Insertion of nitrene and chalcogenolate groups into the Ir-C σ bond in a cyclometalated iridium(III) complex

Treatment of [Cp∗Ir(ppy)Cl] (Cp∗ = η⁵-C₅Me₅, ppyH = 2-(2-pyridyl)phenyl) with Ag(OTf) (OTf⁻ = triflate) in MeOH and MeCN gave the solvento complexes [Cp∗Ir(ppy)(solv)][OTf] (solv = MeOH (1) and MeCN (2)). Complex 1 is capable of catalyzing oxidation and azirdination of styrene with PhIO and PhINTs (Ts = tosyl), respectively. Treatment of 2 with a stoichiometric amount of PhINTs resulted in the insertion of the NTs group into the Ir-C(ppy) bond and formation of [Cp∗Ir(η²-ppy-NTs)(MeCN)][OTf] (3). Treatment of 1 with R₂E₂ afforded [Cp∗Ir(ppy)(η¹-R₂E₂)][OTf] (E = S (4), Se (5), Te (6)). Reactions of 4 and 5 with Ag(OTf) resulted in cleavage of the E-E bond and insertion of an ER group into the Ir-C(ppy) bond. The crystal structures of complexes 2-6 and [Cp∗Ir(η²-ppy-S-p-tol)(H₂O)][OTf]₂ have been determined.     

Iridium(III) silyl alkyl and iridacyclic compounds supported by 4,4'-di-tert-butyl-2,2'-bipyridyl

Treatment of IrCl(3)x H(2)O with one equivalent of 4,4'-di-tert-butyl-2,2'-bipyridyl (dtbpy) in N,N-dimethylformamide (dmf) afforded [IrCl(3)(dmf)(dtbpy)] (1). Alkylation of 1 with Me(3)SiCH(2)MgCl resulted in C--Si cleavage of the Me(3)SiCH(2) group and formation of the Ir(III) silyl dialkyl compound [Ir(CH(2)SiMe(3))(dtbpy)(Me)(SiMe(3))] (2), which reacted with tBuNC to afford [Ir(tBuNC)(CH(2)SiMe(3))(dtbpy)(Me)(SiMe(3))] ([2(tBuNC)]). Reaction of 2 with phenylacetylene afforded dimeric [{Ir(C[triple chemical bond]CPh)(dtbpy)(SiMe(3))}(2)(mu-C[triple chemical bond]CPh)(2)] (3), in which the bridging PhC[triple chemical bond]C(-) ligands are bound to Ir in a mu-sigma:pi fashion. Alkylation of 1 with PhMe(2)CCH(2)MgCl afforded the cyclometalated compound [Ir(dtbpy)(CH(2)CMe(2)C(6)H(4))(2-C(6)H(4)CMe(3))] (4), which features an agostic interaction between the Ir center and the 2-tert-butylphenyl ligand. The cyclic voltammogram of 4 in CH(2)Cl(2) shows a reversible Ir(IV)-Ir(III) couple at about 0.02 V versus ferrocenium/ferrocene. Oxidation of 4 in CH(2)Cl(2) with silver triflate afforded an Ir(IV) species that exhibits an anisotropic electron paramagnetic resonance (EPR) signal in CH(2)Cl(2) glass at 4 K with g( parallel)=2.430 and g( perpendicular)=2.110. Protonation of 4 with HCl and p-toluenesulfonic acid (HOTs) afforded [{Ir(dtbpy)(CH(2)CMe(2)Ph)Cl}(2)(mu-Cl)(2)] (5) and [Ir(dtbpy)(CH(2)CMe(2)Ph)(OTs)(2)] (6), respectively. Reaction of 5 with Li[BEt(3)H] gave the cyclometalated complex [{Ir(dtbpy)(CH(2)CMe(2)C(6)H(4))}(2)(mu-Cl)(2)] (7). Reaction of 4 with tetracyanoethylene in refluxing toluene resulted in electrophilic substitution of the iridacycle by C(2)(CN)(3) with formation of [Ir(dtbpy)(CH(2)CMe(2)C(6)H(3){4-C(2)(CN)(3)})(2-C(6)H(4)CMe(3))] (8). Reaction of 4 with diethyl maleate in refluxing toluene gave the iridafuran compound [Ir(dtbpy)(CH(2)CMe(2)C(6)H(4)){kappa(2)(C,O)-C(CO(2)Et)CH(CO(2)Et)}] (9). Treatment of 9 with 2,6-dimethylphenyl isocyanide (xylNC) led to cleavage of the iridafuran ring and formation of [Ir(dtbpy)(CH(2)CMe(2)C(6)H(4)){C(CO(2)Et)CH(CO(2)Et)}(xylNC)] (10). Protonation of 9 with HBF(4) afforded the dinuclear neophyl complex [(Ir(dtbpy)(CH(2)CMe(2)Ph){kappa(2)(C,O)-C(CO(2)Et)CH(CO(2)Et)})(2)][BF(4)](2) (11). The solid-state structures of complexes 2-5 and 8-11 have been determined.     

