Transition-metal clusters theory

Stone, A.J. A new approach to bonding in transition-metal clusters. Theory. Mol. Phys. 41, 1339 (1980)... 

Although there are a lot of publications on the chemistry of technetium [2-4] and transition-metal clusters [1,5-8], the chemistry of technetium clusters was insufficiently studied until the early eighties [1,2]. Nevertheless, the available scanty data on the compounds with Tc-Tc bonds inspired hope that interesting results would be obtained in the chemistry of technetium in general, in radiochemistry, and in the chemistry of transition-metal cluster compounds. The anticipated results were actually obtained [9-15] and the conclusion was drawn that technetium had a number of anomalous cluster-forming properties [9]. This review looks at the detailed studies of these properties and their interpretation in terms of electronic structure theory. 

Gas phase transition metal cluster chemistry lies along critical connecting paths between different fields of chemistry and physics. For example, from the physicist s point of view, studies of clusters as they grow into metals will present new tests of the theory of metals. Questions like How itinerant are the bonding electrons in these systems and Is there a metal to non-metal phase transition as a function of size are frequently addressed. On the other hand from a chemist point of view very similar questions are asked but using different terminology How localized is the surface chemical bond and What is the difference between surface chemistry and small cluster chemistry Cluster science is filling the void between these different perspectives with a new set of materials and measurements of physical and chemical properties. 

The information available is discussed in light of the effects of excitation energy and the environment on the photofragmentation process of several transition metal cluster complexes. The photochemical information provides a data base directly relevant to electronic structure theories currently used to understand and predict properties of transition metal complexes (1,18,19). 

The accurate quantum mechanical first-principles description of all interactions within a transition-metal cluster represented as a collection of electrons and atomic nuclei is a prerequisite for understanding and predicting such properties. The standard semi-classical theory of the quantum mechanics of electrons and atomic nuclei interacting via electromagnetic waves, i.e., described by Maxwell electrodynamics, turns out to be the theory sufficient to describe all such interactions (21). In semi-classical theory, the motion of the elementary particles of chemistry, i.e., of electrons and nuclei, is described quantum mechanically, while their electromagnetic interactions are described by classical electric and magnetic fields, E and B, often represented in terms of the non-redundant four components of the 4-potential, namely the scalar potential and the vector potential A. 

In this review we shall first establish the theoretical foundations of the semi-classical theory that eventually lead to the formulation of the Breit-Pauli Hamiltonian. The latter is an approximation suited to make the connection to phenomenological model Hamiltonians like the Heisenberg Hamiltonian for the description of electronic spin-spin interactions. The complete derivations have been given in detail in Ref. (21), but turn out to be very involved and are thus scattered over many pages in Ref. (21). For this reason, we aim here at a summary that is as brief and concise as possible so that all relevant connections between different levels of approximation are evident. This allows us to connect present-day quantum chemical methods to phenomenological Hamiltonians and hence to establish and review the current status of these first-principles methods applied to transition-metal clusters. 

An important consequence of the nonutilization of tangential orbitals is that platinum clusters often do not obey the normal electron counting rules and appear to be electron deficient (19,21,29,58,75,76). Electron counts are usually intermediate between those found in normal transition metal clusters (58-68) and those observed in gold clusters (58,78), but no satisfactory general electron counting theory has been developed for Pt-containing clusters. In small Pt clusters constructed from PtL2 units, theoretical studies have shown that the total electron count depends on the relative orientation of the... 

The well-proven computational technique of choice for dealing with transition metal clusters is Density-Functional Theory (DFT) [17]. The main advantage ofDFT over other quantum mechanical methods is that it allows for an integrated treatment of electron correlation effects combined with relatively high computational speed. Both of these are important for transition metal clusters with their high number of... 

Transition metal clusters also have Axy and atomic orbitals, which are classified as 5-type in TSH theory. To represent the transformation properties of these orbitals, we use second derivatives of the spherical harmonics, that is, tensor spherical harmonics - hence the name of the theory. As for the vector surface harmonics, there are again both odd and even 5 cluster orbitals, denoted by L and L, respectively. Usually, both sets are completely filled in transition metal clusters, and we will not consider their properties in any detail in this review. However, the cases of partial occupation are important and have been described in previous articles. ... 

