We report the fabrication of homoleptic alkynylprotected Ag 15 (CC-t Bu) 12 + (abbreviated as Ag 15 )nanocluster and its electrocatalytic properties towardC O 2 reduction reaction. Crystal structure analysis reveals that Ag 15 possesses abody-centered-cubic (BCC) structure with an Ag@Ag 8 @Ag 6 metal core configuration. Interestingly,wefound that Ag 15 can adsorb CO 2 in the air and spontaneously self-assembled into one-dimensional linear material during the crystal growth process.F urthermore,A g 15 can convert CO 2 into CO with af aradaic efficiency of ca. 95.0 %a tÀ0.6 Va nd am aximal turnover frequency of 6.37 s À1 at À1.1 Valong with excellent long-term stability.F inally,d ensity functional theory (DFT) calculations disclosed that Ag 15 (CC-t Bu) 11+ with one alkynyl ligand stripping off from the intact cluster can expose the uncoordinated Ag atom as the catalytically active site for CO formation.

With tunable pore size and rich active metal centers, metal–organic frameworks (MOFs) have been regarded as the one of the promising materials for catalysis. Prospectively, employing MOFs in electrochemistry would notably broaden the scope of electrocatalysis. However, this application is largely hindered by MOFs’ conventionally poor electrical conductivity. Integrating MOFs without compromising their crystalline superiority holds a grand challenge to unveil their pristine electrocatalytic properties. In this work, we introduce an epitaxial growth strategy to accomplish the efficient integration of the insulating MOFs into electrochemistry. Particularly, with pristine-graphene-templated growth, the two-dimensional (2D) single-crystal MOF possesses a large lateral size of ∼23 μm and high aspect ratio up to ∼1500 and exhibits a significant electrochemical enhancement, with a charge transfer resistance of ∼200 ohm and a 30 mA cm–2 current density at only 0.53 V versus a reversible hydrogen electrode. The epitaxial strategy could be further applied to other 2D substrates, such as MoS2. This MOF/graphene 2D architecture sheds light on integrating insulating MOFs into electrochemical applications.

By applying the undetermined coefficient method, this paper finds homoclinic and heteroclinic orbits in the Chen system. It analytically demonstrates that the Chen system has one heteroclinic orbit of Ši'lnikov type that connects two nontrivial singular points. The Ši'lnikov criterion guarantees that the Chen system has Smale horseshoes and the horseshoe chaos. In addition, there also exists one homoclinic orbit joined to the origin. The uniform convergence of the series expansions of these two types of orbits are proved in this paper. It is shown that the heteroclinic and homoclinic orbits together determine the geometric structure of Chen's attractor.

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We report the first homoleptic alkynyl-protected AgCu superatomic nanocluster of [Ag9Cu6(tBuC≡C)12]+ (NC 1, also Ag9Cu6 in short), which holds a body-centered-cubic structure with the Ag1@Ag8@Cu6 metal core. Such configuration is...

In this paper, the complex dynamical behaviors of the chaotic trajectories of Chen's system are analyzed in detail, with its precise bound derived for the first time. In particular, it is rigorously proved that all nontrivial trajectories of the system always travel alternatively through two specific Poincaré projections for infinitely many times. The results provide an insightful understanding of the complex topological structure of Chen's chaotic attractor.

We propose a method for solving the structure alignment problem in an accurate manner at the amino acid level, based on a mean field annealing technique. We define the structure alignment as a mixed integer-programming (MIP) problem. By avoiding complicated combinatorial computation and exploiting the special structure of the continuous partial problem, we transform the MIP into a reduced non-linear continuous optimization problem (NCOP) with a much simpler form. To optimize the reduced NCOP, a mean field annealing procedure is adopted with a modified Potts model, whose solution is generally identical to that of the MIP. There is no 'soft constraint' in our mean field model and all constraints are automatically satisfied throughout the annealing process, thereby not only making the optimization more efficient but also eliminating many unnecessary parameters that depend on problems and usually require careful tuning. A number of benchmark examples are tested by the proposed method with comparisons to several existing approaches.

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