A self-locking molecule operative with a photoresponsive key

Rotary host 1, composed of a ferrocene unit as a rotary module, is conformationally locked internally in apolar solvents such as benzene by a double intramolecular Zn-N coordination between the zinc porphyrin and aniline units, attached to each cyclopentadienyl (Cp) ring. Upon addition of the cis form of 1,2-bispyridylethylene (cis-2) to (+)-1 ([cis-2]/[(+)-1] = 5.0), an enantiomer of 1, the intramolecular Zn-N coordination bonds in (+)-1 are readily cleaved to form an externally locked, cyclodimeric one-to-one complex (+)-1 subset cis-2, accompanying a rotation of the ferrocene module, as visualized by CD spectroscopy. In contrast, use of trans-2, in place of cis-2, under otherwise identical conditions to the above, did not result in releasing the internal double lock of (+)-1. Such a large difference between the isomers of 2 in the affinity toward host 1, along with their capabilities of photochemical interconversion, allowed for the demonstration of a reversible self-locking operation of 1. Namely, the externally locked state of 1, as in the form of 1 supersetcis-2, spontaneously retrieves the internally locked state, after the release of 2 from 1 upon cis-to-trans photochemical isomerization of ligating 2, while the backward photochemical isomerization of 2 in the presence of 1 results in switching of 1 to its externally locked state.     

Stable extendibility of vector bundles over lens spaces mod 3 and the stable splitting problem

Let Lⁿ(3) denote the (2n+1)-dimensional standard lens space mod 3. In this paper, we study the conditions for a given real vector bundle over Lⁿ(3) to be stably extendible to L^m(3) for every mn, and establish the formula on the power ζ^k=ζζ (k-fold) of a real vector bundle ζ over Lⁿ(3). Moreover, we answer the stable splitting problem for real vector bundles over Lⁿ(3) by means of arithmetic conditions.     

Toward long-distance mechanical communication: studies on a ternary complex interconnected by a bridging rotary module

A heterotropic ternary complex was obtained from a photochromic dithienylethene derivative bearing pyridyl groups (1), a chiral tetrasubstituted ferrocene as a scissoring component bearing two pyridyl and free-base porphyrin groups (3*), and a biaryl derivative as an intermediately bridging component bearing four zinc porphyrin handles (2). The three components are connected together via bidentate coordination bonds and mechanically interconnected. Exposure of the ternary complex to UV or visible light allowed for the isomerization of 1. This configurational change gave rise to an angular motion of 2, resulting in a scissoring motion of 3*. In the absence of 2, the isomerization of 1 does not lead to any defined motions of 3*. Thus, the heterotropic ternary complex may be regarded as a prototype of "molecular reacher" for remote manipulation of molecular events.     

Asymptotics of eigenvalues of the Schrödinger operator with a strong δ-interaction on a loop

In this paper we investigate the operator H_β=−Δ−βδ(·−Γ) in , where β>0 and Γ is a closed C⁴ Jordan curve in . We obtain the asymptotic form of each eigenvalue of H_β as β tends to infinity. We also get the asymptotic form of the number of negative eigenvalues of H_β in the strong coupling asymptotic regime.     

Cobalt‐Catalyzed E‐Selective Cross‐Dimerization of Terminal Alkynes: A Mechanism Involving Cobalt(0/II) Redox Cycles

A highly E‐selective cross‐dimerization of terminal alkynes with either terminal silylacetylenes, tert‐butylacetylene, or 1‐trimethylsilyloxy‐1,1‐diphenyl‐2‐propyne in the presence of a dichlorocobalt(II) complex bearing a sterically demanding 2,9‐bis(2,4,6‐triisopropylphenyl)‐1,10‐phenanthroline, activated with two equivalents of EtMgBr, gives a variety of (E)‐1,3‐enynes. A well‐characterized diolefin/cobalt(0) complex, with divinyltetramethyldisiloxane, acted as a catalytically active species without any activation, clearly indicating that a cobalt(0) species is involved in the catalytic cycle.