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Olefin metathesis is a versatile reaction that is applied to a wide range of substrates extending from large-scale industrial processes to fine chemistry. 11-14 It is, for instance, used extensively in the synthesis of natural products 15-17 and polymers 18, 19 and has found applications even in peptide and protein modifications. 20-23 Quite intensive studies of the theoretical and experimental aspects of olefin metathesis became the basis of the wide application of this reaction in organic synthesis and petrochemistry 24

Another important and similar reaction for carbon-carbon coupling transformation is the alkane metathesis. Mid-weight acyclic alkanes, usually containing three to eight carbon atoms per molecule, are undesirable petrochemical feedstocks that are available in large quantities. 1 It is desirable to convert mid-weight alkanes into higher-value alkane homologs. 2, 3 As a potential method for achieving such conversion, alkane metathesis is a class of reaction in which alkane molecules are transformed into higher and lower homologs. 4-6 Kinetic and structure-reactivity investigations have shown that the elementary steps of carbon-carbon bond cleavage and formation are similar to those of olefin metathesis and probably involve metallocarbene hydride intermediates. 7-9 Mikhailov et al. have reported an alkane metathesis mechanism based on similar propagating carbenic species, but with different C-C bond formation and cleavage steps based on alkyl migration and R-alkyl transfer elementary steps. 10 We have therefore investigated the reaction of propene with the proposed alkylidene hydrido tantalum intermediate through DFT calculations.

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Industrial olefin metathesis catalysts are based on Mo, W, or Re oxides (MOx) dispersed onto high-surface-area supports.12, 14, 25-29 The structures of active sites and reaction intermediates in heterogeneous metathesis catalysts are difficult to determine because only a fraction of the metals sites are catalytically active. 13, 30, 31 Despite the recent advances in the design of olefin metathesis catalysts, optimal systems combining high activity, selectivity, stability, and functional group tolerance still need to be discovered, whether or heterogeneous catalysts. Homogeneous or heterogenized metal complexes (Schrock or Grubbs systems) that based on d0 transition metals (Mo, W, Re) or Ru, homogeneous 32, 33 are known as active metathesis catalysts. Heterogeneous catalysts are also known in the art 34-40, including diverse Mo-, W- and Re-supported systems based on different oxide carriers, with alumina being the most abundant one (Handbook of Metathesis, Ed. R.H. Grubbs (Wiley, New York, 2003)). Rhenium-containing heterogeneous catalysts are typically most active among the heterogeneous analogs. 41

Subtle tuning of the ligand environment in homogeneous organometallic group 6 42, 43 and Ru 44, 45 complexes results in high olefin metathesis activities and selectivities. In the specific case of d0 systems, Coperet el al. has shown that asymmetry at the metal center and site isolation through grafting on rigid oxide supports can allow an increase in the performances of these systems: 46-49 The rational design of these catalysts10 relies on structure?activity relationships and on the detailed understanding of the key mechanistic steps. 12, 13, 26 The reaction of organometallic catalyst precursors with hydroxylated oxide supports forms well-defined heterogeneous metathesis catalysts that are active at room temperature and compatible with functionalized olefins. 50-55 This method, referred to as surface organometallic chemistry, 31, 56-60 yields catalysts with high concentrations of active sites 50-52, 55 that can be characterized by spectroscopic techniques. 31, 46, 55, 61-68 Correlation of the alkylidene active site and catalytic activity allows quantitative assessment of structure?activity relationships, 61, 69-71 an approach that is similar to homogeneous catalyst optimization. 

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