The analysis of these molecules is complicated by the presence of the d orbitals, which contribute one orbital of CT symmetry (d 2 in local axes), two of n symmetry (d and Ayg), and two of 5 symmetry (d y and dj2 j,2). There are far more examples of deviations from the usual patterns in transition metal clusters than in main group clusters, and many of these must be treated specifically, although TSH theory may again provide a useful framework in which to perform the analysis. However, in this section the objective will simply be to understand the most common patterns, as set out in Section 3, which are typically found in clusters with u-acceptor ligands such as CO. 

Carbene Complexes Carbonyl Complexes ofthe Transition Metals Cyanide Complexes of the Transition Metals Dinuclear Organometallic Cluster Complexes Electron Transfer in Coordination Compounds Electron Transfer Reactions Theory Electronic Structure of Organometallic Compounds Luminescence Nucleic Acid-Metal Ion Interactions Photochemistry of Transition Metal Complexes Photochemistry of Transition Metal Complexes Theory Polynuclear Organometallic Cluster Complexes. 

Various CNDO and INDO schemes have also been proposed for transition-metal clusters and for chemisorption on them. Although there have been some successes, it remains true that both the level of theory being used and the parameterization are both very much experimental. 

Cluster models have been quite popular for some time now as a basis for the discussion of chemisorption systems (9-11), especially among quantum chemists who were able to contribute with their methods and tools to surface science via these constructs. (The references of this paragraph are intended to provide examples only since an exhaustive list would be too lengthy to be appropriate here.] Transition metal clusters have been the most intensively studied systems ftom the beginning due to the interesting chemisorptive and catalytic properties of such surfaces. At first one-electron aspects dominated cluster model applications (12,13), photoelectron spectra providing the bridge between theory and experiment (14). The simpler quantum chemical methods... 

The isolobal theory, developed by R Hoffman (an excellent account was given by him in the acceptance speech for the Nobel Prize see bibliography), to compare ML cluster fragments from transition metal clusters with CHj and BH cluster fragments from carboranes and boranes has become a very powerful tool to understand the properties and reactivities of main group and transition metal moiehes. 

Naked, Ligated and Supported Transition Metal Clusters 1411 Table 1. Nearest-neighbor Ni -Ni distances in cubic Nig clusters from theory and experiment. 

Transition metal clusters, however, need still to be tested in the engineering of crystalline materials. Crystal engineering has been defined as the capacity to make crystals with a purpose. In transition metal cluster chemistry this purpose is that of utilizing the distinct characteristics mentioned above to construct crystals that can function as the result of the inter-cluster interactions. To do this the experimentalist needs to conceive ways of directing the crystal-building process towards given architectures, i. e. needs to learn how to make non-covalent crystal synthesis. Clearly, the growth and success of a solid-state chemistry of transition metal clusters depends crucially on a close interaction between synthesis, theory, solid state characterization, and evaluation of properties. 

Bonding in clusters and condensed cluster compounds that extend in one, two and three dimensions Principles of bonding and reactivity in transition metal cluster compounds Mathematical cluster chemistry Graph-theory derived models for the skeletal chemical bonding in organometallic metal carbonyl clusters... 

In 1977 we reported a method based on graph theory for study of the skeletal bonding topology in polyhedral boranes, carboranes, and metal clusters Q). Subsequent work has shown this method to be very effective In relating electron count to cluster shape for diverse metal clusters using a minimum of computation. Discrete metal clusters treated effectively by this method Include post-transition metal clusters (, ) > osmium carbonyl clusters (O, gold clusters, platinum carbonyl clusters (J., 7 ) > and... 

Koster, A. M., Calaminici, R, G6mez, Z., and Reveles, U. (2002). Density functional theory calculation of transition metal clusters, in Reviews of Modern Quantum Chemistry, A Celebration of the Contribution of Robert G. Parr (World Scientific, Singapore). 

---