certainly been the most studied. Early qualitative analyses of the aurophilic attraction focused on Au–Au bonding originating from 6s, 6p and 5d orbital mixing. Numerous theoretical studies on metallophilic interactions continue to be carried out at various levels of sophistication which take into account relativistic and correlation effects to describe these van der Waals-type interactions. In this critical review, we would like to focus on the synthesis and structures of heterometallic clusters of the transition metals in which intra- rather than intermolecular d10–d10 interactions are at work, in order to limit the role of packing effects. We wish to provide the reader with a comparative overview of the metal core structures resulting from or favoring metallophilic interactions but do not intend to provide a comprehensive coverage of the literature. We will first examine heterometallic clusters displaying homometallic and then heterometallic d10–d10 interactions. Although the focus of this review is on d10–d10 interactions involving metals from the group 11, we shall also briefly examine for comparison some complexes displaying intramolecular d10–d10 interactions involving metals from other groups (188 references).

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Intramolecular d10–d10 interactions in heterometallic clusters of the transition metals

Chemical bonding models based on graph theory or tensor surface harmonic theory demonstrate the analogy between the aromaticity in two-dimensional planar polygonal hydrocarbons such as benzene and that in three-dimensional deltahedral borane anions of the type BnHn2- (6 < or = n < or = 12). Such models are supported both by diverse computational studies and experimental determinations of electron density distribution. Related methods can be used to study the chemical bonding in the boron polyhedra found in other structures including neutral binary boron hydrides, metallaboranes, various allotropes of elemental boron, and boron-rich solid-state metal borides.

Three-dimensional aromaticity in polyhedral boranes and related molecules.

Publisher Summary This is one of two articles in this volume that is concerned with the borane-carborane structural pattern. In the other, Williams has shown how the pattern reflects the coordination number preferences of the various atoms involved. The purpose of the present article is to note some bonding implications of the pattern, and to show its relevance to a wide range of other compounds, including metal clusters, metal-hydrocarbon 7∼ complexes, and various neutral or charged hydrocarbons. Boranes and carboranes may be regarded as cluster compounds in the sense defined by Cotton; they contain a finite group or skeleton of atoms held together entirely, mainly, or at least to a significant extent by bonding directly between those atoms, even though some other atoms may be associated intimately with the cluster. Examples of their structural pattern, however, can be found far beyond the confines of what is normally regarded as cluster chemistry, so this survey includes many systems not commonly referred to as clusters.

K. Wade

Papers

Structural and Bonding Patterns in Cluster Chemistry