A theorem for the existence of Majorana fermion modes in spin-orbit-coupled semiconductors

We prove an index theorem for the existence of Majorana zero modes in a semiconducting thin film with a sizable spin-orbit coupling when it is adjacent to an s-wave superconductor. The theorem, which is analogous to the Jackiw-Rebbi index theorem for the zero modes in mass domain walls in one-dimensional Dirac theory, applies to vortices with odd flux-quantum in a semiconducting film in which s-wave superconductivity and a Zeeman splitting are induced by proximity effect. The momentum space construction of the zero-mode solution presented here is complementary to the approximate real space solution of the Bogoliubov-de Gennes equations at a vortex core (Sau et al., arXiv:0907.2239 [17]), proving the existence of non-degenerate zero-energy Majorana excitations and the resultant non-Abelian topological order in the semiconductor heterostructure. With increasing magnitude of the proximity-induced pairing potential, the non-Abelian superconducting state makes a topological quantum phase transition to an ordinary s-wave superconducting state which no topological order.     

An Error Analysis of Discontinuous Finite Element Methods for the Optimal Control Problems Governed by Stokes Equation

In this article, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints. A priori error estimates of optimal order are derived for velocity and pressure in the energy norm and the L²-norm, respectively. Moreover, a reliable and efficient a posteriori error estimator is derived. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. In particular, we consider the abstract results with suitable stable pairs of velocity and pressure spaces like as the lowest-order Crouzeix–Raviart finite element and piecewise constant spaces, piecewise linear and constant finite element spaces. The theoretical results are illustrated by the numerical experiments.     

Higher-Order Cyclodextrin Complexes: The Naphthalene System

Naphthalene excited dimer (excimer) fluorescence is observed in the presence of β- and γ-cyclodextrin (CD) at elevated naphthalene (NAP) concentrations (100 μM) but not at low NAP concentrations (5 μM). This is attributed to formation of 2:2 CD:NAP complexes in the former situation. Complexes of NAP with hydroxypropyl β-CD are exclusively 1:1 and no excimer emission is observed. Complexes of NAP with α-CD do not show excimer emission either but the complex stoichiometry is 2:1 CD:NAP in this case. The formation constants for both the 1:1 and 2:2 β-CD:NAP complexes have been determined and they have been found to depend on the ionic strength of the salting out agent NaCl. K_1:1 = 377 ± 35 M^-1 in the absence of salt and 657 ± 60 M^-1 at 1 M NaCl. The corresponding values for K_2:2 are (1.0 ± 0.2) × 10⁴ and (4.0 ± 0.5) × 10⁴ M^-1, respectively. Stern-Volmer fluorescence quenching studies of the 1:1 and 2:2 species by water-based quenchers (NaI and CsBr) show that both types of complexes protect the fluorophore from the quencher. However, the more completely encapsulated NAP in the 2:2 complex is protected to a greater extent. This is also the case for the 2:2 γ-CD:NAP complex. This protective effect is reflected in the observed rate constants for NAP quenching. For example, k_Q = 7.1 × 10⁹ M^-1 s^-1 for NaI in the absence of CD. This is reduced to 2.1 × 10⁹ M^-1 s^-1 for the 1:1 complex and 1.2 × 10⁹ M^-1 s^-1 for the 2:2 complex when 10 mM β-CD is present. A similar pattern is observed for CsBr as quencher. The 2:2 complexes are disrupted in the presence of additives such as linear alcohols and surfactants. The implications of these results for application of CDs for drug stabilization are discussed.