Transition metal clusters, application method

Recent application of the TB method to transition metal clusters often made use of a convenient formulation in the language of second quantization.14 In this formalism, the TB Hamiltonian in the unrestricted Hartree-Fock approximation can be written as a sum of diagonal and nondiagonal terms15... 

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... 

Relativistic effects of the environment are included indirectly due to the solution of the KS-equations for the whole system. Special techniques have been developed for choosing the size and shape of the environment and of an initial electronic density on atomic centers. Application of this method to the calculations of interaction of Cu with Cu-clusters of different size shows good agreement with extended calculations of other workers (see [124] and references therein). The method is presently applied to the calculations of the interaction of the heaviest element 112 and its lighter homolog Hg with transition-metal clusters. First results are reported for those elements interacting with small gold clusters [125] (see Section 3.1). 

We review the Douglas-Kroll-Hess (DKH) approach to relativistic density functional calculations for molecular systems, also in comparison with other two-component approaches and four-component relativistic quantum chemistry methods. The scalar relativistic variant of the DKH method of solving the Dirac-Kohn-Sham problem is an efficient procedure for treating compounds of heavy elements including such complex systems as transition metal clusters, adsorption complexes, and solvated actinide compounds. This method allows routine ad-electron density functional calculations on heavy-element compounds and provides a reliable alternative to the popular approximate strategy based on relativistic effective core potentials. We discuss recent method development aimed at an efficient treatment of spin-orbit interaction in the DKH approach as well as calculations of g tensors. Comparison with results of four-component methods for small molecules reveals that, for many application problems, a two-component treatment of spin-orbit interaction can be competitive with these more precise procedures. 

Far more extensive has been the application of semiempirical TB methods, in which the matrix elements are used as free parameters to fit experimental data, to metal clusters (and to transition-metal clusters in particular). However, a discussion of these applications is beyond the scope of our review. 

In the third step, our ZT-TBMD method has been extended by incorporating the Nose-bath (Nose 1984) and the Multiple Histogram approximations (Fanourgakis et al. 1997), so as to be applicable to cluster studies at finite temperatures in an efficient way (Andriotis et al. 2006, 2007 Fthenakis et al. 2003). This generalization allows one to calculate the caloric curve for the cluster and use this to study the effect of temperature on the structural, electronic, and magnetic properties of transition metal clusters and binary systems containing transition metal and semiconductor atoms. The method has been used to study the variation of structural and magnetic properties with temperature as well as to obtain the caloric curves of the Ni-clusters (Andriotis et al. 2006,2007 Fthenakis et al. 2003). 

In recent years the fundamental ideas of Huckel molecular orbital theory, the Huckel rule, and other aspects of aromaticity have been extended to polyhedral three-dimensional inorganic structures regarded as aromatic like the two-dimensional aromatic hydrocarbons. Such an extension of Huckel molecular orbital theory requires recognition of its topological foundations so that they can be applied to three-dimensional structures as well as two-dimensional structures. In this connection graph theoretical methods can be used to demonstrate the close analogy between the delocalized bonding in two-dimensional planar aromatic systems such as benzene and that in three-dimensional deltahedral boranes, and carboranes. Related ideas can be shown to be applicable for metal carbonyl clusters, bare post-transition metal clusters, and polyoxometallates. ... 

Transition-metal nanopartides are of fundamental interest and technological importance because of their applications to catalysis [22,104-107]. Synthetic routes to metal nanopartides include evaporation and condensation, and chemical or electrochemical reduction of metal salts in the presence of stabilizers [104,105,108-110]. The purpose of the stabilizers, which include polymers, ligands, and surfactants, is to control particle size and prevent agglomeration. However, stabilizers also passivate cluster surfaces. For some applications, such as catalysis, it is desirable to prepare small, stable, but not-fully-passivated, particles so that substrates can access the encapsulated clusters. Another promising method for preparing clusters and colloids involves the use of templates, such as reverse micelles [111,112] and porous membranes [106,113,114]. However, even this approach results in at least partial passivation and mass transfer limitations unless the template is removed. Unfortunately, removal of the template may re-... 

It is very likely that the metal-insulator transition, the unusual catalytic properties, the unusual degree of chemical reactivity, and perhaps even some of the ultramagnetic properties of metal clusters are all linked intimately with the dynamic, vibronic processes inherent in these systems. Consequently, the combination of pump-probe spectroscopy on the femtosecond time scale with theoretical calculations of wavepacket propagation on just this scale offers a tantalizing way to address this class of problems [5]. Here we describe the application of these methods to several kinds of metal clusters with applications to some specific, typical systems first, to the simplest examples of unperturbed dimers then, to trimers, in which internal vibrational redistribution (IVR) starts to play a central role and finally, to larger clusters, where dissociative processes become dominant. 

Polynuclear clusters fill the gap between mononuclear and extended solid transition metal vibronic systems. The applications of the theory of vibronic interaction allow to describe physical and chemical properties of these systems, sometimes directly linked to their application. The Jahn-Teller distortion found for the rhenium clusters defines the architecture of hybrid inorganic-organic materials and, as a result, their electric and magnetic properties. The application of the vibronic theory to the decatungstate cluster elucidates the details of its reactivity in the photocatalytic reaction. The modern DFT methods give a key to the calculations of key parameters of the vibronic theory. In future, we will assist at the combination of these methods with phenomenological approaches leading to the description of vibronic effects in physical and chemical properties of polynuclear clusters from first principles. 

Since polynuclear complexes and cluster compounds are in general rather complicated species, the application of quantitative methods for describing bonding is not only difficult but also impractical. Qualitative approaches and empirical rules often play an important role in treating such cases. We have used the octet rule and bond valence to describe the structure and bonding of boranes and their derivatives (Sections 13.3 and 13.4). Now we use the 18-electron rule and bond valence to discuss the bonding and structure of polynuclear transition-metal complexes and clusters. 

Non-aqueous synthetic methods have recently been used to assemble mesoporous transition metal oxides and sulfides. This approach may afford greater control over the condensation-polymerization chemistry of precursor species and lead to enhanced surface area materials and well ordered structures [38, 39], For the first time, a rational synthesis of mesostructured metal germanium sulfides from the co-assembly of adamantanoid [Ge4S ()]4 cluster precursors was reported [38], Formamide was used as a solvent to co-assemble surfactant and adamantanoid clusters, while M2+/1+ transition metal ions were used to link the clusters (see Fig. 2.2). This produced exceptionally well-ordered mesostructured metal germanium sulfide materials, which could find application in detoxification of heavy metals, sensing of sulfurous vapors and the formation of semiconductor quantum anti-dot devices. 

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