stretch, bend, or otherwise distort one or more bonds. This critical energy is known as the activation energy of the reaction. Activation energy diagrams of the kind shown below plot the total energy input to a reaction system as it proceeds from reactants to products. In examining such diagrams, take special note of the following:
- The "reaction coordinate" plotted along the abscissa represents the changes in atomic coordinates as the system progresses from reactants to products. In the very simplest elementary reactions it might correspond to the stretching or twisting of a particular bond, and be shown to a scale. In general, however, the reaction coordinate is a rather abstract concept that cannot be tied to any single measurable and scalable quantity. - The activated complex (also known as the transition state) represents the structure of the system as it exists at the peak of the activation energy curve. It does not correspond to an identifiable intermediate structure (which would more properly be considered the product of a separate elementary process), but rather to whatever configuration of atoms exists during the collision, which lasts for only about 0.1 picosecond.
Development of supported single-site catalysts using small metal sulfide complexes could significantly help in the development of cost-effective catalytic materials to drive selective hydrogenation and hydrogenolysis. The goal of this study is to contribute to the development of metal sulfide catalysts by calculating the thermodynamics of a catalytic cyclic involving a metal organic framework functionalized by insertion of metal sulfide. Anchored metal sulfide complexes can potentially be designed with ligands with distinctly different electronic and catalytic properties for specific catalytic applications. Here we examine the hydrogenation of ethylene as a model. We use density functional theory to investigate molybdenum–sulfur complexes as active catalysts anchored on the metal–organic framework UiO-66 as a stable support. Our calculations show that the anchored complexes with more than two sulfur ligands are unfavorable for ethylene adsorption, so we study complexes with one or two sulfur ligands. Hydrogenation of the unsaturated carbon double bond requires the transfer of two hydrogen atoms, which can occur via heterolytic activation of hydrogen to form a Mo-hydride and a protonated sulfur – either by hydride transfer followed by proton transfer or via proton transfer followed by hydride transfer, and we find that both mechanisms proceed via two-state reactivity involving two spin states along the reaction path. Of the two catalysts studied in gas the phase, the MoS singl
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