Redox‐Switchable Ring‐Closing Metathesis: Catalyst Design,Synthesis, and Study

High yielding syntheses of 1‐(ferrocenylmethyl)‐3‐mesitylimidazolium iodide ( 1 ) and 1‐(ferrocenylmethyl)‐3‐mesitylimidazol‐2‐ylidene ( 2 ) were developed. Complexation of 2 to [{Ir(cod)Cl}₂] (cod=cis,cis‐1,5‐cyclooctadiene) or [Ru(PCy₃)Cl₂(?CH‐o‐O‐iPrC₆H₄)] (Cy=cyclohexyl) afforded 3 ([Ir( 2 )(cod)Cl]) and 5 ([Ru( 2 )Cl₂(?CH‐o‐O‐iPrC₆H₄)]), respectively. Complex 4 ([Ir( 2 )(CO)₂Cl]) was obtained by bubbling carbon monoxide through a solution of 3 in CH₂Cl₂. Spectroelectrochemical IR analysis of 4 revealed that the oxidation of the ferrocene moiety in 2 significantly reduced the electron‐donating ability of the N‐heterocyclic carbene ligand (ΔTEP=9 cm^?1; TEP=Tolman electronic parameter). The oxidation of 5 with [Fe(η⁵‐C₅H₄COMe)Cp][BF₄] as well as the subsequent reduction of the corresponding product [ 5 ][BF₄] with decamethylferrocene (Fc*) each proceeded in greater than 95 % yield. Mössbauer, UV/Vis and EPR spectroscopy analysis confirmed that [ 5 ][BF₄] contained a ferrocenium species, indicating that the iron center was selectively oxidized over the ruthenium center. Complexes 5 and [ 5 ][BF₄] were found to catalyze the ring‐closing metathesis (RCM) of diethyl diallylmalonate with observed pseudo‐first‐order rate constants (k_obs) of 3.1×10^?4 and 1.2×10^?5 s^?1, respectively. By adding suitable oxidants or reductants over the course of a RCM reaction, complex 5 was switched between different states of catalytic activity. A second‐generation N‐heterocyclic carbene that featured a 1′,2′,3′,4′,5′‐ pentamethylferrocenyl moiety ( 10 ) was also prepared and metal complexes containing this ligand were found to undergo iron‐centered oxidations at lower potentials than analogous complexes supported by 2 (0.30–0.36 V vs. 0.56–0.62 V, respectively). Redox switching experiments using [Ru( 10 )Cl₂(?CH‐o‐O‐iPrC₆H₄)] revealed that greater than 94 % of the initial catalytic activity was restored after an oxidation–reduction cycle.     

On the symplectic structure of instanton moduli spaces

We study the complex symplectic structure of the quiver varieties corresponding to the moduli spaces of SU(2) instantons on both commutative and non-commutative R⁴. We identify global Darboux coordinates and quadratic Hamiltonians on classical phase spaces for which these quiver varieties are natural completions. We also show that the group of non-commutative symplectomorphisms of the corresponding path algebra acts transitively on the moduli spaces of non-commutative instantons. This paper should be viewed as a step towards extending known results for Calogero–Moser spaces to the instanton moduli spaces.     

Entire invariant solutions to Monge-Ampère equations

We prove existence and regularity of entire solutions to Monge-Ampère equations invariant under an irreducible action of a compact Lie group.

     

Chemical reactions modulated by mechanical stress: extended Bell theory

A number of recent studies have shown that mechanical stress can significantly lower or raise the activation barrier of a chemical reaction. Within a common approximation due to Bell [Science 200, 618 (1978)], this barrier is linearly dependent on the applied force. A simple extension of Bell's theory that includes higher order corrections in the force predicts that the force-induced change in the activation energy will be given by -FΔR - ΔχF(2)∕2. Here, ΔR is the change of the distance between the atoms, at which the force F is applied, from the reactant to the transition state, and Δχ is the corresponding change in the mechanical compliance of the molecule. Application of this formula to the electrocyclic ring-opening of cis and trans 1,2-dimethylbenzocyclobutene shows that this extension of Bell's theory essentially recovers the force dependence of the barrier, while the original Bell formula exhibits significant errors. Because the extended Bell theory avoids explicit inclusion of the mechanical stress or strain in electronic structure calculations, it allows a computationally efficient characterization of the effect of mechanical forces on chemical processes. That is, the mechanical susceptibility of any reaction pathway is described in terms of two parameters, ΔR and Δχ, both readily computable at zero force.     

Polymer Brushes via Controlled,Surface‐Initiated Atom Transfer Radical Polymerization (ATRP) from Graphene Oxide

A method for growing polymers directly from the surface of graphene oxide is demonstrated. The technique involves the covalent attachment of an initiator followed by the polymerization of styrene, methyl methacrylate, or butyl acrylate using atom transfer radical polymerization (ATRP). The resulting materials were characterized using a range of techniques and were found to significantly improve the solubility properties of graphene oxide. The surface‐grown polymers were saponified from the surface and also characterized. Based on these results, the ATRP reactions were determined to proceed in a controlled manner and were found to leave the structure of the graphene oxide largely intact.